Comparative evaluation of sliding mode fuzzy controller and PID controller for a boost converter

Electric Power Systems Research 81 (2011) 99–106

Contents lists available at ScienceDirect

Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

Comparative evaluation of sliding mode fuzzy controller and PID controller for a boost converter Liping Guo a,∗ , John Y. Hung b , R.M. Nelms b a b

Department of Technology, SG 203, Northern Illinois University, DeKalb, IL 60115, USA Department of Electrical and Computer Engineering, Auburn University, AL 36849-5201, USA

a r t i c l e

i n f o

Article history: Received 20 May 2010 Received in revised form 16 July 2010 Accepted 20 July 2010

Keywords: Sliding mode fuzzy control PID control Boost converter Digital signal processor Digital control

a b s t r a c t Nonlinear controllers such as fuzzy controllers and sliding mode controllers have been applied to boost converters because of their nonlinear properties. Although both fuzzy and sliding mode controllers have desirable characteristics, they have disadvantages in practice when applied individually. A sliding mode fuzzy controller is proposed to control boost converters. The sliding mode fuzzy controller combines the advantages of both fuzzy controllers and sliding mode controllers. It also has advantages of its own that are well suited for digital control design and implementation. A sliding mode fuzzy controller is designed and verified with experimental results using a prototype boost converter with a DSP-based digital controller. Experimental results of the boost converter using sliding mode fuzzy control are evaluated in comparison with experimental results using a linear PID and PI controller. The comparison indicates that the sliding mode fuzzy controller is able to obtain the desired transient response under varying operating points without chattering. The startup response using sliding mode fuzzy control is superior to the response using PID and PI control, while the load transient response shows no obvious advantage. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Proportional-Integral-Derivative (PID) control is a traditional linear control method used in many applications. Linear PID controllers for dc–dc converters are usually designed by classical frequency response techniques applied to the small-signal models for converters [1]. A Bode plot is adjusted in the design to obtain the desired loop gain, crossover frequency and phase margin. Alternatively, the transient response can be tuned using root locus type approaches [2]. The stability of the system is guaranteed by an adequate phase margin. PID control is typically designed for one nominal operating point, but a dc–dc converter’s small-signal model changes with variations in the operating point [3]. For a boost converter, both poles and a right-half plane zero are dependent on the duty cycle, so the Bode plots can exhibit significant variation. Therefore, a PID controller may not respond well to significant changes in operating points. Many nonlinear controllers are applied to boost converters to solve this problem. Among them are sliding mode controllers and fuzzy controllers [4,5]. Sliding mode control is a powerful method that is able to yield a very robust closed-loop system under plant uncertainties and external disturbances. In theory,

∗ Corresponding author. Tel.: +1 815 753 1350; fax: +1 815 753 3702. E-mail addresses: [email protected] (L. Guo), [email protected] (J.Y. Hung), [email protected] (R.M. Nelms). 0378-7796/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2010.07.018

the system can be entirely independent of effects due to modeling uncertainties, parameter fluctuations and disturbances [6–10]. dc–dc converters are inherently variable structured because of the switching action. Therefore, variable structure control with sliding mode is a suitable control solution for dc–dc converters. However, several disadvantages exist for variable structure control with sliding mode. An assumption for sliding mode control is that the control can be switched from one value to another infinitely fast. In practice, it is impossible to change the control infinitely fast because of the time delay for control computations and physical limitations of switching devices. As a result, the duty cycle oscillates in steady state, which induces oscillation in the output voltage [11]. With some implementations, the switching frequency is not constant [12]. These practical issues prevent variable structure control from being extensively applied to dc–dc converters. Fuzzy control has also been applied to control dc–dc converters. Fuzzy logic controller has recently been implemented as embedded controllers for robotics [13] and renewable energy systems [14]. Motor drive problems have been solved using fuzzy principles [15–17]. Fuzzy controllers are well suited to nonlinear time-variant systems and do not need an exact mathematical model for the system being controlled. They are usually designed based on expert knowledge of the converters. However, because human heuristic knowledge is used in the design of fuzzy controllers, there are few tools for the design and analysis of fuzzy controllers. In the absence of expert understanding, extensive trial and error tuning

100

L. Guo et al. / Electric Power Systems Research 81 (2011) 99–106

is required. A more systematic approach for designing and tuning fuzzy control is desirable. A sliding mode fuzzy controller is applied to control a boost converter in this paper. The sliding mode fuzzy controller combines the advantage of both fuzzy controllers and sliding mode controllers. The output from the sliding mode fuzzy controller is the duty cycle directly; therefore, a constant switching frequency is achieved. Since sliding mode fuzzy controllers can be designed systematically based on the principles of sliding mode control, the amount of time needed for tuning is significantly reduced compared to a regular fuzzy controller and the system’s response can be predicted. Oscillation in steady state is eliminated by incorporating a boundary layer into the rule base of the fuzzy controller. A sliding mode fuzzy controller was implemented on a TI TMS320F2812 DSP for a prototype boost converter. In this paper, PID control and sliding mode fuzzy control are compared in the aspect of design and experimental results. In Section 2, a sliding mode fuzzy controller is designed for the boost converter. Section 3 describes the linear PID and PI control design methods used with the boost converter. Experimental results using the two different control methods are reported and compared in Section 4. 2. Design of sliding mode fuzzy controller for dc–dc converters The proposed design and tuning method is explained with respect to the phase plane defined by error e of the output volt˙ The phase plane is divided into two age and change of error e. semi-planes by means of a switching line. Positive and negative control outputs are generated respectively within the semi-planes. Magnitude of the control outputs is decided by the distance of the state vector from the switching line. Design methods used for variable structure control provide guidance for design and tuning. Moreover, the use of variable structure control makes the system more robust against model uncertainties, parameter fluctuations and external disturbances. There are five steps involved to design a fuzzy controller using variable structure approach: (1) a switching function that represents a desired system dynamics is first designed, (2) from the switching function, inputs to the fuzzy controller and their scaling factors can be determined, (3) a rule base is designed according to the switching function, (4) inference mechanism and (5) defuzzification method. In this section, the five steps will be followed to design a sliding mode fuzzy controller for application to a boost converter. 2.1. Switching function ˙ is first designed to describe the A switching function s(e, e) desired closed-loop dynamics, which is of lower order than the plant model. Since a boost converter’s small-signal model is second order, a first-order switching function is designed, which is shown in (1) and is plotted in state space in Fig. 1. ˙ = e˙ + e( > 0) s(e, e)

(1)

˙ = 0, When the system is in the sliding mode, the function s(e, e) and the dynamics in (1) represent a stable first-order system with a pole at −. In a digital implementation, e˙ is approximated as shown in (2), where e[k] is error of the kth sample of the output voltage and T is the sampling period. e˙ ≈

e[k] − e[k − 1] T

(2)

Fig. 1. Switching function of the sliding mode fuzzy controller for the boost converter.

Substituting (2) into (1) yields the discrete time switching function (3). Note that the discrete time switching function is dependent only upon present and past values of error e. Therefore, the shortened notation s(¯e) is used. s(¯e) =

e[k] − e[k − 1] + e[k] T

(3)

2.2. Inputs and their scaling factors From the switching function in (3), it is determined that the fuzzy controller has two inputs. The first input is the error in the output voltage given by (4), where ADC[k] is the converted digital value of the kth sample of the output voltage and Ref is the digital value corresponding to the desired output voltage. The second input is the difference between successive errors and is given by (5). The two inputs are multiplied by the scaling factors g0 and g1 , respectively, and then fed into the fuzzy controller. e[k] = Ref − ADC[k]

(4)

ce[k] = e[k] − e[k − 1]

(5)

s(¯e) =

ce[k] + e[k] T

(6)

The discrete time switching function in (3) is rewritten using the two inputs e[k] and ce[k], which is shown in (6). The two input scaling factors g0 and g1 have a significant impact on the controller’s performance, and usually requires extensive tuning when designing a fuzzy controller by trial and error. By using variable structure approach, g0 and g1 can be directly determined from the switching function in (6). The scaling factor g0 is determined by the value of the coefficient of e[k] in (6), which is equal to . The scaling factor g1 is determined by the value of the coefficient of ce[k] in (6), which is equal to 1/T. After scaling by , the gains g0 and g1 are given by: g0 = 1 g1 =

1 T

(7) (8)

Each universe of discourse is divided into fuzzy subsets. The variables e (e[k]) and ce (ce[k]) are the membership degrees assigned to each fuzzy subset to quantify the certainty that the input can be classified linguistically into the corresponding fuzzy subsets.

L. Guo et al. / Electric Power Systems Research 81 (2011) 99–106

101

Table 1 7 × 7 rule base of the sliding model fuzzy controller. Change of duty cycle ci

Error (e[k])

Change in error (ce[k])

PB PM PS Z NS NM NB

NB

NM

NS

Z

PS

PM

PB

Z PS PM PM PB PB PB

NS Z PS PM PM PM PB

NM NS Z PS PS PM PB

NM NM NS Z PS PM PM

NB NM NS NS Z PS PM

NB NM NM NM NS Z PS

NB NB NB NM NM NS Z

2.3. Rule base In an ordinary variable structure control with sliding mode, the switching line divides the state space into two semi-planes, as is shown in Fig. 1. Within the semi-planes positive and negative control outputs are applied to move the state vectors towards the ˙ = 0. A fuzzy rule base can be derived based switching line s(e, e) on the principle of variable structure control. The variable ci is the change of the duty cycle in the rule table. The relationship between ci and the discrete time switching function s(¯e) is shown in Fig. 2. The sign of ci is determined by the sign of the switching function s(¯e). ci is negative when s(¯e) > 0, and positive when s(¯e) < 0. The magnitude of ci increases as the distance between the actual state and the switching line s(¯e) = 0 increases. ±L defines the threshold for entering the boundary layer. Outside the boundary layer, the control has a relay characteristic, and within the layer, the control is a high-gain linear control. A small 7 × 7 rule base for the fuzzy controller is shown in Table 1 for illustration purposes. In the table, N stands for negative, P stands for positive, and Z represents zero. B means big, M means medium and S stands for small. For example, NB means negative big. The control surface generated by the rule base in Table 1 is shown in Fig. 3. With inputs e[k] and ce[k] scaled by the scaling factors g0 = 1 and g1 = 1/T respectively, the diagonal line from the upper left corner to the lower right corner of the rule table represents the switching line s(¯e) = 0 in (6). The rule base is designed with respect to the normalized phase plane. ci is negative above the switching line and positive below it. ci is zero on the switching line. |ci | increases as the distance between the actual state and the switching line s(¯e) increases. |ci | should increase as the distance between the actual state and the diagonal line from the upper right corner to the lower left corner of the rule table (the line perpendicular to the switch-

ing line) grows for the following reasons: (1) discontinuities at the boundaries can be reduced, and (2) the central domain of the phase plane can be arrived at quickly. The maximum value of ci with its respective sign is given to ci when |s(¯e)| > L. This forms a boundary layer for the switching line to avoid drastic changes of the control variable and chattering. Traditionally, the rule table of a fuzzy controller is often designed by in-depth knowledge of the plant. It is then tuned using trial and error method. Extensive tuning requires a significant amount of time. On the other hand, the proposed design method determines the rule base of a fuzzy controller based on the principle of variable structure control. The rule base is tuned by varying the function between ci and s(¯e) as shown in Fig. 2. The width of the boundary layer ±L is varied. When the width of the boundary layer increases, the linear gain inside of the boundary layer decreases; and vice versa. The change of the duty cycle ci in the rule table is tuned according to the change of the boundary layer. To reduce chattering in steady state, the width of the boundary layer is increased to reduce the linear gain, this may increase the settling time and transient error, but decrease chattering. On the other hand, the settling time and transient error can be decreased by decreasing the boundary layer and increasing the linear gain. By this heuristic, the sliding mode fuzzy controller is tuned. In comparison, a conventional fuzzy controller is mainly tuned using trial and error. Based on our past experiences with fuzzy control, an acceptable response for a dc–dc converter required roughly 160 man-hours of trial-and-error testing and readjustments. In contrast, the proposed sliding fuzzy controller produced acceptable responses after 40 man-hours of design. Time measurements were not scientifically conducted, but we believe these preliminary anecdotal experiences are worthy of report. The inference mechanism and defuzzification methods remain the same as in previously published works [18,19].

Fig. 2. Function between ci and s(¯e).

Fig. 3. Control surface generated by a 7 × 7 rule table in Table 1.

102

L. Guo et al. / Electric Power Systems Research 81 (2011) 99–106

Table 2 Circuit parameters of the prototype boost converter. Parameter

Value

Units

Filter capacitance, C Filter inductance, L Load resistance, R ESR of capacitor, RC ESR of inductor, RL

1056 250 25 30 10

␮F ␮H  m m

3. Design of PID controller for a boost converter Linear controllers for dc–dc converters are often designed based on mathematical models. To achieve a certain performance objective, an accurate model is essential. A number of ac equivalent circuit modeling techniques have appeared in the literature, including circuit averaging, averaged switch modeling, the current injected approach, and the state-space averaging method [20]. Among these methods, the state-space averaged modeling is most widely used to model dc–dc converters. The control-to-output small-signal transfer function of a boost converter, obtained using standard state-space averaging techniques, is shown in (9). In this equation, D is the nominal duty cycle, Le = L/(1 − D)2 , and D0 = 1 − D.

vˆ o (s) ˆ d(s)

=

Vo (1 − sLe /R)(sRC C + RC /R + 1) D0 Le C s2 + b1 s + b2

(9)

b2 =

(RL /D02 ) + (RC /D0 ) Le (RL /D02 ) + (RC /D0 ) RLe C

ˆ d(s)

1 + RC

+

1 Le C

The transfer function (9) is a second order, low-pass filter with two zeros. The low-pass filter’s cut off frequency is given by (10). The zero in the left half plane is shown in (11), and the zero in the right-half plane is shown in (12). 1−D ωc = √ LC ωzl = −

By fitting the experimental frequency response data using MATLAB® , a transfer function for the boost converter was constructed as shown in (13). The measured transfer function has two zeros at −5.961 × 104 and 1.468 × 104 rad/s, and two complex conjugate poles at −412.6 ± j610 rad/s.

vˆ o (s)

where b1 =

Fig. 4. Measured and theoretical frequency responses of the boost converter.

(10)

1 + RC /R RC C

ωzr = (1 − D)2

R L

(11) (12)

The cutoff frequency ωc and right-half plane zero ωzr are functions of nominal duty cycle D. In a closed-loop voltage-control system, the filter element will change as the duty cycle changes, which means the transfer function will change accordingly. The boost converter under feedback control is a nonlinear function of the duty cycle [3], which makes controller design for the boost converter much more challenging than that for the buck converter from the viewpoint of stability and bandwidth. For the experimental boost converter utilized in this effort, the input voltage Vin = 5 V, the output voltage Vo = 12 V, and the nominal duty cycle D = 0.58. Circuit parameters of the prototype boost converter are listed in Table 2. There is a clear discrepancy between the theoretical model and the measured frequency response as can be seen in Fig. 4. Part of the discrepancy is because there is more damping in the actual plant than in the theoretical model. The circuit elements including the inductor, capacitor and the switching devices in a boost converter are not ideal. In addition, the nonlinear property of the boost converter’s small-signal model may also cause the discrepancy. Effects of the 20 kHz switching frequency also contribute to uncertainty in the high frequency response.

=

−5.6956 × 10−3 s2 − 2.5589 × 102 s + 4.9831 × 106 s2 + 8.2525 × 102 s + 5.4241 × 105

(13)

Both PID and PI controllers were designed for the boost converters for operation during a start up transient and steady state, respectively. The derivative term in the PID controller is susceptible to noise and measurement error of the system, which can cause oscillation in the duty cycle and output voltage during steadystate conditions. However, during a transient, the derivative term is needed to reduce the settling time by predicting the changes in error. In this implementation, the PID controller is employed during transient conditions, and the PI controller is utilized under steady-state conditions [18]. The PID and PI controllers were designed based on the measured small-signal model of the boost converter in (13) using frequency response techniques. One zero of the PID controller was placed at 260 rad/s, and the other zero was placed at 2600 rad/s. The transfer function of the PID controller is shown in (14). The Bode plot of the PID-compensated boost converter is shown in Fig. 5(a). The gain crossover frequency of the PID-compensated system is approximately 290 Hz, and the phase margin is 50◦ . Gc (s) = 0.567 +

134.13 + 1.98 × 10−4 s s

(14)

For the PI controller, a pole was placed at the origin and a zero was placed at 600 rad/s. The transfer function of the PI controller is shown in (15). The Bode plot of the PI-controller-compensated system is shown in Fig. 5(b). The gain crossover frequency of the PI-compensated system is approximately 160 Hz, and the phase margin is 26.3◦ . Gc (s) = 0.1667 +

100 s

(15)

4. Experimental results The sliding mode fuzzy controller and PID controller have been implemented and evaluated using a Texas Instruments (TI) eZdsp F2812. The eZdsp F2812 is a stand-alone evaluation module with a TMS320F2812 Digital Signal Processor (DSP), which is a 32-bit fixed point DSP controller with on-board flash memory. The CPU

L. Guo et al. / Electric Power Systems Research 81 (2011) 99–106

103

Fig. 5. Frequency responses of linearly compensated boost converter. (a) With PID controller and (b) with PI controller.

operates at 150 MHz. The TMS320F2812 supports peripherals used for embedded control applications, such as event manager modules and a dual 12-bit, 16 channel ADC. The sampling and switching frequency of the sliding mode fuzzy controller and PID controller was 150 kHz. Since the clock frequency of the DSP is 150 MHz, in order to obtain 10 bit resolution of the PWM signal, the switching frequency is chosen to be 150 kHz, and the sampling frequency is chosen to be the same as the switching frequency. Experimental results of the boost converter using the sliding mode fuzzy control and PID/PI control are presented in this section. Start up transient response with input voltage variation from 4 to 7 V was evaluated. Load transient response for 100% load increase (from 0.24 to 0.48 A) and 50% load decrease (from 0.48 to 0.24 A) were also evaluated for various input voltages in the range from 4 to 7 V. 4.1. Experimental results of the boost converter using sliding mode fuzzy control The start up transient response using the sliding mode fuzzy control is shown in Fig. 6(a). The settling time is about 10 ms with very little overshoot at the nominal input voltage of 5 V. As the input voltage increased from 5 to 7 V, the settling time remained at about 10 ms.

Fig. 6. Boost converter performance under sliding mode fuzzy control. (a) Startup (2 V/div, 5 ms/div), (b) load decrease: 50% (200 mV/div, 2 ms/div), (c) load increase: 100% (200 mV/div, 2 ms/div).

104

L. Guo et al. / Electric Power Systems Research 81 (2011) 99–106

The load transient response of the boost converter using the sliding mode fuzzy control is shown in Fig. 6(b) and (c). When the load decreased 50% (from 0.48 to 0.24 A), as shown in Fig. 6(b), the settling time was about 10 ms at nominal input voltage of 5 V. The maximum transient error was about 400 mV. The load transient response when the load increased 100% (from 0.24 to 0.48 A) is shown in Fig. 6(c). The settling time was about 10 ms and the maximum transient error was about 400 mV at nominal input voltage. When the input voltage increased from 4 to 7 V, the settling time decreased and the maximum transient error decreased in Fig. 6(b) and (c). Transient responses in Fig. 6(a)–(c) indicate that the experimental result’s settling time and overshoot at nominal input voltage match the desired dynamics represented by the switching function designed for the boost converter. A settling time of 10 ms is achieved. The output voltage was stable in steady state. 4.2. Experimental results of boost converter using PID and PI control The start up transient response using the PID/PI control is shown in Fig. 7(a). The settling time at the nominal input voltage of 5 V was about 25 ms with 8% overshoot. Both the settling time and overshoot decreased as the input voltage increased from 4 to 7 V. The load transient response of the boost converter using PID/PI control is shown in Fig. 7(b) and (c). When the load decreased 50% from 0.48 to 0.24 A as shown in Fig. 7(b), the settling time was 10 ms with 240 mV maximum transient error at a nominal input voltage of 5 V. The maximum transient error decreased when the input voltage increased to 6 and 7 V. When the input voltage was reduced to 4 V, there was oscillation in the output voltage. When the load increased 100% (from 0.24 to 0.48 A) as shown in Fig. 7(c), the settling time was 13 ms with 210 mV maximum transient error at a nominal input voltage of 5 V. The response showed underdamped behavior. When the input voltage increased to 6 and 7 V, the settling time decreased and the maximum transient error decreased. When the input voltage was 4 V, there was oscillation in the output voltage. 4.3. Comparison of experimental results of the boost converter using sliding mode fuzzy controller and using linear PID and PI controller By comparing the startup transient response of the boost converter in Fig. 6(a) obtained using sliding mode fuzzy controller with Fig. 7(a) obtained using PID/PI controller, it can be observed that the settling time using sliding mode fuzzy control at nominal input voltage of 5 V was only 10 ms, which was 15 ms less than that using PID/PI control. There was very little overshoot at nominal input voltage using sliding mode fuzzy control, while there was an 8% overshoot with PID/PI control. In addition, the startup transient response of the boost converter using sliding mode fuzzy control varies less than that using PID/PI control when the input voltage changes from 4 to 7 V. A comparison between the load transient response in Fig. 6(b) obtained using sliding mode fuzzy control and Fig. 7(b) obtained using PID/PI control when the load decreased 50% (from 0.48 to 0.24 A) indicates that both control methods obtained the same settling time. The maximum transient error using PID/PI control was lower than that using sliding mode fuzzy control. When the input voltage was reduced to 4 V, the load transient response oscillated using PID/PI control. With sliding mode fuzzy control, the load transient response remained stable when the input voltage changed from 4 to 7 V. The settling time decreased from 16 to 10 ms when the input voltage increased from 4 to 7 V.

Fig. 7. Boost converter performance under PID/PI control. (a) Startup (2 V/div, 5 ms/div), (b) load decrease: 50% (200 mV/div, 2 ms/div), (c) load increase: 100% (200 mV/div, 5 ms/div).

L. Guo et al. / Electric Power Systems Research 81 (2011) 99–106

105

Table 3 Comparison of sliding mode fuzzy control vs linear PID and PI control for boost converter. Performance specification Startup

Load change

Settling time (ms) Overshoot (%) Decrease Increase

Settling time (ms) Peak error (mV) Settling time (ms) Peak error (mV)

A comparison between the load transient response in Fig. 6(c) obtained using sliding mode fuzzy control and Fig. 7(c) obtained using PID/PI control when the load increased 50% (from 0.24 to 0.48 A) indicates that the settling time using sliding mode fuzzy control at nominal input voltage of 5 V was 10 ms, while the settling time using PID and PI control was 13 ms. The maximum transient error using PID/PI control was 210 mV, which is 190 mV less than that using sliding mode fuzzy control. By using sliding mode fuzzy control, the load transient response with load increase varied less when the input voltage changed from 4 to 7 V. Although the maximum transient error was smaller using PID and PI control, the output voltage was underdamped during load transient. Furthermore, the output voltage oscillated during load increase when the input voltage was 4 V, while the output voltage did not oscillate using sliding mode fuzzy control during load increase. Table 3 compares the performance of sliding mode fuzzy control and PID/PI control for the boost converter at the nominal input voltage of 5 V. Both start up transient response and load transient response are compared. The sliding mode fuzzy controller is able to achieve faster transient response with very little overshoot during startup, more stable load transient response with changing input voltage and less dependence on the operating point. Experimental results show that sliding model fuzzy controllers are more robust against input voltage and load variations than linear PID and PI controllers. The boost converter’s small-signal model is a nonlinear function of the operating point. When the operating point varies, both the shape and the position of Bode plot of the boost converter’s small-signal model changes. Therefore, the linear PID and PI controllers is not able to respond well to large signal variations such as the startup response. 5. Conclusion A sliding mode fuzzy controller has been designed and implemented to control a boost converter. The rule base and the scaling factors are derived from the switching functions. Besides sharing the advantages of sliding mode control and fuzzy control, sliding mode fuzzy control has advantages of its own that are appealing to digital control design and implementation. Oscillation in the duty cycle during steady state is eliminated by including a boundary layer into the rule base. In addition, the controller’s output is duty cycle directly; thus, a constant switching frequency can be maintained. The sliding mode fuzzy controller can be designed systematically; therefore, the amount of time needed for tuning is significantly reduced. The well-known sliding mode concept of continuous approximation in a boundary layer is also presented in the form of a fuzzy rule table. Based on our past experiences with fuzzy control, an acceptable response for a dc–dc converter required roughly 160 man-hours of trial-and-error testing and readjustments. In contrast, the proposed sliding fuzzy controller produced acceptable responses after 40 man-hours of design. The sliding mode fuzzy controllers was implemented as a digital controller using a TMS320F2812 DSP for the prototype boost converter. Experimental results for the boost converter using sliding mode fuzzy control and linear PID/PI control were evaluated and compared. The comparison indicates that the performance of

Sliding mode fuzzy control

PID and PI control

10 0 10 400 10 400

25 8 10 240 13 210

sliding mode fuzzy control is superior to the performance of PID/PI control. The sliding mode fuzzy controller is able to achieve faster transient response with very little overshoot during startup, more stable steady-state response and is more robust against operating point changes, parameter fluctuations and external disturbances than PID and PI controller. Desired transient response that matches the switching function is achieved. The sliding mode fuzzy controller has an improvement in robustness under the disturbance of input voltage and load resistance variations in comparison to PID/PI controllers. Experimental results show the reliability of the system to operate successfully in the presence of uncertainties. Acknowledgments This work was supported by the Center for Space Power and Advanced Electronics with funds from NASA grant NCC3-511, Auburn University, and the Center’s industrial partners. References [1] A. Prodic, D. Maksimovic, Design of a digital PID regulator based on look-up tables for control of high-frequency dc–dc converters, in: Proceedings of IEEE Workshop on Computers in Power Electronics, 2002, pp. 18–22. [2] Y. Duan, H. Jin, Digital controller design for switchmode power converters, in: Proceedings of 14th Annual Applied Power Electronics Conference, 1999, pp. 967–973. [3] R.P. Severns, G. Bloom, Modern DC-To-DC Switchmode Power Converter Circuits, Van Nostrand Reinhold, 1985. [4] S. Pinto, J. Silva, Sliding mode direct control of matrix converters, IET Electric Power Applications 1 (2007) 439–448. [5] P. Mattavelli, L. Rossetto, G. Spiazzi, P. Tenti, General-purpose fuzzy controller for dc–dc converters, IEEE Transactions on Power Electronics 12 (1997) 79–86. [6] V. Utkin, J. Guldner, J.X. Shi, Sliding Mode Control in Electromechanical Systems, Taylor and Francis, 1999. [7] V. Utkin, Sliding Modes in Control Optimization, Springer-Verlag, 1992. [8] J.Y. Hung, W.B. Gao, J.C. Hung, Variable structure control: a survey, IEEE Transactions on Industrial Electronics 40 (1993) 2–22. [9] A.J. Koshkouei, K.J. Burnham, A.S.I. Zinober, Dynamic sliding mode control design, IEE Proceedings of Control Theory and Applications 152 (2005) 392–396. [10] X. Yu, O. Kaynak, Sliding-mode control with soft computing: a survey, IEEE Transactions on Industrial Electronics 56 (2009) 3275–3285. [11] A. Sahbani, K.B. Saad, M. Benrejeb, Chattering phenomenon suppression of buck boost DC–DC converter with fuzzy sliding mode control, International Journal of Electrical and Electronics Engineering 2 (1) (2009). [12] D.C.E.M. Navarro-Lopez, C. Castro, Design of practical sliding-mode controllers with constant switching frequency for power converters, Electric Power Systems Research 79 (2009) 796–802. [13] S. Sanchez-Solano, A.J. Cabrera, I. Baturone, F.J. Moreno-Velo, M. Brox, FPGA implementation of embedded fuzzy controllers for robotic applications, IEEE Transactions on Industrial Electronics 54 (2007) 1937–1945. [14] S. Chakraborty, M.D. Weiss, M.G. Simoes, Distributed intelligent energy management system for a single-phase high-frequency ac microgrid, IEEE Transactions on Industrial Electronics 54 (2007) 97–109. [15] R.-J. Wai, K.-H. Su, Adaptive enhanced fuzzy sliding-mode control for electrical servo drive, IEEE Transactions on Industrial Electronics 53 (2006) 569–580. [16] Y.-S. Kung, C.-C. Huang, M.-H. Tsai, FPGA realization of an adaptive fuzzy controller for PMLSM drive, IEEE Transactions on Industrial Electronics 56 (2009) 2923–2932. [17] A. Luo, C. Tang, Z. Shuai, J. Tang, X.Y. Xu, D. Chen, Fuzzy-PI-based direct-outputvoltage control strategy for the STATCOM used in utility distribution systems, IEEE Transactions on Industrial Electronics 56 (2009) 2401–2411. [18] L. Guo, J.Y. Hung, R.M. Nelms, Evaluation of DSP-based PID and fuzzy controllers for DC–DC converters, IEEE Transactions on Industrial Electronics 56 (2009) 2237–2248. [19] L. Guo, R.M. Nelms, J.Y. Hung, Comparative evaluation of linear PID and fuzzy control for a boost converter, in: Proceedings of 31st Annual Conference of the IEEE Industrial Electronics Society, 2005.

106

L. Guo et al. / Electric Power Systems Research 81 (2011) 99–106

[20] R.W. Erickson, D. Maksimovic, Fundamentals of Power Electronics, Kluwer Academic Publishers, 2001. Liping Guo received the B.E. degree in Automatic Control from Beijing Institute of Technology, Beijing, China in 1997, the M.S. and Ph.D. degrees in Electrical & Computer Engineering from Auburn University, AL, USA in 2001 and 2006, respectively. She is currently an Assistant Professor in the Electrical Engineering Technology Program in the Department of Technology at the Northern Illinois University. Her research interests are mainly in the area of power electronics, alternative energy, embedded systems and control, which include design, modeling and control of power converters. Dr. Guo is a member of the IEEE Industrial Electronics Society and a member of the honor society of Phi Kappa Phi. John Y. Hung received the B.S. degree from the University of Tennessee, Knoxville, the M.S.E. degree from Princeton University, Princeton, NJ, and the Ph.D. degree from the University of Illinois, Urbana-Champaign, in 1979, 1981, and 1989, respectively, all in electrical engineering. From 1981 to 1985, he was with Johnson Controls, Milwaukee, WI, developing microprocessor-based controllers for commercial heating, ventilation, and air conditioning systems. From 1985 to 1989 he was a consultant engineer with Poly-Analytics, Inc. In 1989, he joined Auburn University, Auburn, AL, where he is currently a Professor of Electrical and Computer Engineering. His

teaching and research interests include nonlinear control systems and signal processing with applications in process control, robotics, electric machinery, and power electronics. Prof. Hung has received several awards for his teaching and research, including a Best Paper Award for the IEEE Transactions on Industrial Electronics, and two U.S. patents in the area of control systems. He served as an Associate Editor of the IEEE Transactions on Control System Technology (1997, 1998), and the IEEE Transactions on Industrial Electronics (1996–2005). He was the General Chair for the 34th Annual Conference of the IEEE Industrial Electronics Society (IECON-2008) General co-Chair for the 2010 IEEE International Symposium on Industrial Electronics (ISIE2010), and Technical Program co-Chair for the 36th Annual Conference of the IEEE Industrial Electronics Society (IECON-2010). He was Treasurer of the IEEE Industrial Electronics Society (2002–2007) and is currently the IES Vice-President for Conference Activities. R. M. Nelms received the B.E.E. and M.S. degrees in electrical engineering from Auburn University, AL in 1980 and 1982, respectively. He received the Ph.D. degree in electrical engineering from Virginia Polytechnic Institute and State University, Blacksburg, VA in 1987. He is presently a Professor and Chair of the Department of Electrical and Computer Engineering at Auburn University. His research interests are in power electronics, power systems, and electric machinery. He is a registered professional engineer in Alabama.