Sliding-Mode Observer for IPMSM Sensorless Control by MTPA Control Strategy

17th IFAC Conference on Technology, Culture and International 17th IFAC Conference on Technology, Culture and International Stability 17th IFAC Conference Conference on on Technology, Technology, Culture Culture and International International Stability 17th IFAC October 26-28, 2016. Durrës, Albania Availableand online at www.sciencedirect.com Stability October Stability 26-28, 2016. Durrës, Albania October October 26-28, 26-28, 2016. 2016. Durrës, Durrës, Albania Albania

ScienceDirect

IFAC-PapersOnLine 49-29 (2016) 152–157 Sliding-Mode Sliding-Mode Observer Observer for for IPMSM IPMSM Sensorless Sensorless Control Control by by Sliding-Mode Observer for IPMSM Sensorless Control by MTPA Control Strategy MTPA Control Strategy MTPA Control Strategy

Lindita Dhamo*, Aida Spahiu*. Mitja Nemec**, Vanja Ambrozic** Lindita Dhamo*, Aida Spahiu*. Mitja Nemec**, Vanja Ambrozic** Lindita Lindita Dhamo*, Dhamo*, Aida Aida Spahiu*. Spahiu*. Mitja Mitja Nemec**, Nemec**, Vanja Vanja Ambrozic** Ambrozic**   Faculty 

*Polytechnic University of Tirana, of Electrical Engineering, Tirana , Albania; *Polytechnic University of Tirana, Faculty of Electrical Engineering, Tirana , Albania; (e-mail: [email protected], [email protected] ) *Polytechnic University of Tirana, Faculty Engineering, ,, Albania; *Polytechnic University of Tirana, Faculty of of Electrical Electrical Engineering, Tirana Tirana Albania; (e-mail: [email protected], [email protected] ) **University of Ljubljana, Faculty of [email protected] Engineering, Ljubljana, Slovenia; (e-mail: [email protected], ) (e-mail: [email protected], ) Slovenia; **University of Ljubljana, Faculty of [email protected] Engineering, Ljubljana, (e-mail: [email protected], [email protected] ) **University of Faculty Ljubljana, Slovenia; **University (e-mail: of Ljubljana, Ljubljana, Faculty of of Electrical Electrical Engineering, Engineering, Ljubljana, Slovenia; [email protected], [email protected] ) (e-mail: [email protected], [email protected] ) (e-mail: [email protected], [email protected] ) Abstract: This paper presents a nonlinear sliding mode control (SMC) scheme for interior permanent Abstract: This paper presents a nonlinear sliding mode control (SMC) scheme for interior permanent magnet synchronous motors (IPMSMs).The proposed SMC is able(SMC) to reduce the settling time without an Abstract: This paper papermotors presents nonlinear sliding sliding mode control scheme for interior interior permanent Abstract: This presents aa nonlinear mode control scheme for permanent magnet synchronous (IPMSMs).The proposed SMC is able(SMC) to reduce the settling time without an overshoot by giving a low damping ratio at the initial time and a high damping ratio as the output reaches magnet synchronous motors (IPMSMs).The proposed SMCand is able able to damping reduce the the settling time without an magnet synchronous (IPMSMs).The proposed SMC is to reduce settling without an overshoot by giving amotors low damping ratio at the initial time a high ratio as thetime output reaches the desiredbysetpoint. At the same time, it the enables fastand convergence in finite time. Tooutput improve the overshoot giving aa At lowthe damping ratio at atit initialaatime time high damping damping ratiotime. as the theTo reaches overshoot giving low damping ratio the initial aa high ratio as output reaches the desiredby setpoint. same time, enables fastand convergence in finite improve the efficiency ofsetpoint. a systemAt in the constant torque region, the control system incorporates the maximum torque the desiredof the constant same time, time, it enables enables fast convergence in finite finite time. time. To improve improve the the desired setpoint. the same it aa fast convergence in To the efficiency a systemAt in the torque region, the control system incorporates the maximum torque per ampereof(MTPA) algorithm. The stability of the nonlinear sliding surface is guaranteed by Lyapunov efficiency a system in the constant torque region, the control system incorporates the maximum torque efficiency a systemalgorithm. in the constant torque region, the controlsliding systemsurface incorporates the maximum torque per ampereof(MTPA) The stability of the nonlinear is guaranteed by Lyapunov stability theory. The effectiveness of the proposed nonlinear SMC surface scheme is guaranteed verified experimentally. per ampere (MTPA) The stability of by per ampere (MTPA) algorithm. The of stability of the the nonlinear nonlinear sliding isis guaranteed by Lyapunov Lyapunov stability theory. Thealgorithm. effectiveness the proposed nonlinearsliding SMC surface scheme is verified experimentally. From these experimental results, the proposed nonlinear SMC method reveals a faster transient response, stability theory. The effectiveness of the proposed nonlinear SMC scheme is verified experimentally. stability theory. The effectiveness the proposed nonlinear SMC scheme verified experimentally. From these experimental results, the of proposed nonlinear SMC method reveals is a faster transient response, smaller steady-state speed error, and low sensitivity to system uncertainties. From these experimental the proposed nonlinear SMC method From these experimental results, the low proposed nonlinear SMCuncertainties. method reveals reveals aa faster faster transient transient response, response, smaller steady-state speedresults, error, and sensitivity to system smaller steady-state speed error, and low sensitivity to system uncertainties. smaller speed error, and low sensitivity toMotor system uncertainties. © 2016, steady-state IFAC (International Federation of Automatic Control) Hosting byNonlinear Elsevier Ltd. All rights reserved. Keywords: Interior Permanent Magnet Synchronous (IPMSM), Sliding Surface, Sliding Keywords: Interior Permanent Magnet Synchronous Motor (IPMSM), Nonlinear Sliding Surface, Sliding Mode Controller (SMC), Sliding Mode Observer (SMO), Speed Control. Keywords: Interior Permanent Magnet Synchronous Motor (IPMSM), Nonlinear Sliding Sliding Surface, Surface, Sliding Sliding Keywords: Interior Permanent Magnet Motor (IPMSM), Nonlinear Mode Controller (SMC), Sliding Mode Synchronous Observer (SMO), Speed Control. Mode Controller Controller (SMC), (SMC), Sliding Sliding Mode Mode Observer Observer (SMO), (SMO), Speed Control. Mode Speed Control.   control have been developed to satisfy the strict control  1. INTRODUCTION control have been developed to satisfy the strict control requirements of IPMSM drive to systems. In Mohamed et.al 1. INTRODUCTION control have been developed satisfy strict control have of been developed satisfy Inthe theMohamed strict control control requirements IPMSM drive to systems. et.al 1. INTRODUCTION 1. INTRODUCTION (2006), an adaptive self-tuning MTPA vector control is Permanent Magnet Synchronous Motors (PMSMs) have requirements of drive Mohamed of IPMSM IPMSM drive systems. systems. In Mohamed et.al (2006), an adaptive self-tuning MTPA In vector controlet.al is Permanent Magnet Synchronous Motors (PMSMs) have requirements presented to enhance the performance of IPMSM drives. This become more popular in speedMotors and motion (2006), anto enhance adaptive the self-tuning MTPA vectordrives. control is adaptive self-tuning MTPA vector control is Permanent Magnet Synchronous (PMSMs)control have (2006), presentedan performance of IPMSM This Permanent Magnet Synchronous (PMSMs) have become more popular in speedMotors and motion control method isto enhance simple and robust to of variations of system applications due to their well-known advantages of a compact presented the performance IPMSM drives. This presented to enhance the performance of IPMSM drives. This become more popular in speed and motion control is simple and robust to variations of system become more popular in speedadvantages and motion control method applications due to their well-known of a compact parameters. it isrobust only introduced to control the structure, small size, high efficiency, low ofnoise, and method method is However, simple and and to variations variations of system system is simple to of applications due their advantages aa compact However, it isrobust only introduced to control the applicationssmall due to tosize, their well-known well-known advantages compact structure, high efficiency, low ofnoise, and parameters. currents. More recently, in Uddin et al. (2011), an online robustness. Because of their geometrical differences, parameters. However, it is only introduced to control the parameters. However, it is only introduced to control the structure, small size, high efficiency, low noise, and currents. More recently, in Uddin et al. (2011), an online structure, size, ofhightheir efficiency, low differences, noise, and loss-minimization algorithm based on a fuzzy logic controller robustness. small Because geometrical IPMSMs have these of advantageous characteristics when loss-minimization currents. More recently, in Uddin et al. (2011), an online currents. More recently, in Uddin et al. (2011), an online robustness. Because their geometrical differences, algorithm based on a fuzzy logic controller robustness.have Because their geometrical differences, IPMSMs these of advantageous characteristics when is developed for IPMSM drives to yield a high efficiency and compared SPMSMs: Sim et al. (2014) and Sekour when et al. loss-minimization algorithm based on controller algorithm based on aa fuzzy fuzzy logic controller IPMSMs to have these advantageous advantageous characteristics is developed for IPMSM drives to yield a highlogic efficiency and IPMSMs have these characteristics compared to SPMSMs: Sim et al. (2014) and Sekour when et al. loss-minimization ais high dynamic performance over a wide speed range.and In (2013), confirm that higher speed operation and higher torque developed for IPMSM drives to yield a high efficiency is developed for IPMSM drives to yield a high efficiency and compared to SPMSMs: Sim et al. (2014) and Sekour et al. a high dynamic performance over a wide speed range. In compared to SPMSMs: Sim et al. (2014) and Sekour et al. (2013), confirm that higher speed operation higher torque addition, in Uddin et al. (2007), the authors developed a production advantages that speed resultsoperation from a more robusttorque rotor aaaddition, high performance over aa wide speed range. high dynamic dynamic performance over the wide speed range. In Ina (2013), confirm confirm that higher higher and higher higher in Uddin et al. (2007), authors developed (2013), that and production advantages that speed resultsoperation from a more robusttorque rotor simple fuzzy logic control strategy which is utilized as a structure with magnetsthat buried in the core,robust whilerotor the addition, addition,fuzzy in Uddin Uddin et al. (2007), (2007), thewhich authors developed in al. authors developed production advantages results fromrotor more logic et control strategythe is utilized as aa production advantages results from aa more structure with magnetsthat buried in the rotor core,robust whilerotor the simple speed controller with a reduced computational burdenas toa latter onewith uses the reluctance torque ascore, wellwhile as the simple fuzzy logic control strategy which is utilized simple fuzzy logic control strategy which is utilized structure magnets buried in the rotor the controller with a reduced computational burdenas toa structure magnets buried in the rotorascore, latter onewith uses the reluctance torque wellwhile as the speed achieve high performance for an computational IPMSM aboveburden its rated electromagnetic torque. speed controller with aa reduced reduced to speed with to latter one uses the reluctance torque as well as the achieve high performance for an computational IPMSM aboveburden its rated latter one usestorque. the reluctance torque as well as the speed. controller electromagnetic However, these schemes do not address uncertainty achieve high performance for an IPMSM above its rated achieve high performance for an IPMSM above its rated electromagnetic torque. speed. However, these schemes do not address uncertainty electromagnetic torque.widely for high-performance variable- problems. A neuro-network control method is introduced in IPMSMs are applied However, these do not uncertainty IPMSMs are applied widely for high-performance variable- speed. speed. However, these schemes schemes do method not address address uncertainty problems. A neuro-network control is introduced in speed motor drives such asforindustrial robots, computerKhan et.al A(2010) to precisely control the speed of IPMSM problems. neuro-network control method is introduced in IPMSMs are applied widely high-performance variablespeed motor drives such as industrial robots, computer- problems. A neuro-network control method is introduced in Khan et.al (2010) to precisely control the speed of IPMSM controlled machine tools, household goods, electriccomputervehicles driving systems. Intothis scheme,control the system control achieves speed motor drives such as industrial robots, Khan et.al (2010) precisely the speed of IPMSM speed motor drives such as industrial robots, computercontrolled machine tools, household goods, electric vehicles driving Khan et.al (2010) to precisely control the speed of IPMSM systems. In this scheme, the system control achieves (EVs), andmachine plug-in hybrid electric vehicles Lin et good performance and the systemthe uncertainty problem is well controlled tools, household household goods, (PHEVs), electric vehicles vehicles systems. this scheme, system achieves controlled tools, goods, electric (EVs), andmachine plug-in hybrid electric vehicles (PHEVs), Lin et driving driving systems. In Inand thisthe scheme, system control control achieves good performance systemthe uncertainty problem is well al. (2013). Despite their inherent advantages, the accurate solved. However, this approach requires burdensome (EVs), and plug-in plug-in hybrid electric vehicles vehicles (PHEVs), Lin et et good good performance andthis the system system uncertainty problem is well well (EVs), and electric (PHEVs), Lin al. (2013). Despite hybrid their inherent advantages, the accurate performance and the uncertainty problem is solved. However, approach requires burdensome speed control of IPMSM drives advantages, presents some difficult computation due to a complex online algorithm. al. (2013). Despite their inherent inherent the accurate accurate solved. However, this approach requires burdensome al. (2013). Despite their the speed control of IPMSM drives advantages, presents some difficult solved. However, this approach requires burdensome due to a complex online algorithm. challenges in theofpresence of nonlinear coupling terms Do et computation speed control IPMSM presents some difficult computation due to aa complex complex online algorithm. speed control IPMSMofdrives drives presents some difficult challenges in theofpresence nonlinear coupling terms Do et computation to algorithm. Among the due advanced controlonline methods, the sliding mode al. (2014). In addition, system uncertainties such as external challenges presence of coupling Do the advanced control methods, the sliding mode challenges in the presence of nonlinear nonlinear coupling terms Do et et Among al. (2014). in In the addition, system uncertainties suchterms as external control (SMC) is a better choice in comparison withmode the disturbances and motor parameter variations can considerably Among (SMC) the advanced advanced control methods, the sliding sliding the control methods, the al. addition, system such as control is a better choice in comparison withmode the al. (2014). (2014). In Inand addition, system uncertainties uncertainties suchconsiderably as external external Among disturbances motor parameter variations can others because ofisitsa robustness. TheinSMC is less sensitive to deteriorate the control performances. Accordingly, it is not control (SMC) better choice comparison with the control (SMC) is a better choice in comparison with the others because of its robustness. The SMC is less sensitive to disturbances and motor parameter variations can considerably deteriorate the control performances. Accordingly, it is not parametric uncertainties, unmodeled dynamics, and external easy for conventional PI controllers or LQ regulators to others because of its robustness. The SMC is less sensitive to others because of its robustness. The SMC is less sensitive to deteriorate the control performances. Accordingly, it is not parametric uncertainties, unmodeled dynamics, and external deteriorate the control performances. Accordingly, it is not easy for conventional PI controllers or LQ regulators to disturbances. As a result, it can be invariant to uncertainties achieve good performance for IPMSM drives under the parametric uncertainties, unmodeled dynamics, and external parametric uncertainties, unmodeled dynamics, and external easy for conventional PI controllers or LQ regulators to disturbances. As a result, it can be invariant to uncertainties easy for conventional PI controllers or LQ regulators to achieve good performance for IPMSM drives under the in many cases and it is able to handle the nonlinearity of system uncertainties stated above. aa result, it invariant uncertainties disturbances. Asand result, it can cantobe behandle invariant to uncertainties achieve good performance performance for IPMSM IPMSM drives drives under under the the disturbances. in many casesAs it is able the to nonlinearity of achieve good for system uncertainties stated above. manipulated plants. On the to other hand, the challenging in many cases and it is able handle the nonlinearity of in many cases and it is able to handle the nonlinearity of system uncertainties stated above. manipulated plants. On the other hand, the challenging system uncertainties stated above. In recent years, some advanced control methods such as problems of plants. the SMC are other its chattering phenomenon, manipulated On the hand, the challenging In recent years, some advanced control methods such as manipulated plants. On the other hand, the challenging problems of the SMC are its chattering phenomenon, adaptive control, fuzzyadvanced control and, andmethods neural network uncertainties In recent years, control such problems ofand the sensitivity SMC are are to its mismatched chattering phenomenon, phenomenon, In recent control, years, some some control such as as singularity, adaptive fuzzyadvanced control and, andmethods neural network problems the SMC chattering singularity,of and sensitivity toits mismatched uncertainties adaptive control, fuzzy control and, and neural network singularity, and and sensitivity sensitivity to to mismatched mismatched uncertainties uncertainties adaptive control, fuzzy control and, and neural network singularity, Copyright © 2016, 2016 IFAC 152Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2016 IFAC 152 Peer review under responsibility of International Federation of Automatic Control. Copyright © 152 Copyright © 2016 2016 IFAC IFAC 152 10.1016/j.ifacol.2016.11.092

2017 IFAC TECIS October 26-28, 2016. Durrës, Albania

Lindita Dhamo et al. / IFAC-PapersOnLine 49-29 (2016) 152–157

resulting from a discontinuous switching gain, Yang et al. (2013). This has led to the suggestion of various techniques in the literature, particularly in the field of motor drives. In Castaneda et al. (2012), a neural model based SMC is presented for the trajectory tracking control of dc motors. This controller ensures the stability and robustness of closedloop systems in the absence of a plant model and in the presence of external perturbations. In Veselic et al. (2008), a high performance discrete-time sliding-mode control is presented for induction motor drives. This control structure includes an active disturbance estimator, in which a passive filter is replaced by another discrete-time sliding mode controlled subsystem in order to improve the system robustness and accuracy. By introducing a boundary layer strategy by Jung et.al (2014), the chattering phenomenon can be reduced at the expense of the robustness against parameter uncertainties. Therefore, it is important to make a good compromise between the robustness and the chattering reduction. This paper presents an application of observer-based nonlinear sliding mode control scheme for IPMSMs. By using a nonlinear sliding surface which is designed based on the variable damping concept, the proposed nonlinear SMC can remarkably reduce the settling time with less overshoot. In order to make the proposed SMC more feasible with a fast convergence in finite time, the upper bound of the uncertain term is adaptively estimated since it cannot be directly measured or calculated. In this paper, the maximum torque per ampere (MTPA) control strategy is incorporated to maximize the torque generation in the constant torque region (main working region). The stability of the nonlinear sliding surface as well as the nonlinear SMC is mathematically proven using the Lyapunov stability analysis, but is not presented here, as being a subject of the future paper. Next, a simple sliding mode observer is applied to estimate both the load torque and the system uncertainties. The validity of the proposed nonlinear SMC is experimentally demonstrated using a prototype IPMSM drive system with a Piccolo F28069 controlstick DSP, a microcontroller from TI C2000 family. The experimental results show that the proposed nonlinear SMC attains better control performance with a faster transient response, a smaller steady-state speed error, and less sensitivity than the corresponding linear SMC when the desired speed and load torque change under system parameter uncertainties. 2. MATHEMATICAL MODEL OF AN IPMSM WITH SYSTEM UNCERTAINTIES 2.1 Dynamic Model of an IPMSM Applying Kirchhoff’s voltage law (KVL) to the dq-axis equivalent circuits of a three-phase IPMSM yields the following voltage equations in the synchronously rotating d-q reference frame:

V qs  R s i qs  L qs iqs   L ds i ds   m

(1)

153

V ds  R s ids  Lds ids   Lqs iqs

(2)

Where: Vds and Vqs are the dq-axis voltages, ids and iqs are the dq-axis currents, Rs is the stator resistance, Lds and Lqs are the dq-axis inductances, ω is the electrical rotor speed, and λm is the magnetic flux. In addition, the electromagnetic torque can be obtained from the following electrical and mechanical equations: 3 p

Te 

2 2



i

m qs

Te  T L  B

 ( L ds  L qs ) ids iqs

2

J

p

2





(3)

(4)

p

Where: Te and TL are the electromagnetic and load torques, p is the number of poles, B is the viscous friction coefficient, and J is the rotor inertia. Substituting (3) into (4) yields the following speed dynamic equation: 2

 

3 p m 2 4



3 p

2

2 4

J

iqs 

L ds  L qs J

B



J

p 2J

TL  (5)

ids iqs

By using (1)-(5), the dynamic model of the IPMSM can be expressed as:

  k 1iq s  k 2  k 3T L  k 1 1id s iq s iq s   k 4 iq s  k 5  k 6V q s  k 1 0 id s

(6)

id s   k 7 id s  k 8V d s  k 9 iq s

Where: the k1 to k11 are the coefficients defined in Dang et al. (2013). In addition, taking into consideration the system uncertainties such as motor parameter variations, external disturbances, etc., the system model (6) can be rewritten as follows:

  k 1 i q s  k 2   k 3 d 1  k 1 1 i d s i q s iq s   k 4 i q s  k 5   k 6V q s  k 1 0  i d s  k 6 d 2

(7)

id s   k 7 i d s  k 8V d s  k 9  i q s  k 8 d 3

Where: d1, d2, and d3 are uncertain components in Dang et al. (2013) that represent motor parameter variations and external disturbances. The uncertain components d1, d2, and d3 are unknown. However, they are assumed to be bounded, i.e., there exist the constants γ1, γ2, and γ3 which satisfy |d1| ≤ γ1, |d2| ≤ γ2, and |d3| ≤ γ3. These assumptions are reasonable because variations of motor parameters cannot be infinite.

2017 IFAC TECIS 154 October 26-28, 2016. Durrës, Albania

Lindita Dhamo et al. / IFAC-PapersOnLine 49-29 (2016) 152–157

Based on the vector control of PM machines, two optimal current control schemes can be achieved: one is the Maximum Torque per Ampere (MTPA) control and the other Limited-Voltage Maximum Torque control. By these means, the PM motor can operate with optimal efficiency at low speeds and deliver the maximum power in the flux weakening region. In order to maximize the torque generation of IPMSMs in the constant torque region and increase the efficiency of IPMSM drives, the armature current should be controlled according to the maximum torque per ampere (MTPA) trajectory operation. In this technique, in the IPMSM drives, the MTPA strategy per efficiency control is not achieved at id = 0 because the reluctance torque cannot be used effectively. The d-axis current reference is given by the equation (8) as in Do et al. (2014):

i ds  

( L qs  L ds ) m

2

i qs

(8)

The maximum electromagnetic torque and output power developed by PM machines is ultimately dependent on the allowable inverter current rating and the maximum output voltage which the inverter can apply to the machine. Considering the limited current and voltage capabilities, a specific control scheme may be desirable which yields attractive characteristics of performance including large delivered torque, fast dynamic response, and high efficiency. In a PM machine, which operates at a given speed and torque, optimal efficiency can be obtained by the application of an optimal voltage that minimizes power losses. At low speeds, this optimum will coincide with the condition of maximum torque per stator ampere, assuming the core losses negligible. Such operation leads to minimal copper losses of stator windings and power losses of semiconductor switches in power inverter. Furthermore, minimization of the stator current for the given maximum torque results in lower current rating of the inverter and thus the overall cost of the PMSM drive system is reduced. Therefore, in most cases, the MTPA control mode is preferred for the constant-torque operation of PM machines. The torque-per-ampere ratio in the SPM motors is maximized by setting the direct-axis reference current component ids to zero for all values of torque. So the sinusoidal stator currents are always in-phase with the induced back-EMF. In contrast, the MTPA current trajectory for IPM initially moves along the q-axis for low values of torque before swinging symmetrically into the second or third quadrant along 45° asymptotes reflecting the nature of saliency. 2.3 Rotor Position/Speed Sensorless IPMSM Control System Figure 1 shows the overall block diagram of the proposed discrete SMO-based sensorless control system for an IPMSM. The control system consists of a speed PI regulator, which generates a torque command based on speed error. The base torque is the maximum torque at each speed point and is

calculated according to the actual rotor speed. Since the DC bus voltage also affects the current command, a speedvoltage ratio is used. The current commands are calculated based on both torque percentage and speed-voltage ratio. Other modules of the control system include current PI regulators with feedforward voltage compensation, Park transformation, space vector pulse-width modulation (SVPWM), etc. The rotor position is obtained from the proposed discrete SMO; the rotor speed is then calculated by using a position buffer based on the estimated rotor position. The overall system can be tested under both open-loop and closed-loop modes. In the open-loop mode, the SMO uses the commanded voltages vα and vβ and measured currents ia and ib to estimate the rotor position; however the control system still uses the measured rotor position and speed for feedback control. In the closed-loop mode, the estimated rotor position and speed are used by the control system. In the low-speed region, the back EMF is too small to be estimated accurately. Therefore, a starting algorithm is designed to accelerate the IPMSM to a minimum transition speed and then the SMO is enabled. Speed_ref

torque_ref

PI

PI

reg_speed

reg_iq

vq vb

PI

vd

e PWM

va

reg_id

Angle id

ia

PARK

iq

1

PWM1A 2A 3A 1B 2B 3B

T1 T2 T3

SV

I PARK

id_ref=0

Speed_Fdb

2.2 Control Mode – MTPA

iB

ADC

ib ic

Angle_el

1

2

ia

iA

CLARKE

ib

I N V E R T E R

2

ia

est_speed

Angle

SMO

ib va

I PMSM

vb

Speed_mech

RDIF speed_mech

Angle_mech

Fig. 1. Block diagram of the overall SMO-based sensorless IPMSM drive system. 2.4 Problem description Per previous discussion, phase shift, magnitude variation, and noise will affect the calculation of rotor position; and these effects are normally present together and bring oscillations to the estimated position, leading to the increase of the position error. It is assumed that the back EMF profiles are sinusoidal waveform; however, a phase shift has been added intentionally between eα and eβ. In order to evaluate the effect brought by the phase shift between eα and eβ, a negative (leading the original signal) and positive (lagging the original signal) phase shift has been added to eα, respectively. The inverse tangent method is used to calculate the rotor position based on the back EMF. It is obvious that the negative phase shift of a few electric degrees causes a positive shift in the error waveform from the zero horizontal axis. However, the shift of the error waveform is negative. The phase and magnitude shifts in the estimated back EMF have different effects on the calculated position. Both the

2017 IFAC TECIS October 26-28, 2016. Durrës, Albania

Lindita Dhamo et al. / IFAC-PapersOnLine 49-29 (2016) 152–157

magnitude and fundamental frequency of the position error waveforms are different. The effects of phase and magnitude shifts combine together to make the error between the estimated and measured positions yielding both phase shift and magnitude oscillation. Because of the switching losses, noise, temperature issue, and CPU speed, a further increase of the sampling frequency cannot be a feasible method to mitigate the phase shift and magnitude oscillation of the position error. Methods that can mitigate these effects need to take into account the physical limitations of the system.

155

system and Control scheme of sensorless SMO IPMSM drive, respectively. The hardware circuit consists of an IPMSM, product of Slovenian company Letrika dedicated for electric power steering systems, a three-phase inverter with 6 MOSFET (IRFP4410), a control board with a F28069 controlstick DSP (floating-point), an absolute encoder (Hengstler AD35, 14 bit), two Hall-effect current sensors (LTS15NP), and a load PMSM motor.

2.5 Improved Inverse Tangent Method The inverse tangent method is the most straightforward method to extract the rotor position angle from the estimated back EMF. In this method the rotor position angle is determined from the magnitudes of the αβ back EMF components as follows: ˆ 1 e (9) ˆ  tan (  ) eˆ  However, the position calculated by this method depends on the quality of the estimated back EMF. Because of the low sampling frequency, the estimated back EMF will have both phase and magnitude shifts, which will bring oscillations and phase shift to the estimated position. In order to mitigate the oscillation of the estimated position, an estimated speed feedback algorithm is proposed to improve the inverse tangent method for position calculation, as shown in Fig. 2, and the formula is as (10).

ˆ2 [ k ]  ˆ[ k  1]   [ k  1]  T s

(10)

Block diagram that represent the algorithm for improving the inverse tangent method for rotor position calculation is shown in figure 2.

Fig. 3. Experimental setup of IPMSM drive system The dc-link voltage (24 VDC) is obtained from the utility (AC 230V/50Hz) using a bench power supply. The two phase currents (ia, ib) are measured by LTS15-NP Hall Sensors and then converted into digital form using two 12-bit A/D converters. In addition, the rotor position (θ), which is used to execute the coordinate transformation in the field-oriented control (FOC) technique, is measured by the absolute encoder and fed to Texas Instruments Piccolo F28069 control stick DSP via SPI (Serial Peripheral Interface). Note that the measured rotor speed (ω) required to perform the feedback control can be easily obtained by differentiating θ with respect to time. Moreover, the control inputs Vq and Vd, which are given by the proposed observer-based control algorithm, are transformed to Vα and Vβ in the stationary α-β reference frame.

DC Bus ACin

3 Phase INVERTER

Gate Drivers

AC/DC Converter GD Proccesor Ground

In order to verify the performance and effectiveness of the proposed observer-based nonlinear sliding mode controller, experiments are carried out with a prototype IPMSM drive system based on a Piccolo F28069 control stick DSP. Fig. 1 shows an overall block diagram of the proposed observerbased nonlinear sliding mode speed control system while Fig. 3 and Fig. 4 show the Experimental setup of IPMSM drive

Phase Current Reconstruction

Id_ref Iq_ref

Motor PWMs

Bus V

12 Bit ADC

Trigger

BUS Over voltage

Power Supplies

Over Sync Defekt Current

3. Test setup and Experimental results

GPIO ose PWM

Piccolo F28069

Fig. 2. Block diagram to improve the inverse tangent method for position calculation.

Bus I

Analog Conditioning

ePWM Module

SVPWM

Ubeta

Actual Speed

PI

Torque Reference

Speed Estimator

Observer SMO

`

Serial Interface

S Reference Speed

Angle

Angle

Speed Calculator

Ualpha

FOC

Angle

eQEP

Ualpha Ubeta Ialpha Ibeta

Angle

Fig. 4. Control scheme of sensorless SMO IPMSM drive.

2017 IFAC TECIS 156 October 26-28, 2016. Durrës, Albania

Lindita Dhamo et al. / IFAC-PapersOnLine 49-29 (2016) 152–157

The IPMSM 5drive system is tested at different load conditions, but in this paper we present the group of results 4 for one case only: speed reference abruptly accelerates from 0 rpm to 900 rpm while the load torque (TL) is kept constant at 0,6 Nm, with no3 electrical motor parameter variations. Later, the family of curves of stator currents in the same regime for different values2 of coefficient of SMO optimised by MTPA strategy is shown. It should be pointed out that these results are given to demonstrate the robustness of the proposed 1 observer-based nonlinear SMC MTPA control strategy. These results are shown in Figures 5-9. 0

Table 1 shows the parameters of IPMSM used in experiments. -10 50 100 150 200

7

Pozicioni i rotorit[rad] Rotor position [rad]

6 5 4

2 1 0

kgm

Rotor speed[rev/s]

Shpejtësia[rrot/s]

450

500

-0.54 -0.55 -0.56 -0.57 -0.58 250 -0.59

300

50

100

350

150

200

400

450

250 300 350 Koha [samples, 1 sample = 0.00015s] Time

500

400

450

500

10 5 0 -5 ebeta

-10

ealpha

14 15.5

15.4

15.3

-15 0

50

100

150

200

250

300

350

400

450

500

Koha [samples, 1 sample = 0.00015s] Time

Fig. 8. Experimental results for estimated EMF. 6

ib

5

ia

4 3 2 1 0 -1 -2 -3 -4 -5

15.2

-6 0

15.1

8

400

15

16

10

350

Fig. 7. Experimental results for electromagnetic Torque.

Each plot shows the following: (a) the desired rotor speed, actual rotor speed (calculated by measurements of encoder), estimated rotor speed (by SMO); (b) results for rotor position estimation by SMO and encoder: (c) electromagnetic torque; (d) results for estimated EMF, and 3phase stator currents; (e) results for transient response of rotor speed tracking. These plots are related to an operational point of 15rps.

12

200 250 300 Koha [samples, 1 sample = 0.00015s] Time

-0.53

-0.6 0

Value 600 1250 0.06 0.068 0.086 0.0373 3 0.0001682

2

150

-0.52

lfa, fem beta[V] bemffemalfa beta[V] a ,bemf

Unit W Rpm Ω mH mH Wb

100

-0.51

Rrymat ecurrents matura të statorit[A] Stator’s [A]

Symbol Pn ωn Rs Ld Lq λPM P J

50

Fig. 6. Experimental results for rotor position estimation by SMO and encoder.

Table 1. IPMSM Parameters Parameters Rated power Rated speed Stator resistance d-axis Inductance q-axis Inductance Total linkage flux Pole pairs Inertia

Pozicioni prej encoder enkoderit angle from Pozicioni i vlerësuarwith me SMO SMO angle estimated gabimi këndit errori vlerësimit estimated të angle

3

-1 0

Momenti [Nm][Nm] Torque

Then, the space vector PWM (SVPWM) block generates six gating signals that drive a three-phase MOSFET power module. In this paper, the sampling frequency (Ts) and the 7 PWM switching frequency (fs) are chosen as 50 μs and 20 kHz, respectively, with the system efficiency and control 6 performance taken into account.

50

100

150

200

250

300

350

400

450

500

Koha [samples, 1 sample = 0.00015s] Time

15

14.9

6 14.8

4

14.7

speed calculated from encoder speed estimated from SMO speed reference

14.6

2 0 0

14.5

0

50

100

50

150

100

200

250

150

300

200

350

400

250

450

Shpejtësia prej enkoderit Speed measured by encoder Speed estimated by SMO Shpejtësia vlerësuar me SMO Speed reference Sjpejtësia referencë

500

300

350

400

450

500

Koha [samples, 1 sample = 0.00015s] Time

Fig. 5. Experimental results for Rotor Speed estimation by SMO and calculated by measurements of encoder.

Fig. 9. Experimental results for 3phase stator currents (are shown phase a and phase b). Plots of Figures 5-9, show that the designed SMO estimate accurately the rotor speed and rotor position, with error estimation less than 0.066% and 1.2% respectively. It seems that estimated EMF signal is quasi sinusoidal, with very low noise, in order to guarantee a better rotor position estimation. The real stator currents are sinusoidal too. Fig. 10 shows the family of stator currents curves for different values of SMO’s coefficient “k”.

2017 IFAC TECIS October 26-28, 2016. Durrës, Albania

Lindita Dhamo et al. / IFAC-PapersOnLine 49-29 (2016) 152–157

It is proven experimentally that its optimal values taken by MTPA strategy applied are k=3.5-4.5.

Rryma e matur e statorit në fazën a[A] A-phase stator’s current[A]

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 -2.5 -3 -3.5 -4 -4.5 -5 0

k=1.9 k=1.0 k=2.9 k=3.2 k=4.5-3.5 k=4.0 k=5.5 50

100

150

200

250

300

350

400

450

500

Koha [samples, 1sample=0.00015s] Time

Fig. 10. Family of stator currents curves for different values of SMO’s coefficient “k”. In this case, the currents flowing in each phase of stator are 15% less than currents flowing for coefficient different than as we find optimal, even that fulfil the condition of convergence and stability of SMO (the analysis for that is focus in a different paper). Figure 11 shows the experimental result of transient response of rotor speed tracking. Clearly, is shown that the transient process with SMO is softer, with 7% less overshoot.

Transient Response of Rotor Speed

16 calculated speed from encoder estimated speed from SMO reference speed

14

12

10

8

6

4

2

0

-2

0

50

100

150

200

250

300

350

Time [samples, 1sample=0.00015s]

400

450

500

Fig. 11. Transient response of rotor speed tracking. 4. CONCLUSIONS This paper propose a robust sliding mode speed controller for IPMSM drives to achieve fast and precise speed tracking, whose coefficient is optimised by MTPA control strategy. Through experimental results, it was verified that the proposed SMC method achieved good control performance as faster and more robust, soft dynamic behaviour and smaller steady-state errors, when compared to the conventional vector control method. 5. ACKNOWLEDGMENT This paper presents a part of the work supported by the research program of ERASMUS MUNDUS/Basileus IV (2013-2014), in Laboratories of Department of Mechatronics, Faculty of Electrical Engineering, University of Ljubljana, Slovenia.

157

REFERENCES Castaneda, C. E., Loukianov A. G., Sanchez, E. N. and Castiio-Toledo, B.(2012) “Discrete-time neural slidingmode block control for a DC motor with controlled flux,” IEEE Trans. Ind. Electron., Vol. 59, No. 2, pp. 1194-1207. Dang, D. Q., Vu, N. T. T., Choi, H. H. and Jung, J. W.(2013) “Neural-fuzzy control of interior permanent magnet synchronous motor: stability analysis and implementation,” J. Electr. Eng. Technol., Vol. 8, No. 6, pp. 1439-1450. Do, T. D., Kwak, S., Choi, H. H. and Jung, J. W.,(2014) “Suboptimal control scheme design for interior permanent- magnet synchronous motors: an SDRE-based approach,” IEEE Trans. Power Electron., Vol. 29, No. 6, pp. 3020-3031. Jung, J. W., Leu, V. Q., Dang, D. Q., Choi, H. H. and Kim, T. H. (2014) “Sliding mode control of SPMSM drivers: an online gain tuning approach with unknown system parameters,” Journal of Power Electronics, Vol. 14, No. 5, pp. 980-988, Sep. 2014. Khan M. A. S.,and Rahman, M. A. (2010) “A novel neurowavelet-based self-tuned wavelet controller for IPM motor drives,” IEEE Trans. Ind. Appl., Vol. 46, No. 3, pp. 1194-1203. Lin, H., Hwang, K. Y. and Kwon, B. I. (2013) “An improved flux observer for sensorless permanent magnet synchronous motor drives with parameter identification,” J. Electr. Eng. Technol., Vol. 8, No. 3, pp. 516-523. Mohamed, Y. A. R. I. and Lee, T. K. (2006) “Adaptive selftuning MTPA vector controller for IPMSM drive system,” IEEE Trans. Energy Convers., Vol. 21, No. 3, pp. 636-644. Sekour, M., Hartani, K., Draou, A. and Allali, A., (2013) “Sensorless fuzzy direct torque control for high performance electric vehicle with four in-wheel motors,” J. Electr. Eng. Technol., Vol. 8, No. 3, pp. 530-543. Sim, H. W., Lee, J. S., and Lee, K. B., (2014) “On-line parameter estimation of interior permanent magnet synchronous motor using an extended Kalman filter,” J. Electr. Eng. Technol., Vol. 9, No. 2, pp. 600-608. Uddin, M. N., and Rebeiro, R. S. (2011) “Online efficiency optimization of a fuzzy-logic-controller-based IPMSM drive,” IEEE Trans. Ind. Appl., Vol. 47, No. 2, pp. 10431050. Uddin, M. N. and Rahman, M. A. (2007) “High-speed control of IPMSM drives using improved fuzzy logic algorithms,” IEEE Trans. Ind. Electron., Vol. 54, No. 1, pp. 190-199. Veselic, B. , Perunicic-Drazenovic, B. and Milosavljevic, C. (2008) “High-performance position control of induction motor using discrete-time sliding-mode control,” IEEE Trans. Ind. Electron., Vol. 55, No. 11, pp. 3809-3817. Yang, J., Li, S., Su, J., and Yu, X., (2013) “Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances,” Automatica, Vol. 49, No. 7, pp. 2287-2291.