Linear Phase Lead Compensation Repetitive Control of ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 4, APRIL 2008

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Linear Phase Lead Compensation Repetitive Control of a CVCF PWM Inverter Bin Zhang, Member, IEEE, Danwei Wang, Senior Member, IEEE, Keliang Zhou, Member, IEEE, and Yigang Wang, Student Member, IEEE

Abstract—This paper presents a simple and efficient linear phase lead compensation repetitive control scheme for engineers to develop high-performance power converter systems. The linear phase lead compensation helps a repetitive controller to achieve faster convergence rate, higher tracking accuracy, and wider stability region. In the proposed scheme, the phase lead compensation repetitive controller is plugged into generic statefeedback-controlled converter systems. Its comprehensive synthesis, which involves principle, analysis, design, modeling, implementation, and experiments, is systematically and completely presented in great detail. A complete series of experiments is successfully carried out to verify the solution. Index Terms—Constant-voltage constant-frequency (CVCF) pulsewidth-modulation (PWM) inverter, phase lead compensation, repetitive control (RC), state feedback control.

Furthermore, a complete and systematic solution to synthesize a high-performance RC for CVCF PWM converters needs to be developed. In this paper, an RC scheme with linear phase lead compensation is proposed for CVCF PWM inverter systems to achieve faster convergence rate, lower THD and tracking error, and wider stability region. Its comprehensive synthesis, which involves principle, analysis, design, modeling, implementation, and experiments, is systematically presented. A series of experiments have been successfully carried out to testify the proposed solution. II. I NVERTER M ODELING AND C ONTROL D ESIGN A. Modeling CVCF PWM Inverter

I. I NTRODUCTION

I

N MANY ac power-conditioning systems, such as uninterruptible power supplies (UPSs) and other industrial facilities, constant-voltage constant-frequency (CVCF) pulsewidth-modulation (PWM) dc–ac converters are widely used. Due to nonlinear loads and parameter uncertainties, output voltage often suffers from periodic tracking errors, which are major sources of total harmonic distortion (THD) in ac power systems. Repetitive control (RC) [1], based on the internal model principle [2], is an effective tool to exactly track periodic reference signals and to eliminate periodic errors. Nowadays, RC has been widely studied from various aspects [3]–[9], and its applications can be found in robot manipulator [10], hard disk drive [11], [12] UPS [13], PWM converters [7], [14]–[21], etc. When RC is applied to PWM converters, it can significantly reduce the output THD in the presence of uncertainties and disturbances [8], [21]. Although some promising results are available, it remains to be well addressed on how to effectively improve the tracking accuracy and convergence rate.

Manuscript received September 29, 2005; revised December 5, 2007. B. Zhang was with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798. He is now with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA (e-mail: [email protected]). D. Wang and Y. Wang are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: [email protected]). K. Zhou is with the School of Electrical Engineering, Southeast University, Nanjing 210096, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2008.917105

Fig. 1 shows a single-phase CVCF PWM inverter controlled by a repetitive controller, where vc is the output voltage; io is the output current; iL is the inductor current; iC is the capacitor current; E is the dc bus voltage; Ln , Cn , Rn , and En are the nominal values of inductor L, capacitor C, load R, and dc voltage E, respectively; Lr , Cr , and Rr are the rectifier loads; and vin is the input PWM voltage with the following definition: E, if S2 and S3 are on, S1 and S4 are off vin = (1) −E, if S1 and S4 are on, S2 and S3 are off. The dynamics of this single-phase inverter can be described as follows [22]: X˙ = AX + BU (2) Y = CX + DU 0 1 0 where A = , B= , −1/(Ln Cn ) −1/(C 1/(Ln Cn ) n Rn ) v (t) C = [ 1 0 ], D = 0, X = c , U = vin (t), and Y = vc (t). ic (t) Here, iC (t) is selected as a state, because it is easier to be controlled and a state feedback system with this state has better rejection of load disturbance. A sampled-data form of (2) with a sampling period of T can be written as X(k + 1) = GX(k) + HU (k) (3) Y (k) = CX(k) vc (k) where X(k) = , U (k) = vin (k), Y (k) = vc (k), G = ic (k) g ϕ11 ϕ12 , and H = 1 , with the coefficients therein ϕ21 ϕ22 g2

0278-0046/$25.00 © 2008 IEEE

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Fig. 1. RC inverter system.

being ϕ11 = 1 − (T 2 /(2Ln Cn )), ϕ21 = −(T /(Ln Cn )) + ϕ12 = T − (T 2 /(2Cn Rn )), ϕ22 = (T 2 /(2Ln Cn2 Rn )), 2 1 − (T /(Cn Rn )) − (T /(2Ln Cn )) + (T 2 /(2Cn2 Rn2 )), g1 = T 2 /(2Ln Cn ), g2 = (T /(Ln Cn ))(1 − (T /(2Cn Rn ))). B. Controller Design For the better performance of the RC system, a state feedback controller can be used, and we propose the following controller: u(k) = −KX(k) + g vref (k) vc (k) = [−k1 − k2 ] + g vref (k). ic (k)

Fig. 2. General RC and phase lead compensation RC. (a) General repetitive controller. (b) Phase lead compensation repetitive controller.

(4)

With only the state feedback controller, the state equation of the closed-loop system becomes X(k + 1) =(A−BK)X(k) ϕ11 +g1 k1 ϕ12 + g1 k2 g1 g = X(k)+ v (k). g2 g ref ϕ21 +g2 k1 ϕ22 +g2 k2

(z − (ϕ11 + g1 k1 )) (z − (ϕ22 + g2 k2 )) − (ϕ12 + g1 k2 )(ϕ21 + g2 k1 ) = 0. Then, the poles of the closed-loop system can be arbitrarily assigned by adjusting feedback control gain k1 and k2 . The transfer function of this state feedback control system can be written as m1 z + m 2 z 2 + p1 z + p2

III. L INEAR P HASE L EAD C OMPENSATION RC A. Stability Analysis

The characteristic equation of the closed-loop system is

H(z) =

Due to system modeling uncertainties, unknown time delay, and linear/nonlinear load variation, the inverter system with only the feedback controller cannot always output the desired high-quality voltage. Therefore, a phase lead compensation repetitive controller is to be developed in the sequel.

(5)

where p1 = −(ϕ11 + g1 k1 + ϕ22 + g2 k2 ), p2 = (ϕ11 + g1 k1 )(ϕ22 + g2 k2 ) − (ϕ12 + g1 k2 )(ϕ21 + g2 k1 ), m1 = g1 g, and m2 = (ϕ12 + g1 k2 )g2 g − (ϕ22 + g2 k2 )g1 g.

A general repetitive controller is shown in Fig. 2(a) [10], where kr is the RC gain, Gf (z) is a low-pass filter, E(z) is the tracking error, Ur (z) is the output of the RC, Q(z) is a lowpass filter, and N = fc /f , with f being the reference signal frequency and fc = 1/T being the sampling frequency. The transfer function of the repetitive controller in Fig. 2(a) is Gr (z) = kr

z −N Q(z) Gf (z) 1 − z −N Q(z)

(6)

where Gf (z) is often designed as the inverse of the closed-loop feedback system [4], [10], [17]. Due to various uncertainties and load disturbance in the feedback system, its inverse is often

ZHANG et al.: LINEAR PHASE LEAD COMPENSATION REPETITIVE CONTROL OF A CVCF PWM INVERTER

Fig. 3.

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Plug-in RC system.

not available. In the phase lead compensation RC in Fig. 2(b), a simple Gf (z) is designed as Gf (z) = z m .

(7)

Phase lead compensator z m provides a phase lead θ = m(ω/ωN )180◦ , which reaches m × 180◦ at Nyquist frequency ωN , to compensate the system phase lag, particularly at high frequencies. The delays of the feedback control system can be well compensated by using an appropriate lead step m. The transfer function of this phase lead compensation RC is given as follows: Q(z)z −N +m Gr (z) = kr . 1 − Q(z)z −N

(8)

Remark 1: Equation (7) represents a noncausal operator. However, since N m, the noncausal operator in (7) is merged in the transfer function (8) and becomes implementable. With this phase lead compensation RC being plugged in the feedback control loop G(z) = Gc (z)Gs (z)/(1 + Gc (z)Gs (z)), the structure of the overall system is shown in Fig. 3. The overall transfer function from Yd (z) and D(z) to Y (z) can be derived as follows: 1 − Q(z)z −N (1 − kr z m ) G(z) Y (z) = (9) Yd (z) 1 − Q(z)z −N (1 − kr z m G(z)) 1 − Q(z)z −N 1 Y (z) = . D(z) 1 + Gc (z)Gs (z) 1 − Q(z)z −N [1 − kr z m G(z)] (10) The error for the overall system is derived as follows: 1 − Q(z)z −N (1 − G(z)) E(z) = (Yd (z) − D(z)) . 1 − Q(z)z −N (1 − kr z m G(z)) (11) Then, the overall system holds the stability conditions as follows: 1) The closed-loop feedback system G(z) is stable, and 2) |Q(z) (1 − kr z m G(z))| ≤ 1

∀z = ejω , 0 < ω
0. In practice, a firstorder filter Q(z) = α1 z + α0 + α1 z −1 is generally sufficient [17], [18]. For such a filter, the larger the α0 , the higher the passband. Since Q(z) ≤ 1 (Q(z) → 1 at low frequencies and Q(z) → 0 at high frequencies), a high-frequency tracking error cannot be eliminated. Q(z) makes (14) easier to be satisfied and enhances the robustness of the overall system. Hence, the Q(z) filter brings a tradeoff between the tracking accuracy and robustness. Following the frequency-domain design approach [23], the closed-loop transfer function G(z) can be expressed as G(ejω ) = Ng (ejω ) exp(jθg (ejω )), with Ng (ejω ) and θg (ejω ) being its magnitude characteristics and phase characteristics, respectively. The Q(z) filter can be expressed as Q(ejω ) = Nq (ejω ), with Nq (ejω ) being its magnitude characteristics. The phase characteristics of the Q(z) filter is zero for the filter defined in (15). Then, (14) becomes

jω 1

.

1 − kr Ng (ejω )ej (θg (e )+mω) < Nq (ejω )

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Since kr and Ng (ejω ) are both positive, we have 1 − Nq2 (ejω ) 2 cos θg (ejω ) + mω) + . 0 < kr < 2 jω Ng (ejω ) Nq (e ) kr Ng2 (ejω ) (16) Notice that the first item on the right-hand side of (16) is a nonnegative value due to 0 ≤ Nq (ejω ) ≤ 1. Then, (16) will be satisfied if the following condition holds: 2 cos θg (ejω ) + mω) ∆ m = kupper (17) 0 < kr < Ng (ejω ) m in which 2 cos(θg (ejω ) + mω))/Ng (ejω ) is denoted as kupper . It is clear that the range of the kr determined by (17) is smaller and more conservative than that determined by (16). Condition (17) requires

θg (ejω ) + mω < 90◦ . (18)

It is noticed that, at the frequency where the phase angle crosses over −90◦ or 90◦ , the value of cos(θg (ejω ) + 2ω) is zero; hence, no positive gain kr > 0 can be found to meet the requirement of (12). To solve this problem, (18) is modified as follows:

θg (ejω ) + mω < 90◦ − (19) where is a positive constant for a more stable margin in engineering design. It can be seen that, if condition (19) is satisfied, we can always find a kr to satisfy (17). This modification also provides a large robustness margin against modeling uncertainties. Then, by adjusting m to compensate (θg (ejω ) + mω) close to zero, (19) can be held for a much wider frequency band, so that more error harmonics can be eliminated to achieve a higher tracking accuracy. In addition, with phase compensation, a large m can be used, i.e., m helps overall systems to value of kupper stabilize with a large kr , which results in a fast convergence rate. In an extreme case, supposing that the system model is known and zero-phase error tracking control [3] is available, all error harmonics can be suppressed to obtain zero tracking error, and kr can be the largest value as follows: kr =

min

0≤ω≤ωN

2 . Ng (ejω )

In practice, due to load disturbances (e.g., nonlinear loads, load changes) or parameter uncertainties, an exact inverse of the model is often difficult, if possible at all, to obtain. The linear phase lead compensator provides a simple and efficient solution to compensate phase lag. C. Robustness Taking into account the model uncertainties ∆(z), which are bounded by ∆(z) ≤ δ, the relationship between the true system Gt (z) and the nominal model G(z) can be written as Gt (z) = G(z) (1 + ∆(z)) .

Fig. 4.

Experimental setup.

With this consideration, (16) is written as 0 < kr < k¯

(20)

with k¯ =

1−Nq2 (ejω ) 2 cos θg (ejω )+mω) + . Ng (ejω )(1+δ) Nq2 (ejω ) kr Ng2 (ejω )(1+δ)2

Accordingly, the range of kr that guarantees the stability of the system can be modified as m kupper 2 cos θg (ejω ) + mω) = . (21) 0 < kr < Ng (ejω )(1 + δ) 1+δ It is clear that the larger the δ, the smaller the range of kr . If ∆(z) contains an unknown time delay, it can be compensated by lead step m as well. Notice that (17) contains two parameters: m and kr , whereas (18) contains only one parameter: m. This suggests that parameter m can be chosen based on (18). Then, kr can be determined according to (17). This facilitates the design of m and kr [23]. IV. E XPERIMENT As shown in Fig. 4, a set of dSPACE control kit DS1102 is used to control an insulated-gate bipolar transistor PWM inverter. The output waveforms are recorded by the oscilloscope and dSPACE ControlDesk. A. System Setup The parameters of the inverter system are listed in Table I. With the aforementioned parameters, the closed-loop nominal transfer function G(z) with a linear load R = 22 Ω can be derived as follows: G(z) =

0.525z + 0.479 . z 2 − 0.4564z + 0.4613

(22)


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TABLE I PARAMETERS OF THE INVERTER SYSTEM

Fig. 5.

Trace of poles for R from 0.9 Ω to infinity.

The transfer function (22) will change with the load variation. Fig. 5 shows the trace of poles of the system model when load R changes from 0.9 Ω to infinity. It is clear that, when R < 2 Ω, the poles are located outside the unit circle, and the system is unstable. On the other hand, when load R > 2 Ω up to infinity, the poles are located inside the unit circle, and the system is stable. Hence, the range of load for the overall system stability is [2, ∞)Ω. With model (22), Fig. 6(a) and (b) shows the compensated m for different m’s, respecphase (19) and the curves of kupper tively. Here, the value of is chosen as 15◦ . From the results in Table II, it is clear that m = 2 not only produces a wider stable frequency bandwidth but also guarantees the stability with a much wider range of kr .

Fig. 6. Phase compensation and determination of gain. (a) Phase compensation. (b) Range of kr .

TABLE II FREQUENCY RANGE AND GAIN RANGE FOR STABILITY WITH DIFFERENT m’S

TABLE III THD WITH DIFFERENT kr ’S AND DIFFERENT m’S

B. Experimental Results The THD of the feedback-controlled voltage under rectifier load is 8.03%. It should be noted that the THD contains a small portion of high-frequency harmonics. The harmonics above 1500 Hz contributes only 3.5% of the THD. The tracking error is mainly dominated by harmonics below 1500 Hz. Theoretical analysis in Section III indicates that m = 2 is the optimal value of lead steps for the repetitive controller in our case. In practice, due to various load disturbances and unknown uncertainties, m = 2 is usually insufficient for phase compensation. The optimal value of lead step m should be

determined in the experiments. The Q(z) filter is Q(z) = 0.25z + 0.5 + 0.25z −1 unless stated otherwise. The steady-state response, in terms of the THD of the output voltage, with different kr ’s for different m ∈ {2, 3, 4, 5, 6, 7} is tabulated in Table III. It is clear that the stability range of kr

1600


Fig. 7. Transient response with m = 4 and kr = 1.2. TABLE IV CONVERGENCE TIME AND STEADY ERROR FOR DIFFERENT m’S WITH kr = 1.2

TABLE V CONVERGENCE TIME AND STEADY ERROR FOR DIFFERENT kr ’S WITH m = 5

Fig. 8. Transient responses of two cases with m = 5. (a) kr = 0.2. (b) kr = 2.0.

is different for different m’s. For m ∈ {4, 5, 6}, kr has a much wider stability range, and kr ∈ [0.8, 1.6] yield a very low THD. Fig. 7 shows the transient response for case m = 4 with gain kr = 1.2 under the rectifier load. Table IV shows the transient response, in terms of convergence time and peak error decay for m ∈ {4, 5, 6} with identical kr = 1.2. The convergence rates with the same kr are almost the same. Table V lists the transient responses for different kr ’s with identical m = 5. It indicates that the convergence rate is approximately proportional to kr . Hence, RC with a large kr yields a fast convergence rate. Fig. 8(a) and (b) shows the transient response of two cases with kr = 0.2 and kr = 2.0 under the rectifier load. Note that the time axis of Fig. 8(a) is 1 s, whereas that of Fig. 8(b) is 0.5 s. It is clear that the convergence rate becomes faster for a large gain. From these experimental results, it can be seen that the RC with m ∈ {4, 5, 6} and kr ∈ [0.8, 1.6] yields not only very low

THD but also fast convergence rate. The steady and transient responses of RC inverter with parameters m = 5, kr = 1.2, and Q(z) = 0.25z −1 + 0.5 + 0.25z are illustrated in Fig. 9. The THD of the RC voltage reduces to 0.56%. The results with only the feedback controller show that the tracking error is dominated by harmonics below 1500 Hz. Hence, if the bandwidth of Q(z) is higher than 1500 Hz, the tracking accuracy will not be significantly influenced. To verify this, the convergence rate and THD for different Q(z) filters with m = 5 are investigated, and the results are tabulated in Table VI. The filters used are Q(z) = 0.15z −1 + 0.7 + 0.15z and Q(z) = 0.05z −1 + 0.9 + 0.05z, which are denoted as 0.7 and 0.9, respectively. They have wider passband than Q(z) = 0.25z −1 + 0.5 + 0.25z and are expected to suppress more error harmonics. Compared with Tables III–V, it is clear that the tracking accuracy and convergence rate are almost not influenced by Q(z), and Q(z) = 0.25z −1 + 0.5 + 0.25z brings a wider stability range for kr .


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R EFERENCES

Fig. 9.

RC response. (a) Vc (25 V/div) and io (7.12 A/div). (b) Rectifier load.

TABLE VI CONVERGENCE TIME AND THD WITH VARIOUS Q(z) FILTERS

Although only some experiments under rectifier load are presented, similar results are also obtained under the linear resistor load and no load cases to verify the proposed method. V. C ONCLUSION In this paper, a phase lead compensation RC scheme is proposed for CVCF PWM inverter systems. The experiments show that RC with a well-selected lead step can well compensate the system phase lag, so that more error harmonics can be eliminated to achieve a high tracking accuracy. In addition, phase compensation helps the overall system to be stable with a large gain. The convergence rate is proportional to the gain; hence, a fast convergence rate can be obtained at the same time. A well-designed Q(z) filter, which is mainly used to enhance the robustness of the overall RC system, does not have significant impact on the tracking accuracy and convergence rate. This scheme provides a simple and efficient approach for engineers to design high-performance power converter systems.

[1] T. Haneyoshi, A. Kawamura, and R. G. Hoft, “Waveform compensation of PWM inverter with cyclic fluctuating loads,” in Proc. IEEE Power Electron. Spec. Conf., Blacksburg, VA, Jun. 1987, pp. 745–751. [2] B. A. Francis and W. M. Wonham, “The internal model principle of control theory,” Automatica, vol. 12, no. 5, pp. 457–465, 1976. [3] M. Tomizuka, “Zero phase error tracking algorithm for digital control,” Trans. ASME, J. Dyn. Syst. Meas. Control, vol. 109, no. 2, pp. 65–68, 1987. [4] M. Tomizuka, T. Tsao, and K. Chew, “Analysis and synthesis of discretetime repetitive controllers,” Trans. ASME, J. Dyn. Syst. Meas. Control, vol. 110, pp. 271–280, 1988. [5] H. L. Broberg and R. G. Molyet, “Reduction of repetitive errors in tracking of periodic signals: Theory and application of repetitive control,” in Proc. 1st IEEE Conf. Control Appl., Dayton, OH, Sep. 1992, pp. 1116–1121. [6] M. Sun, Y. Wang, and D. Wang, “Variable-structure repetitive control: A discrete-time strategy,” IEEE Trans. Ind. Electron., vol. 52, no. 2, pp. 610–616, Apr. 2005. [7] R. Costa-Castello, R. Grino, and E. Fossas, “Odd-harmonic digital repetitive control of a single-phase current active filter,” IEEE Trans. Power Electron., vol. 19, no. 4, pp. 1060–1068, Jul. 2004. [8] K. Zhou, K. Low, D. Wang, F. Luo, B. Zhang, and Y. Wang, “Zero-phase odd-harmonic repetitive controller for a single-phase PWM inverter,” IEEE Trans. Power Electron., vol. 21, no. 1, pp. 193–201, Jan. 2006. [9] T. J. Manayathara, T. C. Tsao, J. Bentsman, and D. Ross, “Rejection of unknown periodic load disturbances in continuous steel casting process using learning repetitive control approach,” IEEE Trans. Control Syst. Technol., vol. 4, no. 3, pp. 259–265, May 1996. [10] C. Cosner, G. Anwar, and M. Tomizuka, “Plug in repetitive control for industrial robotic manipulators,” in Proc. IEEE Int. Conf. Robot. Autom., Cincinnati, OH, May 1990, pp. 1970–1975. [11] K. K. Chew and M. Tomizuka, “Digital control of repetitive errors in disk drive systems,” in Proc. Amer. Control Conf., Pittsburgh, PA, Jun. 1989, pp. 540–548. [12] K. K. Chew and M. Tomizuka, “Digital control of repetitive errors in disk drive systems,” IEEE Control Syst. Mag., vol. 10, no. 1, pp. 16–20, Jan. 1990. [13] G. Escobar, P. R. Martinez, J. Leyva-Ramos, and P. Mattavelli, “Repetitive-based controller for a UPS inverter to compensate unbalance and harmonic distortion,” IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 504–510, Feb. 2007. [14] G. Escobar, P. R. Martinez, J. Leyva-Ramos, and P. Mattavelli, “A negative feedback repetitive control scheme for harmonic compensation,” IEEE Trans. Ind. Electron., vol. 53, no. 4, pp. 1383–1386, Jun. 2006. [15] P. Mattavelli and F. Marafao, “Repetitive-based control for selective harmonic compensation in active power filters,” IEEE Trans. Ind. Electron., vol. 51, no. 5, pp. 1018–1024, Oct. 2004. [16] L. Luo, Y. Zhou, J. Xu, and S. Wan, “Parameters self-adjusting fuzzy PI control with repetitive control algorithms for 50 hz on-line UPS controlled by DSP,” in Proc. 30th Annu. Conf. IEEE Ind. Electron. Soc., Busan, Korea, Nov. 2004, pp. 1487–1491. [17] K. Zhou and D. Wang, “Periodic errors elimination in CVCF PWM DC/AC converter systems: Repetitive control approach,” Proc. Inst. Electr. Eng.—Control Theory Applications, vol. 147, no. 6, pp. 694–700, Nov. 2000. [18] K. Zhou and D. Wang, “Digital repetitive learning controller for threephase CVCF PWM inverter,” IEEE Trans. Ind. Electron., vol. 48, no. 4, pp. 820–830, Aug. 2001. [19] B. Zhang, K. Zhou, Y. Ye, and D. Wang, “Design of linear phase lead repetitive control for CVCF PWM DC-AC converters,” in Proc. Amer. Control Conf., Portland, OR, Jun. 2005, pp. 1154–1159. [20] Y. Ye, K. Zhou, B. Zhang, D. Wang, and J. Wang, “High-performance repetitive control of PWM DC-AC converters with real-time phaselead fir filter,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 8, pp. 768–772, Aug. 2006. [21] Y. Ye, B. Zhang, K. Zhou, D. Wang, and Y. Wang, “High-performance cascade-type repetitive controller for CVCF PWM inverter: Analysis and design,” IET Electr. Power Appl., vol. 1, no. 1, pp. 112–118, Jan. 2007. [22] A. Kawamura, T. Haneyoshi, and R. G. Hoft, “Deadbeat controlled PWM inverter with parameter estimation using only voltage sensor,” IEEE Trans. Power Electron., vol. 3, no. 2, pp. 118–125, Apr. 1988. [23] D. Wang and Y. Ye, “Design and experiments of anticipatory learning control: Frequency domain approach,” IEEE/ASME Trans. Mechatronics, vol. 10, no. 3, pp. 305–313, Jun. 2005.

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Bin Zhang (S’04–M’06) received the B.E. and M.S.E. degrees from Nanjing University of Science and Technology, Nanjing, China, in 1993 and 1999, respectively, and the Ph.D. degree from Nanyang Technological University, Singapore, in 2007. Since 2005, he has been a Postdoctoral Researcher with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta. His current research interests are systems and control, iterative/repetitive learning control, intelligent systems, digital signal processing, fault diagnosis and failure prognosis and their applications to robotics, power electronics, and various mechanical systems.

Danwei Wang (S’88–M’89–SM’04) received the B.E. degree from the South China University of Technology, China, in 1982 and the M.S.E. and Ph.D. degrees from the University of Michigan, Ann Arbor, in 1985 and 1989, respectively. Since 1989, he has been with the School of Electrical and Electronic Engineering, Nanyang Technological University (NTU), Singapore, where he is currently an Associate Professor, the Head of the Division of Control and Instrumentation, and a Director of the Centre for Intelligent Machines, NTU. He is an Associate Editor for the International Journal of Humanoid Robotics. He has published many technical articles in the areas of iterative learning control, repetitive control, robust control and adaptive control systems, and manipulator/mobile robot dynamics, path planning, and control. His research interests include robotics, control theory, and applications. Prof. Wang has served as general chairman and technical chairman, and on various positions in international conferences, such as the ICARCVs, IEEE RAM, and ACCV. He is an Associate Editor for the Conference Editorial Board and the IEEE Control Systems Society, and a Deputy Chairman of the IEEE Singapore Robotics and Automation Chapter. He was a recipient of the Alexander von Humboldt Fellowship, Germany.


Keliang Zhou (M’04) received the B.E. degree from the Huazhong University of Science and Technology, Wuhan, China, in 1992, the M.Eng. degree from Wuhan University of Transportation, Wuhan, in 1995, and the Ph.D. degree from Nanyang Technological University, Singapore, in 2002. Since 2006, he has been with the School of Electrical Engineering, Southeast University (SEU), Nanjing, China. He is currently a Professor with the School of Electrical Engineering and the Deputy Director of the Wind Generation Research Center, SEU. He has authored or coauthored more than 40 published technical articles in the relevant areas. His research interests include power electronics and electric machines drives, advanced control theory and its applications, and renewable energy generation.

Yigang Wang (S’04) received the B.E. and M.S.E. degrees from Harbin Institute of Technology, Harbin, China, in 2001 and 2003, respectively. He is currently with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His current research interests are repetitive and learning control and robust, adaptive and multirate filtering and control, with applications to PWM inverters and mechatronic systems.