A survey on sliding mode control strategies for induction motors

Annual Reviews in Control 37 (2013) 289–307

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Review

A survey on sliding mode control strategies for induction motors V.M. Panchade a,⇑, R.H. Chile b, B.M. Patre b a b

Department of Electrical Engineering, G.H. Raisoni Institute of Engineering and Technology, Pune 412 207, India Department of Instrumentation Engineering, S.G.G.S. Institute of Engineering and Technology, Nanded 431 606, India

a r t i c l e

i n f o

Article history: Received 5 December 2012 Accepted 9 September 2013 Available online 14 October 2013

a b s t r a c t A state of the art review of control and estimation methods for induction motor (IM) based on conventional approaches, sliding mode control (SMC) and sensorless SMC is presented. The objective of this survey paper is to summarize the different control approaches for IMs including field oriented control (FOC), direct torque control (DTC), speed observer, observer based flux estimation, sliding mode (SM) flux and speed observer, current regulation by SMC, sensorless SMC, etc. The applications of SMC to IMs has been widespread in recent years. The increasing interest in SMC is because of its interesting features such as invariance, robustness, order reduction and control chattering. Particularly robustness of SM approach with respect to parameter variations and external disturbance is vital for the control system. The review covers the sensorless SMC schemes by integrating controller and observer design to guarantee convergence of the estimates to the real states. It also covers the chattering problems, encountered often in SMC area dealt by using an asymptotic observer. Ó 2013 Elsevier Ltd. All rights reserved.

Contents 1. 2. 2. 3.

4.

5.

6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamic model of an induction motor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamic model of an induction motor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Related literature review on control and observation of induction machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Field oriented control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Direct torque control (DTC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Adaptive speed observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Observer based flux estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1. Open loop flux observers and estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature review on sliding mode control for induction motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Current regulation by SMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. The chattering problem and solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. Boundary layer solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2. Observer based solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3. Regular form solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4. Disturbance rejection solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Sliding mode flux and speed observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Recent trends in SMC for IM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Literature review on sensorless sliding mode control for induction motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Sensorless sliding mode flux/speed observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Sensorless sliding mode torque regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Sensorless sliding mode speed and rotor time constant observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Recent trends in sensorless sliding mode control for induction motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

⇑ Corresponding author. Tel.: +91 20 27052813, mobile: +91 9420330090; fax: +91 20 27052814. E-mail addresses: [email protected] (V.M. Panchade), [email protected] (R.H. Chile), [email protected] (B.M. Patre). 1367-5788/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.arcontrol.2013.09.008

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1. Introduction Control system has a long distinguished tradition stretching back to nineteenth century dynamics and stability theory. Its establishment as a major engineering discipline in the 1950s arose, essentially, from second world war driven work on frequency response methods by, amongst others, Nyquist, Bode and Wiener. The intervening 40 years has been quite unparalleled developments in the underlying theory with applications ranging from the ubiquitous proportional integral differential (PID) controller widely encountered in the process industries through to highperformance/fidelity controllers typical of aerospace applications. This developments has been increasingly underpinned by the rapid developments in the, essentially enabling, technology of computing software and hardware. In industrial applications, control engineers often have to deal with complex systems, having multiple variable and multiple parameter models with perhaps nonlinear coupling. The conventional approaches for understanding and predicting the behavior of such systems based on analytical techniques can prove to be inadequate, even at the initial stages of establishing an appropriate mathematical model. The formulation of any control problem there will typically be discrepancies between the actual plant and the mathematical model developed for controller design. This mismatch may be due to unmodelled dynamics, variation in system parameters or the approximation of complex plant behavior by a straight forward model. The engineer must ensure that the resulting controller has the ability produce the required performance levels in practice despite such plant /model mismatches. This has led to an intense interest in the development so called robust control methods which seeks to solve this problem. One particular approach robust controller design is the so called sliding mode control (SMC) methodology. SMC is a particular type of variable structure control (VSC). Variable structure control systems (VSCS) are characterized by a suite of feedback control law decision rule. The decision rule, termed the switching function, has as its input some measure of the current system behavior and produces as an output the particular feedback controller which should be used at that instant in time. The result is a variable structure system (VSS), which may regarded as a combination subsystems where each subsystem has a fixed control structure and is valid for specified region of system behavior. SMC, VSCS are designed to drive and then constrain the system state to lie within a neighborhood of the switching function. There are two main advantages to this approach. Firstly, the dynamics behavior of the system may be tailored by the particular choice of switching function. Second, the closed loop response becomes totally insensitive to a particular class of uncertainty in the system; this provides a very strong and inherent robustness to the resulting controllers. Finally, analysis of the discontinuous signals applied to the system can be used as a technique to model the signal activity required in order to achieve the ideal performance from the system. VSC with SMC was first proposed and elaborated in the early 1950s in the Soviet Union by Emelyanov and several co researchers (Emelyanov, 1959; Utkin, 1977; Hung, Gao, & Hung, 1993; Young, Utkin, & Ozguner, 1999). However, due to the implementation difficulties of high speed switching, it was not until the 1970s that the approach received the attention it deserved. In their pioneer works, the plant considered was a linear second order system modeled in phase variable form. Since then, VSC has developed into a general design method being examined for a wide spectrum of system types including nonlinear systems, multi input and multi output (MIMO) systems, discrete time models, large scale and infinite dimensional systems, and stochastic systems. In addition, the goals

of VSC has been greatly extended from stabilization to other control functions. The most distinguished feature of VSC is its ability to result in very robust control systems; in many cases invariant control systems result. Loosely speaking, the term invariant means that the system is completely insensitive to parametric uncertainty and external disturbances. Today, research and development continue to apply VSC to a wide variety of engineering systems. A detailed review of SMC development applied to IM are briefly described. This review paper presents a comprehensive review of the literature in the areas of control and observation of IMs in concerned with different approaches: field oriented control (FOC), direct torque control (DTC), speed observer, observer based flux estimation, sliding mode (SM) flux and speed observer and sensorless SMC. Further extensions of SMC concepts to other aims are briefly described. The methods proposed in this paper for both control and estimation is the so called SM approach chosen because of its robustness and ability to reduce the order of the motion models. Known Studies of sensorless SMC for IM are noted. These so called sensorless systems are free of maintenance and exhibit high reliability and low cost. Due to the above reasons, many sensorless control schemes have been developed. High order models of alternating current (AC) machines like IM, nonlinearities in motion equations, uncertainties in model parameters and disturbances are the main obstacles hindering the development and secondly mathematical analysis of such items is rigorous.

Fig. 1. Two-pole, 3-phase, Y-connected induction motor.

Fig. 2. Magnetic axes of a three phase induction motor.

V.M. Panchade et al. / Annual Reviews in Control 37 (2013) 289–307



ua



ub 

ia ib



2

291

3

ua 6 7 ¼ Aabc u 4 b5 ab

ð7Þ

uc 2

ia

3

6 7 ¼ Aabc ab 4 ib 5

ð8Þ

ic

where Aabc a:b denotes the transformation matrix

Aabc ab ¼

Fig. 3. Coordinate system of induction motor model: he is the electrical rotor angular position and x is the electrical rotor angular speed; q is the angular position of the rotor flux and xq the angular speed of the rotor flux.

2. Dynamic model of an induction motor The winding arrangement for a 2 pole, 3 phase, wye connected, symmetrical induction machine is shown in Fig. 1. The stator windings are identical, sinusoidally distributed windings displaced 120°. The rotor windings, which may be wound or forged as a squirrel cage winding, will also be considered as three identical sinusoidally distributed windings, displaced 120°. The magnetic axis of three IM with positive direction is shown in Fig. 2. Four frames of reference are normally used in describing the dynamic behavior of an IM is shown in Fig. 3: the phase frame in (a, b, c) coordinates, the stator frame in (a, b) coordinates, the rotor frame in (x, y) coordinates and the field oriented frame in (d, q) coordinates. The motor model in (a,b) coordinates can be obtained by transforming the motor model from (a, b, c) coordinates frame into the (a, b) coordinates frame. Equations for an IM in the orthogonal stator frame ((a, b) coordinate) can be expressed as Leonard (1985) and Vas (1998) Stator current equations

dia 1 ¼ bgka þ bxkb  cia þ u dt rLs a dib 1 ¼ bgkb  bxka  cib þ u dt rLs b

ð1Þ ð2Þ

Rotor flux equations

dka ¼ gka  xkb þ gLm ia dt dkb ¼ gkb þ xka þ gLm ib dt

ð3Þ ð4Þ

Mechanical Equations

3Nr Lm ðib ka  ia kb Þ 2 Lr   dx d dhe 1 ¼ ðT  T l Þ ¼ dt dt J dt

T¼

ð5Þ

  2 1 1=2 1=2 pffiffiffi pffiffiffi 3 0 3=2  3=2

Rs and Rr are stator and rotor resistances; Ls and Lr are stator and rotor inductances; and Lm is the mutual inductance. x is the electrical rotor speed, two-dimensional vectors kT = (ka, kb), iT = (ia, ib) and uT = (ua, ub) are rotor fluxes, stator currents, and stator voltages in (a, b) coordinate, respectively; T and Tl are the torque developed by the motor and the load torque; J is the moment of inertia; Nr is the number of pole pairs; and (ua, ub, uc)T and (ia, ib, ic)T are three phase voltage and current respectively. u1, u2, u3 are unit vectors of the three phase windings a, b, and c. 3. Related literature review on control and observation of induction machines 3.1. Field oriented control The high performance applications of IM had been achieved through FOC (Novotny & Lipo, 1996). In FOC, the IM can be controlled in the same manner that of separately excited direct current (DC) motors. The system block diagram of FOC is shown in Fig. 4. The nomenclature is listed in Table 1. The basic idea is that torque control is decoupled into two tasks: the control of the torque current component, iq, and of the flux current component, id independent of one another. Decoupling is achieved in the synchronous rotating frame when the rotor flux vector is aligned with the d-axis of the rotating frame, i.e., the so-called field orientation. This decoupling control between the flux and torque makes quick dynamic response possible. According to the approach used to achieve field orientation, there are two classes in FOC: direct field oriented control(DFOC) and indirect field oriented control (IFOC). In DFOC, there are two ways to obtain the rotor flux position. One is to install a flux sensor to measure the air gap flux, then algebraically compute the rotor flux. The block diagram of this method is shown in Fig. 5. The disadvantage of this approach is that special flux sensors are necessary; this installation is not possible in commercial off the shell motors. The second method is to first integrate the sensed stator voltage and current to calculate the stator flux, and then compute the rotor flux from the stator flux. The block diagram of this method is shown in Fig. 6. The drawback of this method is its parameter sensitivity (especially with respect to the stator

ð6Þ

with g, r, b, and c are positive constants defined as

g¼

  Rr ;r ¼ Lr

1

!   L2m Lm ;b ¼ Ls Lr rLs Lr

and

1 L2 c¼ Rs þ m2 Rr rLs Lr

!

Stator voltage and current vector defined as

ð9Þ

Fig. 4. Field oriented control system block diagram.

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V.M. Panchade et al. / Annual Reviews in Control 37 (2013) 289–307

Table 1 Nomenclature in FOC for induction machine. id, iq id ; iq

Two phase stator currents in (d, q) field oriented or rotationary frame Two phase stator reference currents in (d, q) rotationary frame

ud ; uq

Two phase stator voltage command in (d, q) rotationary frame

ua ; ub ; uc T(q) T1(q) uqd, iqd, kqd kdr, kqr kqdm

Stator voltage command in (a, b, c) phase or stationary frame The reference frame transformation from stationary to rotationary The reference frame transformation from rotationary to stationary Complex space vector for two phase stator voltages, stator currents and stator fluxes in (d, q) rotationary frame Rotor fluxes in (d, q) rotationary frame Complex space vector for air gap flux in (d, q) rotationary frame

the dynamic behavior of an IM is rather similar to a linear system. However, the uncertainties, such as mechanical parametric variation, external load disturbance and unmodeled dynamics in practical applications, influence the designed control performance seriously. Therefore, an IOCS is proposed to confront these uncertainties existed in the control of the induction servo motor drive. The control laws for the IOCS are derived in the sense of the optimal control technique and Lyapunov stability theorem, so that system tracking stability can be guaranteed in the closed loop system. With the proposed IOCS, the controlled induction servo motor drive possesses the advantages of good tracking control performance and robustness to uncertainties under wide operating ranges. Moreover, the advantages of the proposed control system are indicated in comparison with the SMC system. 3.2. Direct torque control (DTC)

Fig. 5. Direct FOC method 1.

resistance) and integration problems at a low rotor speed due to the stator IR voltage drop. In IFOC, angular position of the rotor flux signals first measures stator currents and rotor speed for then deriving rotor flux angle proper by summing the rotor angular position corresponding to the rotor speed and the calculated reference value of slip angle corresponding to the slip frequency xs. In IFOC, the angular speed of the rotor flux is obtained by adding the slip frequency with rotor speed. Here slip frequency is time derivatives of slip, which is difference between angular position of the rotor flux and electrical rotor angular position. All state and control variables in the field oriented coordinate frame are transformed based on rotor flux angular position q, called the rotor flux angle. The Calculation of rotor flux angle in IFOC is shown in Fig. 7. Thus an incremental encoder is needed for rotor speed measurement in IFOC, and the slip frequency calculation is directly related to the rotor time constant, Lr/Rr which is changing with temperature and with varying flux level. In addition to the limitations mentioned above, it should also be observed that it is customary to employ proportional integral (PI) controllers in conjunction with FOC methods. Such controllers require tuning for good control performance. Wai (2003) proposed control schemes for application of an intelligent optimal control system (IOCS) to control an IFOC induction servo motor drive for tracking periodic commands via a wavelet neural network (WNN). With the field orientation mechanism,

DTC of IMs was developed more than ten years ago (Takahashi & Noguchi, 1986; Depenbrock, 1988). Unlike FOC, DTC does not tend to reproduce the electromechanical behavior of a DC motor, but is aimed at a complete exploitation of the flux and torque producing capabilities of an IM fed by a pulse width modulation (PWM) inverter. The principle of DTC is based on hysteresis control using an optimal PWM output. The control system is designed based on the machine model in terms of stator current and flux in a stationary reference frame. The instantaneous torque and flux values are calculated from the stator voltage and current. They are controlled directly and independently by selecting optimal inverter switching modes. In DTC, no speed information is needed and it can be regarded as one kind of sensorless control based on transient and steady state response. In the transient state, the highest torque response can be obtained by selecting the fastest accelerating voltage vector to produce the maximum slip frequency. In steady state, by selecting the accelerating vector and the zero voltage vector alternately, the torque can be maintained constant with minimum switching frequency by the hysteresis comparator of torque. Accordingly, the harmonic losses and the acoustic noise level of the motor can be reduced. The amplitude of the primary flux is also controlled to attain the maximum efficiency in steady-state operation. The flux level can be automatically adjusted to get the optimum efficiency in the steady state and the highest torque response in the transient state at the same time by using a nonlinear active filter. In spite of its quick dynamic response and implementation simplicity, there are two main restrictions. One is how to select the optimum inverter switching pattern; and second is how to obtain the stator flux. Sometimes a compromise has to be made since there is no scheme that is optimal for all motor operating conditions. The traditional way is to integrate stator voltage and current. Obviously, this approach has the usual problems inherent to integration and is heavily influenced by the variability in stator resistance. Further, how to determine an optimal switching scheme is still an open research topic. 3.3. Adaptive speed observer

Fig. 6. Direct FOC method 2.

Fig. 7. Indirect FOC.

A speed identifier by the approach of model reference adaptive systems (MRAS) is proposed in Tamai, Sugimoto, and Yano (1987). However, the identifier design is based on a linearized IM model, so the time constant in the identifier needs to be varied online to reduce the influence of different machine operating points. Schauder (1992) also employs MRAS on the rotor flux model in stationary frame for speed estimation in IFOC, which uses the errors between the rotor flux from the reference and adjustable model to drive the speed estimation. Unfortunately, the reference model has a pure integrator, which causes problems with initial conditions and drift. Besides, although the rotor time constant has little effect on the

V.M. Panchade et al. / Annual Reviews in Control 37 (2013) 289–307

speed estimation, the stator resistance does have some influence. To avoid the need for pure integration, Feng and Fukao (1994) presents a MRAS scheme in terms of the auxiliary state variables (the counter electromotive force), which is completely independent of stator resistance variance. The estimated speed is used for both field orientation and speed feedback in the indirect speed FOC. It is shown that the rotor resistance variance does not destroy the field orientation, it only produces an error in the speed feedback. Tajima and Hori (1993) uses the same MRAS as in Schauder (1992) direct speed FOC. Since flux estimation is necessary in DFOC, a Gopinath flux observer (Gopinath, 1971) is constructed, which in turn requires speed information from the MRAS. Complete insensitivity to rotor resistance is obtained in this DFOC using the estimated speed. Another adaptive sensorless scheme is proposed for DFOC in Kubota, Matsuse, and Nakano (1993). Instead of MRAS, the adaptation law is designed on a Lyapunov approach. The rotor flux and speed are estimated at the same time. However, both stator and rotor resistance affect the estimation.

293

field orientation, the stationary reference is the most suitable. Therefore, with the stationary reference implied and all rotor quantities referred to the stator, the IM electrical dynamics are characterized by the following equations (Bose, 2004):

v qd ¼ Rs iqd þ pkqd

ð10Þ

0 ¼ Rr iqdr þ ðp  jxÞkqdr

ð11Þ

where p is the differential operator and the flux linkages are

kqd ¼ Ls iqd þ Lm iqdr

ð12Þ

kqdr ¼ Lr iqdr þ Lm iqd

ð13Þ

In addition, it will prove useful to define the following complex impedances

Z s ¼ Rs þ rLs p

ð14Þ

Z 0s ¼ R0s þ rLs p

ð15Þ

Z r ¼ Lr ðp þ xb Þ

ð16Þ

where r is the leakage factor or coupling factor, 3.4. Observer based flux estimation In Verghese and Sanders (1988), studies the flux observers assuming stator voltage, current and rotor speed known. By studying different observers based on rotor, stator circuits, it is shown the feedback of a corrective prediction error term can speed up the estimation convergence and reduce the sensitivity to parameter variations compared with the pure real time simulation of the dynamic models. Jansen and Lorenz (1993) presents a combination of the closed loop flux observer in Jansen and Lorenz (1994) with MRAS speed estimator (Schauder, 1992; Tajima & Hori, 1993). In this sensorless scheme, the flux estimates are used by MRAS for speed estimation. Jansen and Lorenz (1993) reported on the accuracy and robustness limitations of direct field oriented (DFO) systems incorporating velocity estimation that are based solely upon measured stator voltages and currents. The analysis is limited to integrated velocity and flux estimation methods that rely upon the IM back emf. An improved topology utilizing an integrated closed loop flux observer and a mechanical system model is proposed and experimentally verified. For known machine loads the proposed observer can potentially improve both the velocity estimation dynamics and the transient low speed field orientation. However, it does not overcome the fundamental lack of robustness at zero speed and loss of accuracy due to parameter sensitivity. A physical approach for rotor flux observer design is proposed in Jansen and Lorenz (1994). In this paper, real time model simulation is presented as open loop observers while those with feedback correction term are called closed loop observers. By the proposed use of frequency response functions (FRF), the traditional current model and voltage model open loop observers are analyzed, where their sensitivity to machine parameters and limitation of use are discussed. A superior closed loop observer combining the current and voltage model with speed invariant dynamics is proposed. Various alternative methods for observer based DFOC have been analyzed and compared in Jansen, Lorenz, and Novotny (1994). The difficulty to acquire an accurate mechanical model is a major disadvantage of this scheme. Complex Vector Induction Machine Model The analysis of observers for symmetric IM can be simplified considerably by the use of complex vector notation. Complex vector notation reduces the order of the system by a factor of two and also simplifies the cross coupling between the q and d axes through the use of the inherent 90° phase shift provided by j . It thus allows the treatment of the rotor flux as a single vector quantity allowing the development of FRF. In general, the complex quantities are written in the form, fqd = fq  jfd. For implementing direct rotor flux

R0s ¼ Rs þ Rr

L2m L2r

and

xb ¼

Rr  jx Lr

Note that Z 0s is a stator transient impedance. Eqs. (10)–(13) can be arranged in terms of the stator current and rotor flux in a form similar to a state space model with the current and flux being the state variables.

  1 L v qd  R0s iqd þ m xb kqdr rLs Lr Rr ¼ Lm iqd  xb kqdr Lr

piqd ¼

ð17Þ

pkqdr

ð18Þ

From (17) and (18), the IM electrical model can be formulated into a nonlinear with stator voltage and rotor velocity treated as system inputs (Jansen & Lorenz, 1994). 3.4.1. Open loop flux observers and estimators There are three basic topologies for open-loop flux observers as dictated by the measured state/inputs and corresponding flux model. Two are reduced order models that have been referred to as the current and the voltage models; with a third observer being essentially a full order model with respect to the IM electrical model. In addition there is an estimator based on cancelation methods. 3.4.1.1. Current model open-loop flux observers. From (18), it is apparent that an open-loop rotor flux observer can be formed if the stator current and the rotor velocity are measured in real time. From machine parameter estimates (denoted by ^), the governing equation of the open-loop rotor flux observer is:

b b r L m iqd  x ^ b ^kqdr p^kqdr ¼ R b Lr

ð19Þ

The parameter estimates used within the observer are never exactly correct. To evaluate the parameter dependent accuracy of the estimated flux, a FRF relating the estimated and actual fluxes has been found to be insightful and helpful. From (18) and (19), the estimated flux can be expressed as a response to the actual flux;

  b r bL m ðp þ xb Þ R br b ^kqdr bL r R Lm Zr  ¼  ¼ FRF c ¼ Lm b kqdr ^ R Rr Lr ðp þ xb Þ r Lm Z r

ð20Þ

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for Steady state operation, p may be replaced by excitation frequency, jxe, and the response function can be expressed as a function of the slip frequency, xs, where xs = xe  x. At high slip the rotor flux magnitude response is sensitive primarily to the rotor resistance, while the estimated rotor flux phase angle is very insensitive to all parameter estimates. Near rated slip, both the flux angle and magnitude are sensitive to the estimated rotor resistance and magnetizing inductance. 3.4.1.2. Voltage model open-loop flux observers. The voltage model utilizes the measured stator voltages and currents, but not x. From (10), the stator flux can be estimated by integration of the following equation,

p^kqd ¼ v qd  R^s iqd

ð21Þ

ipated to share the zero/low speed implementation problems. ⁄ The cancelation method open loop estimation method is the least desirable due to its inherent susceptibility to low speed noise and parameter estimate errors. ⁄ The cancelation method acts as an implicit flux reference within both the full order and the Gopinath style closed loop observers. ⁄ The closed loop, velocity invariant, flux observer with current model input has the desirable low speed attributes of the current model, and the desirable high speed attributes of the voltage model. 4. Literature review on sliding mode control for induction motor

from which the rotor flux is then obtained using (12) and (13),

b ^ ^kqdr ¼ L r k^qd  r b L i ^ m qd b 1r Lm

ð22Þ

The corresponding flux estimation FRF is :

" #   ^kqdr Lm b Lr L2r p þ xb b ðZ s  Z s Þ ¼ FRF v ¼ 1þ kqdr b p Rr L2m L m Lr

ð23Þ

3.4.1.3. Full order open-loop flux observers. The full order open-loop flux observer (with respect to the machine electrical model) is derived directly from the IM electrical model characterized by (17) and (18). The observer utilizes measured stator voltage and rotor velocity. The stator current is estimated as an intermediary quantity only. The corresponding FRF can be written:

^kqdr FRF Fn ¼ ¼ FRF F kqdr FRF Fd

ð24Þ

3.4.1.4. Cancelation method open-loop flux estimators. It is possible to construct a cancelation method open-loop flux estimator based on the rotor and stator flux linkage and voltage loop equations as combined in (17) after substituting the estimated machine parameters and measured terminal properties as follows.

^kqdr ¼

  i b Lr h b0 þ r ^b L s p iqd v qd þ R s b ^b Lmx

ð25Þ

The corresponding FRF can be obtained by solving (17), (18) and (25) simultaneously to achieve

  b 0  Z0 ^kqdr LLmr xb þ RrZLrm Z s s ¼ ¼ FRF E bL m ^ kqdr x b bL r

ð26Þ

The primary conclusions on the observer topologies are Jansen and Lorenz (1994): ⁄ The current and voltage model open loop flux observers and the closed loop, velocity invariant flux observer all provide flux angular position estimate errors which are relatively small for the 10 hp machine. The net differences in torque characteristics are thus small, except at low frequencies (low speeds) where the current model and the velocity invariant flux observers are superior to the voltage model observer. ⁄ The estimation dynamics and parameter sensitivity of the full order open loop observer are considerably more complex than the other open loop observers. Like the voltage model, it requires measured voltage input and is thus antic-

Sabanovic and Izosimov (1981) reports the first application of SMC method to the IM for control of torque, speed and position. In Sabanovic and Bilalovic (1989), a unified approach for control of AC machines by SM is presented. Three types of AC machines are under consideration, i.e. induction, synchronous and permanent magnet (PM) synchronous machines. Unlike in Sabanovic and Izosimov (1981), the state variables for the machine model are selected to be the currents and fluxes, so that all the sliding surfaces can be selected in terms of current to eliminate the requirement of flux measurement or observation. Another basic difference between (Sabanovic & Izosimov, 1981; Sabanovic & Bilalovic, 1989) is that in Sabanovic and Izosimov (1981) the SM is enforced by the control input in the form of the three phase input voltages ua, ub and uc, so they can be implemented directly by the inverter; in Sabanovic and Bilalovic (1989), the control to enforce the SM consists of the two voltages ud and uq in the synchronous rotating frame so a mapping rule is necessary to find ua, ub and uc, for every pair of ud and uq. In terms of control complexity, there is a tradeoff between the effort to calculate ua, ub and uc, in Sabanovic and Izosimov (1981) and that to be spent on the mapping process in Sabanovic and Bilalovic (1989). Another SMC method is reported for IM position control in Bose (1985). However, what is really under consideration in this report is the simplest second order speed and position system with torque as the control input. SMC is only used to produce the torque command, while the inner loop is just the traditional IFOC. Some general guidelines to design SM controllers for electric drives are given in Utkin (1993), including DC motors, IMs and synchronous motors. The chattering problem which is often met in practice is discussed, and possible solutions are given. For the IM, the control methodology is formulated in the model based on the stationary frame. This makes it necessary to use a machine parameter dependent transformation to obtain the control input, i.e. the three phase terminal voltages. A novel SM speed and rotor flux control strategy for IM is proposed in Soto and Yeung (1995). The model used is similar to that in Sabanovic and Izosimov (1981). The control inputs are formulated in the two voltage components ua, ub in the stationary frame. They are specially designed so that there is a direct relation between ua, ub and ua, ub, uc i.e. no mapping is needed. But the disadvantage is that only four switching states in the inverter are used among all eight possible states. To compute the rotor flux, the traditional integration method is used, so that problems inherent to numerical integration are unavoidable. A nonlinear sliding surface is selected in Qi and Hoft (1994) to reduce the complexity in designing SM controllers. This approach has the feature that the surface becomes linear when rotor flux reaches the steady state. The controller design is based on the model in the synchronous rotating frame with rotor flux, speed and their derivatives as state variables. The use of the synchronous rotating frame has the advantage that it avoids the nonsingular

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transformation in the diagonalization method (Utkin, 1993), which is machine parameter dependent. On the other hand, because of the use of synchronous rotating frame, a mapping table is needed for the inverter voltage control. The flux information is obtained in the same way as Soto and Yeung (1995). Another SM controller using nonlinear SM surfaces is presented in Benchaib, Rachid, Audrezet, and Tadjine (1999) and Benchaib, Rachid, and Audrezet (1999). Benchaib et al. (1999) compares SMC performances with FOC and input output linearization control by experiments. In Benchaib et al. (1999) and Depenbrock (1988) the boundary layer method is used for chattering reduction. The boundary layer approach avoids generating SM by replacing the discontinuous switching actions with a continuous saturation function. Thus the voltage inputs from the proposed SM controller cannot drive the inverter directly, instead they have to be implemented by PWM algorithm. One of the benefits of the boundary layer approach is that SMC design methodologies can be exploited to drive a continuous controller. The invariance property of SMC is partially preserved in the sense that the system trajectories are confined to a d(e)-vicinity of the sliding manifold s(t) = 0, instead of exactly to s(t) = 0 as in ideal SM. Within the d(e)-vicinity, however, the system behavior is not determined, i.e. further convergence to zero is not guaranteed. This type of control design is part of a class of robust controllers which satisfy the globally uniform ultimate boundedness condition. Note that no real SM takes place, since the switching action is replaced by a continuous approximation. 4.1. Current regulation by SMC Current controller is the basic block of any high performance drive system. Current tracking gives precisional control of flux, torque and speed regardless of what control methodology is used. Current regulators for AC drives are more complex than DC drives because AC current regulator must control both the amplitude and phase of the stator current. The steady state currents in controllers are always AC, not DC. That inhabits the straightforward use of conventional PI controllers used in DC drive to regulate the steady currents in AC controllers. Recently much efforts were directed towards the development of AC current controllers. Yan, Jin, and Utkin (2000) has used SM approach to regulate the current. They have considered the current control problem by defining switching functions as the error between the real current i and the reference current i⁄, i.e. 

sa ¼ ia  ia

ð27Þ

 ib

ð28Þ

sb ¼

 ib

Design the discontinuous control as

ua ¼ U 0 signðsa Þ

ð29Þ

ub ¼ U 0 signðsb Þ

ð30Þ

In practical implementation, the discontinuous function sign() is replaced by continuous approximation and U0 should be selected such that DC bus voltage is used to full extent. To enforce the SM, the DC bus voltage U0 should be high enough such that the conditions for SM to exist sa s_a < 0 and sb s_b < 0 hold (Utkin, 1993).

dia 1 ¼ bgka þ bxkb  cia þ u dt rLs a dib 1 ¼ bgkb  bxka  cib þ u dt rLs b

ð31Þ ð32Þ

Design the discontinuous control similar to (29) and (30), then



U0 sa s_a ¼ sa ia  bgka  bxkb þ cia  js j rLs a   U 0  js j sb s_b ¼ sb ib  bgkb  bxka þ cib  rLs b

ð33Þ ð34Þ

If U0 satisfies

U 0 > max

n







rLs ia  bgka  bxkb þ cia ; rLs ib  bgkb  bxka þ cib

o

ð35Þ then current tracking in IM is achieved. 4.2. The chattering problem and solutions The term chattering describes the phenomenon of finite frequency, finite amplitude oscillations appearing in many SM implementations. These oscillations are caused by the high frequency switching of a SMC exciting unmodelled dynamics in the closed loop. Unmodelled dynamics may refer to sensors and actuators neglected in the principal modeling process since they are generally significantly faster than the main system dynamics. However, since ideal SM systems are infinitely fast, all system dynamics should be considered in the control design. In applications of SMC, unmodelled dynamics in the control loop are often excited by the discontinuous switching action of a SMC, leading to oscillations in the motion trajectory. Due to the acoustic noise these oscillations may cause in mechanical systems, this phenomenon is also known as chattering. This subsection seek to provide the chattering problem and introduces four solutions. Following four solutions to the chattering problem reliably eliminate chattering in the control loop (Utkin, Guldner, & Shi, 1999). 4.2.1. Boundary layer solution Boundary layer method substitutes the discontinuity of a SMC by a saturation function and yields motion in a boundary layer of the sliding manifold instead of true sliding along the manifold. Effectively, SM methodology is used to design a continuous high gain controller which respects bounds on the control resources. 4.2.2. Observer based solution Yan et al. (2000) are proposed an asymptotic current observer in the control loop to eliminate chattering. In IM, the chattering phenomenon is caused by the load or machine parameter inaccuracy because the parameters are not needed in the control system at all. The parameters inaccuracy does not play any role in the chattering issue if we know their ranges. The only possible reason for the chattering are the unmodelled dynamics in the system, e.g. the lag or transport delay in the inverter or the sensors. For chattering prevention by observers, the key idea is to generate ideal SM in an auxiliary observer loop rather than in the main control loop. Ideal SM is possible in the observer loop since it is entirely generated in the control software and thus does not contain any unmodelled dynamics. The main loop follows the observer loop according to the observer dynamics. Despite applying a discontinuous control signal with switching action to the plant, no chattering occurs. Fig. 8 shows the basic idea of chattering suppression using state observer. As it is shown in the block diagram, an asymptotic observer serves as bypass for high frequency component, therefore the unmodelled dynamics is not excited. Observer based method shifts the switching action of the SMC into an auxiliary observer loop, thus circumventing unmodelled dynamics in the main loop and achieving ideal SM in the observer loop. The plant follows the ideal trajectory of the observer according to the observer performance. Since the control input to the plant is still discontinuous, this method is ideal for systems which already have an observer in the control structure or for systems with inherently discontinuous control inputs like voltage inputs of electrical drives. Implementations of a continuous controller in a system with discontinuous inputs generally requires PWM, where as direct implementation of SMC with an observer avoids

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the unmodelled dynamics into account for the control design. In this sense they are no longer unmodelled, but rather part of the overall system model. 4.2.4. Disturbance rejection solution This method combines a continuous and a discontinuous controller to achieve good performance without chattering. The continuous part is to control the overall motion and discontinuous part is to reject the influence of parametric uncertainty and disturbances. This method is a special case of integral SM and is especially useful for systems with large uncertainties and/or disturbances. Fig. 8. Control loop with auxiliary observer loop. Ideal SM occurs in observer manifold since the observer loop is free of unmodelled dynamics. The plant output x follows the observer output ^ x without chattering despite discontinuous control u applied to the main loop with actuator dynamics.

PWM. An asymptotic observer in the control loop can eliminate chattering despite discontinuous control laws. The mathematical formulation for the design of an asymptotic observer is given as follows. A simple first order plant with second order unmodelled actuator dynamics is used as an example for illustration purposes. The model of the first order system with state and output x is given by Utkin et al. (1999)

x_ ¼ ax þ d þ bw 

ð36Þ +



+

where a 6 a 6 a and 0 < b 6 b 6 b are unknown parameters within known bounds, w is the control variable and disturbance d is assumed to be uniformly bounded for all operating conditions x as jdj 6 d+. Define a first order observer for system (36) as

^x_ ¼ ax þ bu þ L1 x

ð37Þ

where L1 is the linear feedback gain for the observation error x ¼ x  ^x. Exact knowledge of the system parameters a and b is assumed in (37) for simplicity of presentation. The linear dynamics of the observation error are governed by

x_ ¼ d  L1 x

ð38Þ

x in (38) is stable and bounded by Error  þ

jxj 6

d L1

With the disturbance bounded by jdj 6 d+. Introducing an observer sliding manifold

^s ¼ xd  ^x allows definition of an ideal SMC for the observer loop as

u ¼ Msign^s where M is control gain. In this way, observer based solution is provided for elimination chattering and disturbance effect. It requires slightly more effort in the control design. However, in many control applications, observers for unmeasurable states are vital parts of the overall system and can be readily included into the control design. Note that the design of the actual observer depends on the system specifications. 4.2.3. Regular form solution Regular form method is mainly designed for systems where some knowledge of the unmodelled dynamics and intermediate measurements are available, e.g. known actuators dynamics. Such systems consisting of separate blocks may be controlled with a cascade control structure which avoids chattering by explicitly taking

4.3. Sliding mode flux and speed observer A SM rotor flux observer is proposed in Benchaib et al. (1999) and Benchaib et al. (1999). The error between the measured currents and estimated currents is used to construct SM surfaces so that after SM happens, the estimated flux values are driven to converge to real ones exponentially. Proof of the observer stability is given and robustness against modeling uncertainites and measurement errors are shown in Depenbrock (1988). Current sensors and a position encoder for speed information are needed. In Tursini, Petrella, and Parasiliti (2000), a sensorless control scheme is presented, in which the rotor flux and speed are observed by an adaptive sliding mode observer (SMO). After SM is enforced in the switching surface, i.e. current estimation error, the flux and speed estimation convergence is shown by analysis of Lyapunov function. However, the authors are not able to prove the stability of the global control system. Further, the theoretical analysis is based on the assumption that the machine parameters are exactly known and the speed variation is slow, although the experimental results claim to show the robustness with respect to the machine parameter variation. 4.4. Recent trends in SMC for IM The main arguments in favor of SMC are order reduction, decoupling design procedure, disturbance rejection, insensitivity to parameter variations, and simple implementation by means of power converter, is one of the prospective control methodologies for electrical machines. The design principles of SMC to electric drives were demonstrated in Utkin (1993). A hybrid control system using a recurrent fuzzy neural network (RFNN) to control a linear induction motor (LIM) servo drive is proposed in Lin and Wai (2001). First, the feedback linearization theory is used to decouple the thrust force and the flux amplitude of the LIM. Then, a hybrid control system is proposed to control the mover of the LIM for periodic motion. In the hybrid control system, the RFNN controller is the main tracking controller, which is used to mimic a perfect control law, and the compensated controller is proposed to compensate the difference between the perfect control law and the RFNN controller. Moreover, an on line parameter training methodology, which is derived using the Lyapunov stability theorem and the gradient descent method, is proposed to increase the learning capability of the RFNN. A LIM servo drive using an adaptive recurrent neural network controller (ARNNC) is proposed in Wai and Lin (2001). Furthermore, the advantages of the proposed control system are indicated in comparison with the SMC system. First, the secondary flux of the LIM is estimated with an adaptive flux observer on the stationary reference frame and the feedback linearization theory is used to decouple the thrust force and the flux amplitude of the LIM. Then, an ARNNC is proposed to control the mover of the LIM for periodic motion. In the proposed controller, the LIM servo drive system is identified by a recurrent neural network identifier (RNNI) to

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provide the sensitivity information of the drive system to an adaptive controller. The back propagation algorithm is used to train the RNNI on line. Moreover, to guarantee the convergence of identification and tracking errors, analytical methods based on a discrete type Lyapunov function are proposed to determine the varied learning rates of the RNNI and the optimal learning rate of the adaptive controller. VSS controller is proposed in Liaw, Lin, and Chao (2001) to generate a compensation control signal to reduce the control performance degradation with model reference speed response for an IM drive. An IFO induction motor drive is first implemented, and its dynamic model at a nominal operating condition is estimated from measured data. Then, a two degrees of freedom linear model controller is designed to meet the prescribed tracking and load regulation speed responses at the nominal case. As the variations of system parameters and operating condition occur, the prescribed control specifications may not be satisfied further. The proposed VSS controller is easy to implement, since only the output variable is sensed. The existence condition of SMC is derived, and the chattering suppression during the static period is also considered. Good model following tracking and load regulation speed responses are obtained by the designed VSS controller. In Lin and Wai (2002), a robust controller scheme is proposed that combines the merits of integral proportional (IP) position control and neural network (NN) observed technique, is designed for a LIM servo drive. First, the secondary flux of the LIM is estimated using a SM flux observer on the stationary reference frame and the feedback linearization theory is used to decouple the thrust and the flux amplitude of the LIM. Then, the IP position controller is designed according to the estimated mover parameters to match the time domain command tracking specifications. Moreover, a robust controller is formulated using the NN uncertainty observer, which is implemented to estimate the lumped uncertainty of the controlled plant, as an inner loop force controller to increase the robustness of the LIM servo drive system. Furthermore, in the derivation of the online training algorithm of the NN, an error function is used in the Lyapunov function to avoid the real time identification of the system Jacobian. In addition, to increase the speed and accuracy of the estimated flux, the sliding mode flux observer is implemented using a 32 bit floating point digital signal processor (DSP) with a high sampling rate. Two adaptive/variable structure identifiers based on different standing assumptions are proposed in Bartolini, Pisano, and Pisu (2003), both providing an exponentially convergent estimate of the rotor resistance. One of the main problems in IM control is the lack of knowledge about the actual value of the rotor resistance, which is subjected to large variations during operation. Due to the unavailability of the rotor electrical quantities, it is not easy to define an error signal suitable to be used as engine for the identification mechanism. The high simplicity of the overall schemes, and the low dimension of the regressor vectors (which leads to mild persistence of excitation requirements) constitute the main positive features of the proposed approach. The SM flux observation system is implemented using a DSP with a high sampling rate to make it possible to achieve good dynamics. Wai and Liu (2003) proposed control system to design nonlinear control strategy to control a LIM servo drive for periodic motion under the occurrence of possible uncertainties and different reference trajectories. The merits of the proposed control system are indicated in comparison with a traditional optimal control system. Based on the concept of the nonlinear state feedback theory and optimal technique, a nonlinear control strategy, which is composed of an adaptive optimal control system and a SM flux observation system, is developed to improve the drawbacks in previous works concerned with complicate intelligent control. The control and estimation methodologies are derived in

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the sense of Lyapunov theorem so that the stability of the control system can be guaranteed. To design of switching control strategies which, as in the case of classical DTC, aim to directly regulate two outputs: torque and flux amplitude is proposed in Escobar, Stankovicic, Galvan, Carrasco, and Ortega (2003). Quadratic and absolute value criterion in terms of the error and/or the prediction in one step ahead on these outputs is proposed to design the switching sequence. As a result, a control vector, i.e., the switch position, is directly selected without the requirement of an auxiliary space vector or other modulation technique. The development of a decoupling mechanism and a speed control scheme based on total sliding mode control (TSMC) theory for a direct rotor field oriented (DRFO) IM is focused in Wa and Lin (2005). First, a robust decoupling mechanism including an adaptive flux observer and a SM current estimator is investigated to decouple the complicated flux and torque dynamics of an IM. The acquired flux angle is utilized for the DRFO object such that the dynamic behavior of the IM is like that of a separately excited dc motor. However, the control performance of the IM is still influenced seriously by the system uncertainties including electrical and mechanical parameter variation, external load disturbance, nonideal field oriented transient responses, and unmodeled dynamics in practical applications. In order to enhance the robustness of the DRFO IM drive for high performance applications, a TSMC scheme is constructed without the reaching phase in conventional SMC. The control strategy is derived in the sense of Lyapunov stability theorem such that the stable tracking performance can be ensured under the occurrence of system uncertainties. Naassani, Monmasson, and Louis (2005) synthesize the direct torque and rotor flux control (DTRFC) algorithms of IM using SM theory. The choice of the SM theory has been motivated by the presence of switches in the voltage source inverter (VSI). Changes in the state of the switches cause the variation in the topology of the controlled system. In addition, this theory offers a mathematical process that allows rigorous procedures of analysis and synthesis. The developed voltage vector is generated by two methods: direct control of the VSI (hysteresis VSI control), and indirect control of the VSI using space vector modulation. In addition, taking into account the complementarity of the advantages of each VSI control algorithm, the high dynamic performance of the direct control and the smoothness of the indirect control, the idea of the dynamic reconfiguration of DTRFC algorithms is proposed. Design and properties of an adaptive enhanced fuzzy sliding mode control (AEFSMC) system is proposed and addressed in Wai and Su (2006) for an IFOC IM drive to track periodic commands. A newly designed enhanced fuzzy sliding mode control (EFSMC) system, in which a translation width idea is embedded into the fuzzy sliding mode control (FSMC), is introduced initially. Moreover, to confront the uncertainties existed in practical applications, an adaptive tuner, which is derived in the sense of the Lyapunov stability theorem, is utilized to adjust the EFSMC parameter for further assuring robust and optimal control performance. The indirect field oriented IM drive with the AEFSMC scheme possesses the salient advantages of simple control framework, free from chattering, stable tracking control performance, and robust to uncertainties. The proposed control strategy, and its advantages are indicated in comparison with FSMC and EFSMC systems. A formal derivation of DTC based on singular perturbation and nonlinear control tools is presented in Sorchini and Krein (2006). DTC is an IM control technique that has been successful because it explicitly considers the inverter stage and uses few machine parameters, while being more robust to parameter uncertainty than FOC. The derivation elaborates an explicit relationship between DTC performance and machine characteristics; low leakage

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machines are expected to perform better under DTC. It is shown that DTC is a special case of a SM controller based on the multiple time scale properties of the IM. The known troublesome machine operating regimes are predicted and justified. Explicit conditions to guarantee stability are presented. DTC is shown to be a suboptimal controller because it uses more control effort than is required for flux regulation. Finally, compensation strategies that extend DTC are discussed. The derivation does not require space vector concepts thus, it is established that the traditional link between DTC and space vectors is not fundamental. Wai (2007) proposed control strategy, and its advantages are indicated in comparison with the conventional SMC system and the SMC system with a boundary layer. This study mainly deals with the key problem of chattering phenomena on the conventional SMC and investigates an adaptive fuzzy sliding mode control (AFSMC) system for an IFOC IM drive to track periodic commands. First, an IFOC method for an IM drive is introduced briefly. Moreover, a fuzzy logic inference mechanism is utilized for implementing a fuzzy hitting control law to remove completely the chattering phenomena on the conventional SMC. In addition, to confront the uncertainties existed in practical applications, an adaptive algorithm, which is derived in the sense of Lyapunov stability theorem, is utilized to adjust the fuzzy parameter for further assuring robust and optimal control performance. The IFOC IM drive with the AFSMC scheme possesses the salient advantages of simple control framework, free from chattering, stable tracking control performance, and robust to uncertainties. A novel sensorless integral SMC for IMs is discussed in Barambones, Garrido, and Maseda (2007). However the proposed observer provide high performance dynamic characteristics and that this scheme is robust with respect to plant parameter variations and external load disturbances over a real IM. Besides, the control scheme provides global asymptotic speed tracking in the presence of unknown parameters and load torque. For this purpose, the control scheme makes use of an improved method of speed estimation operating on the principle of a speed adaptive flux and current observer. As it is known, an observer is basically an estimator that uses a plant model and a feedback loop. In particular, an observer is constructed, which provides a speed estimation on the basis of the measured stator voltages and currents. Then a SM controller with an integral switching surface is considered. Using the Lyapunov stability theory the closed loop stability of the proposed controller is proved under parameter uncertainties and load disturbances, A robust vector control strategy intended for a doubly fed IM model is proposed in Drid, Tadjine, and Nait Said (2007). The state all flux IM model with a flux orientation constraint is replaced by a simpler control model. The double flux orientation leads to orthogonality between the stator and rotor fluxes, resulting in a linear and decoupled machine control and an optimal developed torque. The inner flux controllers are designed using the Lyapunov linearization approach. This flux control is exponentially stabilized independently of the speed. Associated with SMC, this solution shows good robustness with respect to parameter variations, measurement errors and noise. Finally, a speed controller is designed using two methods: the first with a PI controller and the second with the Lyapunov method associated with a backstepping procedure, especially employed for the unknown load torques. This second solution shows good robustness with respect to inertia variation and guarantees torque and speed tracking. The global asymptotic stability of the overall system is proven theoretically. A field programmable gate array (FPGA) based adaptive backstepping SM controller is proposed (Lin, Chang, & Huang, 2007) to control the mover position of a LIM drive to compensate for the uncertainties including the friction force. First, the dynamic model of an IFOC LIM drive is derived. Next, a backstepping SM

approach is designed to compensate the uncertainties occurring in the motion control system. Moreover, the uncertainties are lumped and the upper bound of the lumped uncertainty is necessary in the design of the backstepping SM controller. However, the upper bound of the lumped uncertainty is difficult to obtain in advance of practical applications. Therefore, an adaptive law is derived to adapt the value of the lumped uncertainty in real time, and an adaptive backstepping SMC law is the result. Then, an FPGA chip is adopted to implement the indirect field oriented mechanism and the developed control algorithms for possible low cost and high performance industrial applications. With the adaptive backstepping SM controller, the mover position of the FPGA based LIM drive possesses the advantages of good transient control performance and robustness to uncertainties in the tracking of periodic reference trajectories. Fiengo, Glielmo, and Vasca (2007) proposed control strategy for electric power generation in modern hybrid electric vehicles using auxiliary power units (APUs). In the consideration of the APU, a common shaft connects an internal combustion engine and an electrical IM which is used as a starting motor and as a battery charger. Dynamic models of both engine and motor are used for the design of the APU controller. A FOC scheme and a decoupling controller with two independent current control loops is used for the motor. A torque controller, based on a SM torque estimator, regulates the engine transients. Control of the whole APU is obtained by coupling the engine and motor controllers through a reference governor of the requested power both in steady state and during transients. FPGA based robust radial basis function network (RBFN) control system (Lin, Teng, Chen, & Chang, 2008) proposed to control the mover position of a LIM. First, the IFOC mechanism is adopted for the control of LIM. Next, an equivalent control law bases on SMC is designed, in which the uncertainties are lumped by a conservative constant. However, the lumped uncertainty is unknown and difficult to obtain in advance in practical applications. Therefore, a RBFN is derived to approximate the equivalent control law in real time, and a robust RBFN control system with online training ability is resulted. Then, a FPGA chip is adopted to implement the IFOC mechanism and the developed control algorithms for possible low cost and high performance industrial applications. With the robust RBFN control system, the mover position of the FPGA based LIM drive possesses the advantages of good transient control performance and robustness to uncertainties in the tracking of periodic reference trajectories. Estimation of rotor fluxes and load torque in discrete time reduced order observer is designed in Castillo Toledo, Di Gennaro, Loukianov, and Rivera (2008). A continuous feedback is first applied to obtain a discrete time model in closed form. Then, on the basis of these exact sampled dynamics, a discrete time controller ensuring speed and flux modulus reference tracking is determined, making use of the SM technique. The resulting controller is hence hybrid, in the sense that it contains both continuous and discrete time terms. It is shown how to implement such a hybrid controller using the so called exponential holder, which is the only device to be implemented analogically, together with an analog integrator. The speed of a single or two phase IM using diametrical inversion (DI) of the stator voltages is suggested in Guerreiro, Foito, and Cordeiro (2010). DI is a particular reversal of the sequence phases characterized by replacement of the voltage phasor by another that is diametrically opposed to it and rotating in the opposite direction. Every DI is provoked by a change in the sign of the simplest switching function (speed error) of a SM. These changes cause jumps of 180° of the stator voltage phasor and successive discontinuities of its angular velocity. The main and auxiliary windings are always connected, the speed error sign decides the rotating field

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direction, and so, the actual rotor velocity can be reduced (braked) or increased (accelerated). The motor is fed by a rectifier associated with a three phase inverter. The common point of the windings is connected to the inverter’s middle leg, which is switched at high frequency with a duty cycle of 50%. The core of the drive command is a 16-b dsPIC device, which receives the speed error sign and generates the appropriate pulse width modulated signals to the three phase inverter. A new control approach for real time speed synchronization of multiple IMs during speed acceleration and load changes is developed in Zhao, Li, and Ren (2010). The control strategy is to stabilize speed tracking of each motor while synchronizing its motion with other motors’ motions so that differential speed errors among multiple motors converge to zero. An adjacent cross coupling control architecture incorporating SMC method is proposed, and the asymptotic convergence to zero of both speed tracking errors and speed synchronization errors have been realized via Lyapunov stability analysis. Performance comparisons with PI control and decoupling control are investigated on a four motor system. Fnaiech, Betin, Capolino, and Fnaiech (2010) suggested the application of fuzzy logic and SMC in order to obtain a high accuracy positioning of a six phase IM rotor in both healthy and faulted modes. The faulted mode of a six phase IM denotes that the motor is working with one or more missing phases. This situation leads to torque oscillations and poor tracking behavior. Therefore, the design of a suitable robust control is a challenging task. The two control strategies are completely different from a theoretical point of view, but the final objectives are to remove the drawbacks of the specific fault on interest. In Wai, Chuang, and Lee (2010), the design of an on line levitation and propulsion control is proposed for a magnetic-levitation (maglev) transportation system. First, the dynamic model of a maglev transportation system including levitated electromagnets driven by linear servo amplifiers and a propulsive LIM based on the concepts of mechanical geometry and motion dynamics is developed. Then, a TSMC strategy is introduced, and the concept of TSMC is incorporated into particle swarm optimization (PSO) to form an on line total sliding mode PSO (TSPSO) control framework with varied inertial weights for preserving the robust control characteristics and reducing the chattering control phenomena of TSMC. In this TSPSO control scheme, a PSO control system is utilized to be the major controller, and the stability can be indirectly ensured by the concept of TSMC control without strict constraint and detailed system knowledge. In order to further directly stabilize the system states around a predefined bound region and effectively accelerate the searching speed of the PSO control, a supervisory mechanism is embedded into the TSPSO control to constitute a supervisory TSPSO control strategy. The superiority of the supervisory TSPSO control scheme is indicated in comparison with the adaptive fuzzy NN, PSO based PID, TSMC and TSPSO control strategies. Two nonlinear controllers, one of SM type and the other PI fuzzy logic based, define a new control structure and Barrero, Gonzalez, Torralba, Galvan, and Franquelo (2002) presented a new approach to indirect vector control (IVC) of IMs. Both controllers are combined by means of an expert system based on Takagi-Sugeno fuzzy reasoning. The SM controller acts mainly in a transient state while the PI like fuzzy controller acts in the steady state. The new structure embodies the advantages that both nonlinear controllers offer: SM controllers increasing system stability limits and PI like fuzzy logic based controllers reducing the chattering in permanent state. Shyu and Lai (2002) suggested methods to solve a particular incremental motion control problem, which is specified by the trapezoidal velocity profile, using multi segment SMC to a synchronous reluctance motor system. Each segment of the multi segment

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switching surfaces is designed to match the corresponding part of the trapezoidal velocity profile, so that the motor dynamics on the specified segment switching surface have the desired velocity or acceleration corresponding to the trapezoidal profile. The synthesis and practical implementation of a robust digital differentiator that provides the first and second derivative of a sampled smooth signal. The robustness of the proposed digital device, based on second order SMs, is analyzed with respect to measurement errors in Bartolini et al. (2003). Fast and accurate estimates of speed and torque can be obtained in several operating conditions by double differentiation of the encoder position measurement in an IM drive. A WNN control system is utilized to predict the uncertain system dynamics online to relax the requirement of uncertainty bound in the design of a traditional SM controller. In Wai, Duan, Lee, and Chang (2003), an adaptive observation system and WNN control system are addressed for achieving the favorable decoupling control and high-precision position tracking performance of an IM drive. First, an adaptive observation system with an inverse rotor time constant observer is derived on the basis of MRAS theory to preserve the decoupling control characteristic of an indirect field oriented IM drive. The adaptive observation system is implemented using a DSP with a high sampling rate to make it possible to achieve good dynamics. Moreover, a WNN control system is developed via the principle of SMC to increase the robustness of the IFOC IM drive with the adaptive observation system for high performance applications. The design and properties of a robust wavelet neural network sliding mode control (WNNSMC) system is presented in Wai and Chang (2003) for an indirect field oriented induction servo motor drive to track periodic commands. First, a TSMC system with an integral operation switching surface, which is insensitive to uncertainties in the whole control process, is introduced. In the TSMC system the controlled system has a total sliding motion without a reaching phase. Moreover, to relax the requirement for the bound of uncertainties, a WNNSMC system is investigated to control the induction servo motor. In the WNNSMC system, a WNN is utilized to estimate the bound of uncertainties on line. In addition, a robust WNNSMC system is proposed to alleviate the chattering phenomena in the control effort. In the robust WNNSMC system, a boundary layer is introduced into the TSMC system, and a WNN is used to estimate the width of the boundary layer and the uncertainty bound. AFSMC system is comprised of a fuzzy controller and a compensation controller for induction servomotor system control in Lin and Hsu (2004). The conventional fuzzy controller is the main tracking controller, which is used to approximate an ideal computational controller. The compensation controller is designed to compensate for the difference between the ideal computational controller and the fuzzy controller. A tuning methodology is derived to tune the premise and consequence parts of the fuzzy rules. The online tuning algorithm is derived in the Lyapunov sense; thus, the stability of the control system can be guaranteed. Moreover, to relax the requirement for the uncertain bound in the compensation controller, an estimation mechanism is investigated to observe the uncertain bound, so that the chattering phenomena of the control efforts can be relaxed. An evaluation of a new AFSMC used for speed and flux regulation for an IM drive system as compared to classical control methods is presented in Agamy (2005). The proposed controller has the merits of SMC: fast response, robustness to plant parameter variations and simplicity of implementation and it also avoids the problems of chattering and the need of a large control effort achieve the control objective by means of using and optimization technique to vary the gains of the SM controller according to the position of the operating point on the state trajectory.

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Two novel SM, MRAS observers for speed estimation in a sensorless vector controlled IM drive is presented in Comanescu and Xu (2006). Both methods use the flux estimated by the voltage model observer as the reference and construct SM flux observers that allow speed estimation. Stability and dynamics of the two proposed SM flux observers are discussed. The observers are compared with the classical MRAS observer. The proposed estimators seem very robust and easy to tune. Unlike the classical MRAS, the speed estimation process is based on algebraic calculations that do not exhibit under damped poles or zeros on the right hand plane. Field orientation techniques without flux measurements depend on the parameters of the motor, particularly on the rotor resistance or rotor time constant (for rotor field orientation) is suggested in Proca and Keyhani (2007). Since these parameters change continuously as a function of temperature, it is important that the value of rotor resistance is continuously estimated online. A fourth order SM flux observer is developed. Two sliding surfaces representing combinations of estimated flux and current errors are used to enforce the flux and current estimates to their real values. Switching functions are used to drive the sliding surfaces to zero. The equivalent values of the switching functions (low frequency components) are proven to be the rotor resistance and the inverse of the rotor time constant. This property is used to simultaneously estimate the rotor resistance and the inverse of the time constant without prior knowledge of either the rotor resistance or the magnetizing inductance. A position control of a class of servomotors is addressed in Shahnazi, Shanechi, and Pariz (2008) via a novel adaptive fuzzy PI SMC. However method in controlling uncertain induction servomotor in terms of significant reduction in chattering while maintaining asymptotic convergence and a model of DC servomotor with unknown parameters and uncertainty in load condition is proposed. The premise and the consequence parts of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control is approximated by an adaptive PI control structure. Moreover, the bound of the discontinuous control term is assumed to be unknown, and an adaptive mechanism is used to estimate this bound. All adaptive laws are derived via Lyapunov synthesis method, thereby guaranteeing the closed loop stability. The proposed approach has the added advantage that, for external disturbances, it only requires a bound to exist, without needing to know the magnitude of this bound. The necessity of the compactness of the converters in many applications imposes the reduction of the size of their different components when it is possible. In Liutanakul, Pierfederici, and Meibody Tabar (2008), a control method allowing the use of a small size DC link capacitor Co for the cascade of voltage controlled rectifier/inverter motor drive system is proposed. This is achieved by adding the power balance equation in the system’s model and the application of an exact I/O feedback linearization technique in a way that the rectifier controller compensates any sudden change in the inverter load, which is here an IM. Since the exact I/O feedback linearization technique is sensitive to the uncertainties over system parameters, a robust control strategy based on SMC is proposed. By this approach, the DC link voltage vdc becomes almost insensitive to the load variations. As a result, the level of vdc could be stabilized with a small Co. Without any considerations of the squareroot mean square (RMS) current stress on the Co, a calculation method of a minimum DC link capacitor Co(min) based on its storage energy is proposed. SMC design technique on the new class of the AC drives: an IM fed by a three level VSI is proposed in Ryvkin, Schmidt Obermoeller, and Steimel (2008). A comprehensive investigation of possible drive variable structures was carried out. Based on this analysis, an original two step design procedure allows the use of the classical result of SM theory for the real VSS with more than 2m variable

structures (m is the control space order). Based on this design procedure, the original control algorithm that includes a choice condition for three level VSI input DC voltage and a switch table for the three level VSI semiconductor switches are designed. A new way of IM position control for high performance applications is developed in Veselic, Perunicic Drazenovic, and Milosavljevic (2008) using discrete time sliding mode (DSM) control. In addition to the main DSM position controller, the proposed control structure includes an active disturbance estimator (ADE), in which a passive filter is replaced by another DSM controlled subsystem, in order to improve system robustness and accuracy. Furthermore, the application of an ADE makes possible the design of both controllers using the knowledge of the nominal system only. High efficiency servo system under the influence of large parameter perturbations and external disturbances in the presence of unmodeled dynamics verified. The performance and efficiency of an IM drive system can be enhanced by online estimation of the critical parameters, such as the rotor time constant and stator resistance. A novel Luenberger SMO with parameter adaptation algorithm is proposed in Hasan and Husain (2009) to compensate for the parameter variation effects. The observer is simple and robust when compared with the previously developed observers, and suitable for online implementation. A FPGA based controller has been implemented, and demonstrated using hardware. The problem of meeting the requirements of controllers for the control of speed of IMs, but under the constraint of not using speed and flux sensors: the so called sensorless control problem. In Rao, Buss, and Utkin (2009) proposed an observer based solution and present the design of two observers which provide motor speed, flux, and rotor resistance estimates simultaneously. Both observers, based on the rotor flux model in the stationary reference frame, are designed with inputs that enforce first (conventional) and second order SMs, respectively, on appropriately chosen switching surfaces. Current and input voltage measurements are needed for accurate speed and flux estimation even in the presence of unknown parameters. A speed estimation method for an IM drive that is based on a special current control scheme called integral sliding mode-current control (ISM-CC). Classic current control for the IM drive is done by regulating the d  q synchronous reference frame currents using PI controllers with or without a decoupling compensator. If a decoupling compensator is used, the speed and the motor parameters are needed to compute the decoupling voltages. Often, the speed (or the speed estimate) is not available, and the decoupling compensator is omitted; this leads to a degraded performance of the current controller. In Comanescu (2009), ISM-CC scheme was developed for the decoupled control of the d  q currents and does not require the knowledge of the speed. In the ISM-CC, PI controllers act on simulated ideal plant models, and the resulting command voltages are complemented with voltages generated by SM controllers. It is shown that the SM controllers play the same role as the compensation voltages produced by a decoupling compensator. A high order NN structure is used to identify the plant model, and based on this model, a discrete time control law is derived, which combines discrete time block control and SM techniques. Alanis, Sanchez, Loukianov, and Perez Cisneros (2010) includes the respective stability analysis for the whole system with a strategy to avoid adaptive weight zero crossing. It deals with real time adaptive tracking for discrete time IMs in the presence of bounded disturbances. The concept of a model reference adaptive control of a sensorless IM drive with elastic joint is proposed in Orlowska Kowalska, Dybkowski, and Szabat (2010). An adaptive speed controller uses fuzzy neural network equipped with an additional option for

V.M. Panchade et al. / Annual Reviews in Control 37 (2013) 289–307

online tuning of its chosen parameters. A SM neuro-fuzzy controller is used as the speed controller, whose connective weights are trained online according to the error between the estimated motor speed and the speed given by the reference model. The speed of the vector controlled IM is estimated using the MRAS rotor speed and a flux estimator. Such a control structure is proposed to damp torsional vibrations in a two mass system in an effective way. It is shown that torsional oscillations can be successfully suppressed in the proposed control structure, using only one basic feedback from the motor speed given by the proposed speed estimator. Two novel adaptation schemes are proposed to replace the classical PI controller used in model reference adaptive speed estimation schemes that are based on rotor flux in Gadoue, Giaouris, and Finch (2010). The first proposed adaptation scheme is based on SM theory. A new speed estimation adaptation law is derived using Lyapunov theory to ensure estimation stability, as well as fast error dynamics. The other adaptation mechanism is based on fuzzy logic strategy. A detailed experimental comparison between the new and conventional schemes is carried out in both open and closed loop sensorless modes of operation when a vector control drive is working at very low speed. A design of digitally controlled in an IM positional systems with Euler velocity estimation within the framework of the DSM is presented in Veselic, Perunicic Drazenovic, and Milosavljevic (2010). The effects of quantization and simple velocity estimation on DSM quality are analyzed. It is shown that the introduced and amplified quantization noise degrades sliding motion into the quasi SM and threatens to provoke chattering. Furthermore, a new DSM control algorithm is proposed, featuring a two scale reaching law and a supplemental integral action. This algorithm avoids chattering and provides excellent performance. A classical SMO is designed for the estimation of unmeasurable variables like rotor fluxes and magnetization currents in Rivera Dominguez, Mora Soto, Ortega Cisneros, Raygoza Panduro, and Loukianov (2012). For the load torque, a Luenberger observer is designed. A novel nonlinear affine model for an IM with core loss is developed in the well known (a,b) stationary reference frame, where the core is represented with a resistance in parallel with a magnetization inductance. Then, an optimal rotor flux modulus is calculated such that the power loss due to stator, rotor, and core resistances is minimized, and as a consequence, the motor efficiency is raised; therefore, this flux modulus is forced to be tracked by the IM along with a desired rotor velocity by means of a high order SM controller, the super twisting algorithm. Using a novel Lyapunov function, the closed loop stability of the system is demonstrated. 5. Literature review on sensorless sliding mode control for induction motor Sensorless control of IM drives is now receiving wide attention. The main reason is that the speed sensor spoils the ruggedness and simplicity of IMs. In a hostile environment, speed sensors cannot even be mounted. However, due to the high order and nonlinearity of the dynamics of an IM, estimation of the angle speed and rotor flux without the measurement of mechanical variables becomes a challenging problem. To overcome these difficulties, various control algorithms have been devised in the literature. Bose and Simoes (1995) proposed a hybrid vector control where IVC mode at zero-speed transitions to direct vector control (DVC) at high speed, and then transitions back to IVC at zero speed. Kubota et al. (1993) suggested a speed adaptive flux observer with an adaptive compensator for the variation of the rotor resistance. Based on the model reference adaptive control theory, a speed estimator with pole placement in Schauder (1989) was developed. Tajima and Hori (1993) proposed speed estimation by the output difference of the current model and voltage model. Dixon and

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Rivarola (1996) developed a speed and position estimator based on the introduction of a constant-frequency carrier signal in the stator currents. Kim and Sul (1996) proposed a novel estimation strategy for the very low speed operation to estimate both the instantaneous speed and disturbance load torque using Kalman filter. It is a common feature of many of the sensorless techniques that they depend on machine parameters: they may depend on the temperature, saturation levels, frequency, etc. To compensate for the parameter variations, various parameter adaptation schemes have also been proposed. In an ideal sensorless drive, speed information and control is provided with an accuracy of 0.5 or better, from zero speed to the highest speed, for all operating conditions and independent of saturation levels and parameter variations. In the only industrial sensorless implementation of a DTC drive, an improved mathematical model is used to estimate the speed, and it is claimed that the drive can work even at zero speed. However, it is believed that in the not distant future, artificial intelligence based techniques (fuzzy, neural, fuzzy neural, etc.) will have a more dominant role in sensorless drives and in particular, complicated mathematical models will not be required for speed or position estimation. It is known that the rotor flux is needed for the implementation of torque or speed control. Unfortunately, the rotor flux cannot be measured directly. If the angle speed is available, the flux can be estimated with a second order observer and its convergence is guaranteed for any speed (Utkin, 1993). However, if no information about the mechanical variables is acquired, the design of the observer is no more a trivial problem. In Yan et al. (2000), a torque or speed tracking controller is designed for the IM given by (1) and (6) without measurement of mechanical variables. Therefore, Yan et al. (2000) designed a flux/speed observer to estimate the flux and speed simultaneously based on the measurement of the stator currents and voltages, and then design a corresponding controller to guarantee that the real torque or speed tracks the desired torque or speed. Yan et al. (2000) suggested a nonlinear observer/controller with the basic ideas. First, in the framework of the approach offered in Izosimov (1983) and Yan et al. (2000) designed a flux and current observer with discontinuous parameters and stator currents and voltages as its inputs such that the estimated currents converge to the real currents. Then, an ideal SM controller for flux/torque is designed for estimated values of the flux and speed. The stability analysis of the observer/controller shows that the real flux converges to the estimated flux and the average value of the discontinuous parameter of the observer is equal to the real speed. 5.1. Sensorless sliding mode flux/speed observer In this SMC scheme, Yan and Utkin (2002) designed a rotor flux/ speed observer to estimate the rotor flux and speed simultaneously based on the measurement of stator currents and voltages and then design a corresponding controller to guarantee that the real torque or speed tracks the desired torque or speed . Applying the same structure of (1)–(6), the SM rotor flux, stator current and speed observer are proposed as Izosimov (1983)

dk^a ^ k^b þ gLm ia þ C k^b l ¼ gk^a  x dt dk^b ^ k^a þ gLm ib  C k^a l ¼ gk^b þ x dt di^a 1 ^ k^b  cia þ ¼ bgk^a þ bx u  bk^a l dt rLs a di^b 1 ^ k^a  cib þ ¼ bgk^b  bx u  bk^b l dt rLs b

ð39Þ ð40Þ ð41Þ ð42Þ

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In which k^a ; k^b are the estimates rotor flux components; i^b ; i^a are estimated stator currents used for generating SM; C is a parameter ^ is the estimate for the electrical rotor speed and to be selected. x auxiliary variable l, which are discontinues parameters given by

^ ¼ x0 signðsn Þ x l ¼ l0 signðsl Þ

ð44Þ

where FT = (f1, f2, 0) are continuous state functions,

ð45Þ

ð47Þ ð48Þ

ð49Þ ð50Þ

will tend to zero and the average value of the discontinuous func^ tends to the real speed x. tion x 5.2. Sensorless sliding mode torque regulation The control objective in this section is to design a torque tracking controller for the electromechanical system given by (1)–(6). Based on the rotor flux and speed estimation strategy described in the previous section, Yan et al. (2000) designed a corresponding SM torque controller to guarantee the asymptotic stability of the SMO and the torque tracking controller. The additional goal of control dictated by technological requirements is to make the flux track the reference flux input. In this section, the designs of the observer and the controller are integrated rather than be performed separately. Three sliding surfaces are designed as Yan et al. (2000) and Yan and Utkin (2002)

s1 ¼ T 0  Tb d s2 ¼ c2 ðk0  k^kkÞ þ ðk0  k^kkÞ dt Z t ðua þ ub þ uc Þdt s3 ¼



sT ¼ s1 ; s2 ; s3  T   

ðsigns Þ ¼ signs1 ; signs2 ; signs3 s ¼ D T s

ð46Þ

are equal to zero. Then a SMC will be designed and it will be shown that the flux estimation errors

ka ¼ k^a  ka kb ¼ k^b  kb



u ¼ U 0 signs

By selecting constant values x0 and l0 such that SM occurs in the surfaces of sn = 0 and sl = 0 and as a result, the estimation errors

ia ¼ i^a  ia ib ¼ i^b  ib

Following the design methodology introduced in Utkin (1993), select the discontinuous control

ð43Þ

where x0, l0 are constants. Sliding surface sn and sl are nonlinear functions of the stator current errors and estimated rotor flux, are defined as Novotny and Lipo (1996)

sn ¼ ði^b  ib Þk^a  ði^a  ia Þk^b sl ¼ ði^a  ia Þk^a þ ði^b  ib Þk^b

v_ ¼ sT ðF þ DuÞ

ð51Þ ð52Þ

and U0 is a DC bus voltage.

22

a1 ðea  ^kÞ 6 2 ^ D ¼ 4 a2 ðea  kÞ 3 3

1

 ^kÞ 2 ^ a ðe  kÞ 3 2 b

3  ^kÞ 2 ^ 7 5 a ðe  kÞ 3 2 c

2 a ðe 3 1 b

2 a ðe 3 1 c

1

1

with det D – 0 and

ei  ^k ¼ eia ^kb  eib ^ka ; ei  k^ ¼ eia k^a þ eib k^b ; i ¼ a; b; c: By this SMC working together with the observer, the estimated flux ka ! ka ; ^ kb ! kb ) and and torque will converge to the true values (i.e.^ ^ tends to the the average value of the discontinuous parameter x real speed x. Manifold s3 is used just to constitute a three phase balanced system if all three phase voltage may be selected arbitrarily. 5.3. Sensorless sliding mode speed and rotor time constant observer After rewriting the machine parameter c, the current Eqs. (1) and (2) can be written as

  dia Rs 1 ¼ bgka þ bxkb  þ bLm g ia þ u dt rLs rLs a   dib Rs 1 ¼ bgkb  bxka  þ bLm g ib þ u dt rLs rLs b

ð54Þ ð55Þ

Here Yan and Utkin (2002) suggested a nonlinear robust observer with discontinuous parameters and stator currents and voltages as its inputs, so that the motor speed and rotor time constant can be estimated simultaneously without the measurement of mechanical variables. Then the flux may be calculated directly. The SMO is designed as follows Yan and Utkin (2002)

ð53Þ

0

where

3Nr Lm Tb ¼ ðib k^a  ia k^b Þ 2 Lr is the estimated torque (Vas, 1998), T0 and k0 are the reference torque and the reference magnitude of flux, c2 is positive constant parameter which determines the converge speed of the error ðk0  k^ kkÞ in the SM. In this controller scheme, should SM occur on manifolds s1 = 0 and s2 = 0 the estimated torque and the magnitude of the rotor flux converge to the reference value. Indeed, s1 = 0 b and s2 = 0 means ðk0  k^ means that T 0 ¼ T kkÞ tends to zero exponentially. The design task is reduced to enforcing SM in the manifolds s = 0, sT = (s1, s2, s3), with control uT = (ua, ub, uc). To find the discontinuous controls such that SM is enforced in the manifold s = 0, se

lect Lyapunov candidate function v ¼ 12 sT s P 0. Its time derivative on the state trajectories of system

d^ia Rs ^ 1 i þ ¼ u þ Va dt rLs a rLs a d^ib Rs ^ 1 i þ ¼ u þ Vb dt rLs b rLs b

ð56Þ ð57Þ

where ^ia ; ^ib are estimates of the stator current components. Va and Vb are discontinuous functions of the current errors

V a ¼ V 0 signðsa Þ ¼ V 0 signð^ia  ia Þ V b ¼ V 0 signðsb Þ ¼ V 0 signð^ib  ib Þ

ð58Þ ð59Þ

It is shown that there exists constant values V0 such that SM arises in the surfaces of sa = 0 and sb = 0 and as a result, the estimation errors ia ¼ ^ia  ia ; ib ¼ ^ib  ib are equal to zero. The SM equations on sa = 0 and sb = 0 can be derived by replacing the discontinuous functions Va and Vb by their equivalent control component Vaeq and Vbeq obtained by setting s_ a ¼ 0; sa ¼ 0 and s_ b ¼ 0; sb ¼ 0 (Utkin, 1993)

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V aeq ¼ bgka þ bxkb  bLm gia

ð60Þ

V beq ¼ bgkb  bxka  bLm gib

ð61Þ

The difference is that Vaeq and Vbeq information is needed for the observer implementation while it is not needed in the flux observer. The values of Vaeq and Vbeq cannot be calculated directly by the above two equations, since they contain unknown real rotor flux ka and kb. In Fact, the two discontinuous functions Va and Vb have slow and high frequency components, of which the slow components are equal to Vaeq and Vbeq respectively. So Vaeq and Vbeq may be obtained through a low pass filter (Utkin, 1992) with discontinuous values Va and Vb as the inputs, i.e.,

sz_ a þ za ¼ V a ; za  V aeq sz_ b þ zb ¼ V b ; zb  V beq

ð62Þ ð63Þ

where s is a small time constant of the low pass filter. s should be chosen small enough as compared with the slow component of the real value Va and Vb but large enough to filter out the high rate component (Utkin, 1992). The output za and zb of the low pass filter are taken as Vaeq and Vbeq. For the notation convenience, let us define La = Vaeq and Lb = _ ¼ 0 and g_ ¼ 0 if their variaVbeq. It is reasonable to assume that x tions are very slow compared with the electrical variables such as stator currents and rotor flux. The observers for La and Lb are designed as

2

3 " # " #    _ _ia b ^ ^ La x La L 4 a5¼ g ^ K  bLm g _b _ ^ ^ L  x g Lb i b b Lb

ð64Þ

^ are the estimates of g, x and K is a positive constant to ^; x where g be chosen. La ¼ b L a  La and Lb ¼ b L b  Lb denotes the errors. The adaptive law is chosen as

"

#

"

g_ L þ bLm _ia Lb þ bLm i_b ¼ a _ x Lb La

#"

La Lb

# ð65Þ

 are _ ¼ 0, which means g  and x _ ¼ 0 and x From (65), we know, g constant values. On the other hand, substituting La ¼ 0Lb ¼ 0 into (64), we get



 g x  g  x



La Lb



"  þ bLm g

i_a i_b

# ¼

  0 0

ð66Þ

i.e.,

"

La þ bLm i_a Lb þ bLm i_b

Lb La

#



 

g 0 ¼  0 x

ð67Þ

It is proven that for the observer (64), under the adaptive law (65), the estimated rotor speed and rotor time constant will converge to their real values. 5.4. Recent trends in sensorless sliding mode control for induction motor In Rodic and Jezernik (2002), the proposed control technique is a new structure of rotor flux observer aimed at the speed sensorless operation of an IM servo drive at both low and high speed, where rapid speed changes can occur. The control differs from the conventional FOC. Stator and rotor flux in stator fixed coordinates are controlled instead of the stator current components in rotor field coordinates. In principle, the proposed method is based on driving the stator flux toward the reference stator flux vector defined by the input command, which are the reference torque and the reference rotor flux. The magnitude and orientation angle of the rotor flux of the IM are determined by the output of the closed loop rotor flux observer based on SMC and Lyapunov theory.

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A new SM sensorless control algorithm is proposed for the field oriented IM drive. Derdiyok, Guven, Rehman, Inanc, and Xu (2002) proposed a new SM sensorless control algorithm, the terms containing flux, speed, and rotor time constant, which are common in both current and flux equations, in the current model of the IMs are estimated by a sliding function. The flux and speed estimation accuracy is guaranteed when the error between the actual current and observed current converges to zero. Hence, the fourth order system is reduced to two second order systems, and the speed estimation becomes very simple and robust to the parameter uncertainties. Algorithm is proposed for a new close loop current and flux observer to estimate the rotor flux, position and velocity of an IM in Rehman, Derdiyok, Guven, and Xu (2002). The current observer includes carefully designed SM functions which are derivative of the fluxes along the and axes. Therefore, when the estimated current converges to the measured one, the flux estimation is a mere integration of the SM function. The rotor speed can then be derived from the SM functions and the estimated flux. In the current and flux observers all of the terms that contain the rotor time constant and the rotor speed have been replaced by the SM functions, thus making the proposed current and flux estimations completely insensitive to the rotor time constant variation and any error in the estimated speed. A sensorless torque control system for IM system allows for fast and precise torque tracking over a wide range of speed. The identification and parameter estimation of an IM model with parameters varying as functions of the operating conditions encountered in hybrid electric vehicles applications is also presented in Proca, Keyhani, and Miller (2003). An adaptive SM speed flux observer is developed and a cascade of DSM controllers is used for flux and current control. In Lascu and Trzynadlowski (2004), the principles of SMC, DTC, and space vector modulation are combined to ensure high performance operation, both in the steady state and under transient conditions. Also presented the robustness, accuracy, quickness, and low chattering, wide speed range operation of the sensorless IM drive. Merits of the classic DTC transient behavior are preserved, while the steady state operation is significantly improved. The torque and flux controllers, and motor state observer are of the SM type. The inverter is directly controlled on the basis of torque and flux errors, using space vector PWM. DTC is known to produce fast response and robust control in AC adjustable speed drives. However, in the steady state operation, notable torque, flux, and current pulsations occur. In Lascu, Boldea, and Blaabjerg (2004) a new, direct torque and flux control strategy based on VSC and space vector PWM is proposed for IM sensorless drives. The DTC transient merits and robustness are preserved and the steady state behavior is improved by reducing the torque and flux pulsations. A SMO using a dual reference frame motor model is introduced and tested. Various control algorithms and a new scheme for the speed sensorless control of an IM are proposed. These sensorless algorithms are mainly based on the speed feedback with the flux and speed estimations. In Kwon and Kim (2004), the proposed scheme is based on the current estimation without the flux and speed estimations, in which the controlled stator voltage is applied to the IM so that the difference between stator currents of the mathematical model and motor may be forced to decay to zero. In Lascu, Boldea, and Blaabjerg (2005), the principles of VSC and DTC are combined to ensure high performance operation in the steady state and under transient conditions for IM drive. The drive employs a new torque and flux controller, the linear and VSC, which realizes accurate and robust control in a wide speed range. Conventional DTC transient merits are preserved, while the steady state behavior is significantly improved. The full order state

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observer is a SM one, which does not require the rotor speed adaptation and provides accurate state estimation in the entire speed range. The proposed scheme is a complete variable structure solution that allows persistent sensorless operation of the drive at very low speeds, including zero and 3 r/min, with full load. It also confirmed the robustness, accuracy, quickness, and low chattering operation of the drive. Proposed approach is robust with regard to variations of motor mechanical parameters and load torque disturbances in Wang and Chen (2005). At first, the IM is proved to be a state strictly passive system. Then, a SM position controller with an adaptive load torque estimator is designed to control the position of the IM such that the chattering effects associated with a classical SM position controller can be eliminated. The stability analysis of the overall position control system is carried out by the passivity theory. Finally, good position tracking can be obtained without the rotor flux observer. Adaptive SM flux observer for sensorless speed control of IMs is proposed in Jingchuan, Xu, and Zhang (2005). Two SM current observers are used in the method to make flux and speed estimation robust to parameter variations. The adaptive speed estimation is derived from the stability theory based on the current and flux observers. Continuous approach of SM current and flux observers structure both decouples an IM equations and makes them completely insensitive to rotor resistance variation. An estimation algorithm based on these observers is proposed in Derdiyok (2005) to calculate speed and rotor resistance independently. In the proposed algorithm, the speed and rotor resistance are considered to be unknown constants, because the speed and rotor resistance change slowly compared to the electrical variables such as currents and fluxes. The proposed method is investigated for IM speed sensorless control, allowing operation at low and zero speed, optimizing torque response and efficiency, will be presented in Edelbaher, Jezernik, and Urlep (2006). The magnitude and the orientation angle of the rotor flux of the IM are determined by the output of the closed loop rotor flux observer based on the calculation of the extended electromotive force of the machine. The proposed rotor flux oriented control scheme is robust to parameter variations and external disturbances. Both observer and controller utilize the continuous SM and Lyapunov theory. A smooth transition into the field weakening region and the full utilization of the inverter current and voltage capability are thus possible. The produced torque is a continuous output variable of control. State observers are key components of modern AC drives. A comparative analysis of two state observers for IM drives: the speed adaptive observer and the inherently sensorless observer are presented in Lascu, Boldea, and Blaabjerg (2006). The adaptive observer employs the time variable full order motor model with the rotor speed as the adaptive quantity. Thus, the speed estimation accuracy significantly impacts on the flux observer. It is shown that the popular MRAS speed estimator displays reduced bandwidth, and does not deliver adequate performance for the flux estimation. The inherently sensorless observer employs a full order dual reference frame model in order to eliminate the speed adaptation. In this way, it becomes decoupled from the speed estimator and its performance is superior to that of its adaptive counterpart. Theoretical aspects and comparative simulation results are discussed for both observers. Very low speed operation (3 r/min) capability of the drive with the sensorless observer is reviewed. In Zhang, Xu, Xu, and Heilman (2006), three related techniques, SM flux observer, SM speed controller, and direct rotor speed estimator are presented for the application of sensorless DFOC of three phase IMs based on SM and applied to domestic washing machine drives. Specifically, the investigations focus on how improving

speed regulation, system robustness, and some special technical issues in washing machine drives. The complete control schemes have been developed and implemented in a low cost DSP based electronic controller. The developed sensorless DFOC not only achieves satisfied steady as well as a dynamic performance, but also is robust for washing machine driving applications. The effectiveness of state estimation is confirmed by a steady state and transient sensorless operation at very low speed with rated load torque and step speed reversal. Two flux observers for wide speed range DTC of sensorless IM drives are presented and compared in Lascu and Andreescu (2006). The first one is a full order SMO with PI compensation, without rotor speed adaptation. The second one is based on a zero phase delay improved integrator of the voltage model, which uses only a PI flux amplitude control with stator flux reference magnitude in the correction loop. In both cases, an estimated DC offset is built up and memorized by the PI integral component and this totally compensates for all DC offsets and drifts originated in the acquisition channels. Two feasible solutions for on line stator resistance identification are proposed. Most sensorless algorithms for a motor drive are based on a mathematical model including electrical variables such as motor current and voltage. Therefore, the accuracy of such variables largely influences the performance of the sensorless motor drive. However, the output voltage of the space vector PWM of the VSI supplying a motor is error prone in the motor’s low speed range because it has a poor resolution in a low output voltage command. A variation of the DC link voltage as a high performance strategy for overcoming the above problem in a sensorless IM drive is proposed in Kwon and Kim (2007). Cascade and high gain observers based on interconnected form to estimate the mechanical and magnetic states of sensorless IM drives are considered. Furthermore, in Ghanes, De Leon, and Glumineau (2008) a flux and speed SM controller is proposed and combined with the observers to achieve the tracking of rotor flux and mechanical speed for IM without the need of flux, speed and load torque measurements. On the basis of the Lyapunov theory, the stability analysis of the proposed observers, the controller and the closed loop observer controller are given. The observers, combined with the controller in closed loop, are compared in terms of their speed tracking capability and their sensitivity to parameter variations on reference trajectories of a sensorless IM control benchmark, particularly when an IM state is unobservable. The problems of current decoupling control and controller tuning associated with sensorless vector controlled IM drives are discussed in Comanescu, Xu, and Batzel (2008). In FOC, the d  q synchronous frame currents should be regulated to have independent dynamics such that the torque production of the IM resembles that of a separately excited DC motor. However, these currents are not naturally decoupled, and decoupling compensators should be used. Current loop tuning is an additional problem, since controller gains obtained by theoretical methods or simulation, quite often, do not work well on the real system. It proposed a new approach for current control that uses integral SM controllers to achieve decoupling. The synchronous frame control voltages are synthesized as the sum of two controller outputs: a traditional one PI that acts on an ideal plant model and an integral SM controller. The integral SM controller decouples the d-q currents and compensates the parameter variations in the current loops of the machine. An adaptive interconnected observer and high order SMC of IMs without mechanical sensors (speed sensor and load torque sensor) are proposed in Traore, Plestan, Glumineau, and de Leon (2008). The adaptive interconnected observer estimates fluxes, angular velocity, load torque, and stator resistance. Stability based on Lyapunov theory is proved to guarantee the observer controller stability.

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Recently, the development of speed estimation methods for sensorless control of IM drives has found great interest in the research community. Parameter adaptation schemes play an important role for better speed estimation over a wide range from zero to high levels beyond the rated speed. Therefore, parallel identification schemes for both speed and stator resistance of sensorless IM drives are proposed for a wide range of speed estimation in Zaky, Khater, Shokralla, and Yasin (2009). These estimation algorithms combine a SM current observer with Popov’s hyperstability theory. Low and zero speed operations of the proposed SMO based speed estimation combined with an online stator resistance adaptation scheme are investigated. A modified SMO based speed estimation scheme for field weakening operation is also introduced. The mismatch problem of magnetizing inductance in the field weakening region is treated by an online identification scheme. Magnetizing inductance, estimated in this way, is further utilized within the SMO, so that the main flux saturation variation is taken into consideration. The performance of the proposed SMO and its speed estimation accuracy, with an IFOC IM, are verified over a wide speed range from zero to high values beyond the base speed. A sensorless output feedback controller is designed in order to drive an IM without the use of flux and speed sensors in Ghanes and Zheng (2009). First, a new SMO that uses only the measured stator currents is synthesized to estimate the speed, flux, and load torque. Second, a current based field oriented SMC is developed so as to steer the estimated speed and flux magnitude to the desired references. A stability analysis based on the Lyapunov theory is also presented in order to guarantee the closed loop stability of the proposed observer control system. A new family of speed sensorless SMO for IM drives that represent a feasible alternative to the classical speed adaptive flux observers. Three topologies are investigated in order to determine their feasibility, parameter sensitivity, and practical applicability in Lascu, Boldea, and Blaabjerg (2009). The most significant feature of all schemes is that they do not require the rotor speed adaptation, i.e., they are inherently sensorless observers. The most versatile and robust is a dual reference frame full order flux observer. The other two schemes are flux observers implemented in stator frame and rotor frame, respectively. These are simpler than the first one and make use of the SM invariance over a specified range of modeling uncertainties and disturbances. The employment of the differential evolution (DE) to offline optimized the covariance matrices of a new reduced delayed state Kalman filter (DSKF) based algorithm which estimates the stator flux linkage components, in the stationary reference frame, to realize sensorless control of IMs. The DSKF-based algorithm uses the derivatives of the stator flux components as mathematical model and the stator voltage equations as observation model so that only a vector of four variables has to be offline optimized. It show that the proposed DE based approach is very promising and clearly outperforms a classical local search and three popular metaheuristics in terms of quality of the final solution for the problem considered in this paper. A novel simple stator flux oriented SMC scheme is online used in conjunction with the optimized DSKF based algorithm to improve the robustness of the sensorless IM drive at low speed in Salvatore, Caponio, Neri, Stasi, and Cascella (2010). The stator flux oriented SMC scheme has closed loops of torque and stator flux linkage without PI controllers so that a minimum number of gains has to be tuned. Efficiency optimization of IM drives is a major subject, based on these drives extensive use in the industry. Among the different proposed methods, a model based approach seems to be the fast one. However, this method needs the motor parameters that must be correctly identified. On the other hand, a search based approach is a parameter independent method but needs a greater convergence time. A novel model based loss minimization approach,

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which is combined with a back stepping DTC of the IM drive is presented in Hajian, Soltani, Markadeh, and Hosseinnia (2010). The proposed controller is realized in the stationary reference frame and has a fast tracking capability of rotor flux and electromagnetic torque. Moreover, a SM rotor flux observer is introduced, which is employed for simultaneous determination of rotor flux space vector, rotor speed, and rotor time constant. Two kinds of observers are applied for flux and speed estimation, i.e., SM full order observer and reduced order observer in Davari, Khaburi, Wang, and Kennel (2012). Also proposed two kinds observer based sensorless predictive torque control. The predictive method is based on examining feasible voltage vectors (VVs) in a prescribed cost function. The VV that minimizes the cost function is selected. A novel robust prediction model includes SM feedbacks. 6. Conclusion This paper summarized the significant contributions made by researchers to control, estimation algorithms and methods for IM based on conventional approaches, SMC and sensorless SMC. These approaches are reviewed in view of the FOC, DTC, speed observer, observer based flux estimation, SM flux and speed observer and sensorless SMC. SMC is well established as a general control method and its feasibility has increasingly recognized by control professionals, although there are still problems to be investigated. More importantly, SMC is applicable to many control systems where there are no other design methods are not available. The SMC has given satisfactory performance in many practical areas of industrial electronics. The FOC is promising for IM considering its lower energy consumption resulting in increasing the efficiency which in turn reduces the operating costs. DTC offers simple implementation and a fast dynamic response moreover the absence of coordinate transformation, current regulator and separate voltage modulation block makes DTC foremost control approach. The paper has outlined SMC design philosophy oriented to control and estimation strategies for IM. Acknowledgments This research work is supported by BCUD (Board of College and University Development), University of Pune under the research Project (Grant No. BCUD/OSD/390). The authors would like to express their sincere gratitude to the Editor-in chief and anonymous reviewers whose constructive comments have helped us to significantly improve both the technical quality and presentation of this paper. We are also deeply grateful to Dr. S.B. Sadale, Shivaji University Kolhapur, M.S., India for fruitful discussion and guidance in the preparation of this manuscript. References Emelyanov, S. V. (1959). Control of first order delay systems by means of an astatic controller and nonlinear correction. Automatic Remote Control (8), 983–991. Utkin, V. I. (1977). Variable structure systems with sliding modes. IEEE Transactions on Automatic Control, AC-22(2), 212–222. Hung, J. Y., Gao, W., & Hung, J. C. (1993). Variable structure control: A survey. IEEE Transactions on Industrial Electronics, 40(1), 1–9. Young, K. D., Utkin, V. I., & Ozguner, U. (1999). A control engineer’s guide to sliding mode control. IEEE Transactions on Control Systems Technology, 7(3), 328–342. Leonard, W. (1985). Control of electrical drives. Berlin, Germany: Springer Verlag. Vas, Peter (1998). Sensorless vector and direct torque control. Oxford University Press. Novotny, D. W., & Lipo, T. A. (1996). Vector control and dynamics of AC drives. London, UK: Oxford Univ. Press. Wai, Rong Jong (2003). Development of intelligent position control system using optimal design technique. IEEE Transactions on Industrial Electronics, 50(1), 218–231. Takahashi, I., & Noguchi, T. (1986). A new quick response and high efficiency control strategy of an induction motor. IEEE Transactions on Industry Applications, 22, 820–827.

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Kwon, Y. A., & Kim, S. K. (2007). A high performance strategy for sensorless induction motor drive using variable link voltage. IEEE Transactions on Power Electronics, 22(1), 329–332. Ghanes, M., De Leon, J., & Glumineau, A. (2008). Cascade and high gain observers comparison for sensorless closed loop induction motor control. IET Control Theory and Applications, 2(2), 133–150. Comanescu, M., Xu, Longya, & Batzel, T. D. (2008). Decoupled current control of sensorless induction motor drives by integral sliding mode. IEEE Transactions on Industrial Electronics, 55(11), 3836–3845. Traore, D., Plestan, F., Glumineau, A., & de Leon, J. (2008). Sensorless induction motor: High order sliding-mode controller and adaptive interconnected observer. IEEE Transactions on Industrial Electronics, 55(11), 3818–3827. Zaky, M. S., Khater, M. M., Shokralla, S. S., & Yasin, H. A. (2009). Wide-speed-range estimation with online parameter identification schemes of sensorless induction motor drives. IEEE Transactions on Industrial Electronics, 56(5), 1699–1707. Ghanes, M., & Zheng, G. (2009). On sensorless induction motor drives: Sliding mode observer and output feedback controller. IEEE Transactions on Industrial Electronics, 56(9), 3404–3413. Lascu, C., Boldea, I., & Blaabjerg, F. (2009). A class of speed sensorless sliding mode observers for high performance induction motor drives. IEEE Transactions on Industrial Electronics, 56(9), 3394–3403. Salvatore, N., Caponio, A., Neri, F., Stasi, S., & Cascella, G. L. (2010). Optimization of delayed state Kalman filter based algorithm via differential evolution for sensorless control of induction motors. IEEE Transactions on Industrial Electronics, 57(1), 385–394. Hajian, M., Soltani, J., Markadeh, G. A., & Hosseinnia, S. (2010). Adaptive nonlinear direct torque control of sensorless IM drives with efficiency optimization. IEEE Transactions on Industrial Electronics, 57(3), 975–985. Davari, S. A., Khaburi, D. A., Wang, Fengxiang, & Kennel, R. M. (2012). Using full order and reduced order observers for robust sensorless predictive torque control of induction motors. IEEE Transactions on Power Electronics, 27(7), 3424–3433. V.M. Panchade received the degree in Electrical Engineering from Government College of Engineering, Aurangabad, India, in 1993. He also received the M.E. degree in Instrumentation Engineering from SGGS Institute of Engineering and Technology, Nanded, India, in 2006. Currently he is a Research Scholar in the Department of Electrical Engineering at SGGS Institute of Engineering and Technology, Nanded, India. Presently, he is working as a Assistant Professor in the Department of Electrical Engineering at G.H. Raisoni Institute of Engineering and Technology, Pune, India. His research interests include sliding mode control as applied to electric drives. He has published extensively in these areas of research with one book chapter and 5 referred journal and conference papers. He is a reviewer for Elsevier Control Engineering Practice journal. R.H. Chile received his B.E. and M.E. degrees in Instrumentation Engineering from SGGS Institute of Engineering and Technology, Nanded, India in 1987 and 1992 respectively. He received the Ph.D. degree from IIT, Roorkee, India in 1999. He is a member of ISOI, ISTE and was worked on various committees formed by AICTE, DTE and Universities. Presently, he is working as a Professor in Department of Instrumentation Engineering at SGGS Institute of Engineering and Technology, Nanded. Six students completed the Ph.D. under his guidance and research work of four Ph.D. students is in progress. His teaching and research interests include process instrumentation, sliding mode control, adaptive control as applied to electric drives, power systems control, robotics and process industries. He has published about 60 referred journal and conference papers and has served as a reviewer for different international conferences. B.M. Patre received his B.E. and M.E. degrees in Instrumentation Engineering from the SGGS Institute of Engineering and Technology, Nanded, India, in 1986 and 1990 respectively, and the Ph.D. degree in Systems and Control Engineering from IIT Bombay, India, in 1998. He was Dean (R & D) and Head, Department of Instrumentation Engineering at SGGS Institute of Engineering and Technology, Nanded. Currently, he is a Professor in the Department of Instrumentation Engineering at SGGS Institute of Engineering and Technology, Nanded, India. He was worked on various committees formed by AICTE, DTE and Universities. He has published about 130 referred journal and conference papers. He is reviewer for IEEE, IET, Elsevier, Springer, Wiley, and Taylor-Francis Journals. His research interest covers robust control, output feedback control, sliding mode control and intelligent control. He received research grants from AICTE, DST, BARC, and BRNS. He is a member of ISTE, IETE, IE (India), ISOI, IEE and Senior Member of IEEE.