970 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 3, MAY/JUNE 2012

Transcription

1 970 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 3, MAY/JUNE 2012 Control Method Suitable for Direct-Torque-Control-Based Motor Drive System Satisfying Voltage and Current Limitations Yukinori Inoue, Member, IEEE, Shigeo Morimoto, Member, IEEE, and Masayuki Sanada, Member, IEEE Abstract This paper proposes a control method suitable for limited armature voltage and current in a permanent-magnet synchronous motor drive system based on direct torque control (DTC). First, this paper proposes torque-limiting and fluxweakening controls that are suitable for a DTC-based motor drive system. The proposed method utilizes a mathematical model in a rotating reference frame synchronized to the stator flux linkage. Second, this paper proposes an antiwindup scheme for the torque controller of the DTC system. Windup of the controller degrades the performances of torque-limiting (current-limiting) control and of torque control. Applying the antiwindup results improves the performance of the proposed torque-limiting method in the transient state. This paper presents a DTC-based drive system combined with a speed controller. The proposed system can achieve stable control, and its effectiveness is confirmed experimentally. Index Terms Antiwindup, direct torque control (DTC), permanent-magnet synchronous motor (PMSM), wide-speedrange operation. I. INTRODUCTION DIRECT-TORQUE-CONTROLLED permanent-magnet synchronous motor (PMSM) drive systems have several advantages. For example, an accurate motor model is not required to estimate the torque and the stator flux linkage 1], 2]. In addition, no rotor position sensor is needed because direct torque control (DTC) operates in a stationary reference frame 3], 4]. Optimal controls, such as maximum torque per ampere (MTPA) control and flux-weakening (FW) control, and voltage and current limitations are important for high-performance motor drives 5]. A DTC system can achieve optimal control by providing the reference torque and the reference flux based on the operating conditions. However, in most cases, DTCbased motor drives utilize control laws based on a mathematical Manuscript received August 7, 2011; revised October 31, 2011; accepted December 3, Date of publication March 15, 2012; date of current version May 15, Paper 2011-IDC-435.R1, presented at the 2010 International Power Electronics Conference, Sapporo, Japan, June 21 24, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLI- CATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. The authors are with Osaka Prefecture University, Sakai , Japan ( inoue@eis.osakafu-u.ac.jp; morimoto@eis.osakafu-u.ac.jp; sanada@ eis.osakafu-u.ac.jp). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TIA model in the rotating d q reference frame, which is synchronized to the rotor magnet 6] 8]. Thus, it is necessary to calculate the d- and q-axis currents to determine the relationship between the torque and the flux. In addition, motor parameters, such as the inductance and magnet flux, are required for these controls. A control law based on the mathematical model in the d q frame does not appear to be suitable for DTC and fluxoriented control. It is expected to be possible to derive a simple expression for the control law by using a novel mathematical model. Several studies have investigated the control laws defined in a rotating reference frame that is synchronized with the stator flux linkage 9] 12]. In 9], a control method for unity power factor operation of the rotating-field-type synchronous machine is proposed. In 10], a control method is proposed for the flux and the current component orthogonal to the flux. In 11] and 12], a control method for the flux and the torque is proposed, and torque limiting utilizes the reactive torque, which is calculated by taking the product of the flux and the current. This paper proposes a novel method for calculating the reference torque and the reference flux that are suitable for DTC-based motor drive systems. The proposed method consists of torque limiting that is capable of current limiting and FW control for limiting the voltage. These control laws are derived from mathematical equations in a rotating reference frame that is synchronized to the stator flux linkage. The proposed method for the FW and the torque limiting has several advantages, including simplicity of calculation and insensitivity to parameter variation because it does not require the values of the magnet flux and inductance. This paper also proposes an antiwindup scheme for the torque controller of a DTC system that is based on proportional and integral (PI) control. Windup of the controller generally occurs when the terminal output voltage of the inverter is saturated. Windup degrades the performances of torque-limiting (current-limiting) control and torque control. In the proposed antiwindup scheme, the controller gain is changed according to the degree of voltage saturation, which is detected using the estimated flux linkage. Consequently, the proposed torquelimiting method is confirmed to be valid for both steady and transient states. This paper proposes a DTC-based drive system combined with a speed controller, and the effectiveness of the proposed method is confirmed from experimental results /$ IEEE

2 INOUE et al.: CONTROL METHOD SUITABLE FOR DTC-BASED MOTOR DRIVE SYSTEM 971 Fig. 1. DTC-based PMSM drive system. II. DTC MOTOR DRIVE SYSTEM Fig. 1 shows a block diagram of the direct-torque-controlled PMSM drive system. This system is equipped with a speed controller based on PI control. The DTC system requires appropriate reference values for the torque and the stator flux linkage for high-performance control. The DTC system is based on control of the stator flux linkage, which is estimated using the following equations 1] 4], 6], 7]: { ˆψα = (v α R a i α ) dt ˆψ β = (1) (v β R a i β ) dt ˆΨ s = ˆψ2 α + ˆψ 2 β (2) ˆθ s = tan 1 ˆψ β ˆψ α. (3) Here, v α and v β are the armature voltages, i α and i β are the armature currents in the stationary α β reference frame, R a is the armature resistance, ˆΨ α and ˆΨ β are the α- and β-axis components of the estimated stator flux linkage, respectively, ˆΨ s is the estimated stator flux linkage, and ˆθ s is the estimated position of the stator flux linkage in the α β frame. It is generally difficult for inverter-fed motor drives to measure the armature voltages in the motor terminals (v α and v β ). Instead, the reference voltages (vα and vβ ) are used to estimate the flux, as shown in Fig. 1. Various compositions of the torque and flux controller shown in Fig. 1 have been proposed (e.g., 1] 4]). The DTC method used to evaluate the method proposed in this paper is described in Section IV. III. CONTROL METHOD OF TORQUE AND FLUX A. Mathematical Model in M T Frame Fig. 2 shows the vector diagram and coordinate axes under steady-state operating condition. The α β reference frame is a stationary reference frame, whereas the d q reference frame is a rotating frame that is synchronized to the rotor. The α-axis corresponds to the direction of the u-phase of the stator windings, Fig. 2. Vector diagram of PMSM and coordinate axes. and the d-axis corresponds to the direction of the stator flux linkage of the rotor magnet (Ψ a ).TheM T reference frame is a rotating reference frame that is synchronized to the statorflux-linkage vector (ψ s ) 9]. The angle θ s indicates the position of the stator-flux-linkage vector. In the steady state, the voltage equation of the PMSM in the M T frame is given by vm v T ] = R a im i T ] ] 0 + ωψ s where v M and v T are the armature voltages, i M and i T are the armature currents in the M T frame, and ω is the electrical rotor angular velocity. The electromagnetic torque is given by where P n is the number of pole pairs. (4) T e = P n Ψ s i T (5) B. Calculator of Reference Torque and Reference Flux Fig. 3 shows the proposed reference torque and reference flux calculator. In this paper, the torque limiting required for current limitation and the FW required for voltage limitation are implemented as limiters. The control laws for torque limiting and FW are obtained using equations in the M T frame, as described later. However, for MTPA control only, the relationship between the torque and the flux is calculated from equations

3 972 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 3, MAY/JUNE 2012 Fig. 3. Proposed calculator for reference torque and reference flux. in the d q frame. The control law for MTPA control 5] is given by Ψ a i d = 2(L q L d ) Ψ 2 a 4(L q L d ) 2 + i2 q (6) where i d and i q are the d- and q-axis currents, respectively, Ψ a is the stator flux linkage due to the rotor magnet, and L d and L q are the d- and q-axis inductances, respectively. The relationship between the torque and the flux can be calculated using the following equations to satisfy (6): ψd ψ q ] Ld 0 = 0 L q Ψ s = ] id i q ] + Ψ a 0 ] (7) ψ 2 d + ψ2 q (8) T e = P n (ψ d i q ψ q i d ). (9) Since this calculation for MTPA control is complicated, a lookup table is used in Fig. 3. The effect of the parameter variation should be considered when the magnetic saturation is significant. For example, the q-axis inductance is modeled as a function of the q-axis current. C. Torque Limiting The torque is restricted to satisfy the current limiting, which is determined by the capabilities of the inverter and the motor. For interior PMSMs, which can utilize the reluctance torque, the relationship between the torque and the current is nonlinear, and thus, deriving this relationship is complicated. In the M T frame, however, the limiting torque can be calculated using (5) as follows: T lim = P n Ψ s i Tm (10) where i Tm is the limiting value of the T -axis current. When the limiting current is I am, i Tm is given by i Tm = Iam 2 i 2 M. (11) This control law can be applied in both the MTPA and the FW regions. In 11] and 12], the limiting torque is calculated using T lim = (P n Ψ s I am ) 2 T 2 r (12) Fig. 4. Torque and flux controller for RFVC DTC (PI-controller-based DTC). where T r is termed the reactive torque and is defined by T r = P n Ψ s i M. (13) Substituting (13) into (12) gives control laws that are equivalent to (10) and (12). D. FW Control In contrast to the conventional control method in the d q frame, it is easy for a DTC system to accomplish FW control because DTC directly controls the stator flux linkage. The proposed system uses an FW control method to maintain the armature voltage V a at its limiting value V am. The proposed method is derived from the voltage equation in the M T frame. Using V a = vm 2 + v2 T and solving (4) for the variable Ψ s yield the stator flux linkage Ψ s FW for the case when V a = V am, as follows: Ψ s FW = 1 { R a i T + } Vam ω 2 (R a i M ) 2. (14) IV. ANTIWINDUP SCHEME OF TORQUE CONTROLLER This study adopts a DTC method using a reference flux vector calculator (referred to hereafter as RFVC DTC) 3], 4], 7]. The torque and flux controller used by this method is shown in Fig. 4. The RFVC DTC system has several advantages, including a fixed switching frequency and a low torque ripple. The RFVC DTC system has a PI controller for torque control. Windup of the PI controller generally occurs when the terminal output voltage of the inverter is saturated. The performance of the current limitation based on torque limiting depends on the response characteristic of the torque control system. This paper proposes an antiwindup scheme for the torque controller. Fig. 5 shows a vector diagram for voltage saturation. Here, the voltage drop in the resistance is neglected. ˆψ s k] is the vector of the estimated stator flux linkage. In the DTC system, this vector is controlled to obtain the torque and the flux based on the reference values. ψ sk] is the reference vector of the stator flux linkage, and it corresponds to the reference flux (Ψ s) and the reference position (θ s), which are shown in Fig. 4. In the RFVC DTC system, the reference voltage calculation is based

4 INOUE et al.: CONTROL METHOD SUITABLE FOR DTC-BASED MOTOR DRIVE SYSTEM 973 TABLE I EXPERIMENTAL SYSTEM PARAMETERS Fig. 5. Vector diagram for voltage saturation. K a is determined through performing simulation and experiment. Note that the antiwindup is disabled when K a =0. Details regarding the torque controller and the gain design in the RFVC DTC system have been reported in 13]. The PI gains of the torque controller can be determined from the damping factor and the natural angular frequency of the quadratic transfer function. Fig. 6. Antiwindup implementation for torque controller. on time subtraction of the flux. Hence, the desired armature voltage is (ψ sk] ˆψ s k])/t s, where t s is the sampling period. In Fig. 5, the desired voltage vector exceeds the voltage-limiting circle, which corresponds to the maximum available voltage of the inverter. Thus, voltage saturation occurs, and v k] is the actual voltage vector applied to the motor. In the torque and flux controller shown in Fig. 4, the reference voltage vector v k] is generated in the reference voltage vector calculator, and then, voltage limiting according to the available output voltage of the inverter is applied. The estimated vector of the stator flux linkage in the next control period is ˆψ s k +1]. When voltage saturation occurs, the estimated position ˆθ s k +1]differs from the reference position θ sk], as shown in Fig. 5. The angular difference between the reference and estimated positions of the stator flux linkage is defined by θ ε = θ sk 1] ˆθ s k]. (15) An antiwindup scheme utilizing the value θ ε is proposed to improve the torque control performance. Fig. 6 shows the modified PI controller with antiwindup. In the proposed antiwindup scheme, the gain of the integral element is varied according to the variable γ i. Consequently, the input quantity to the integrator becomes suppressed. The variable γ i should have a value of unity for an angular difference θ ε of zero. It should also approach zero as θ ε increases. A function that satisfies these conditions is given by 1 γ i = 1+K a θ ε where K a is the antiwindup gain, and it satisfies K a > 0. (16) V. E XPERIMENTAL RESULTS A. Experimental Setup The effectiveness of the proposed system is evaluated experimentally. Table I lists the parameters of the PMSM drive system considered in this study. All the controls are processed through a digital signal processor (Texas Instruments, TMS320C6713). The speed control period is 5 ms, and the sampling period of the other control is 100 μs. An insulated-gate bipolar transistor module is used for the inverter, and the pulsewidth-modulation carrier frequency is 10 khz. The rotor speed is detected by an incremental encoder attached to the tested motor. Flux estimation is based on a firstorder low-pass filter instead of a pure integrator to reduce the effects of the dc offset of the experimental system and the error of the initial value used to estimate the flux. B. Effectiveness of Antiwindup Scheme Fig. 7 shows the characteristics of the torque step response to confirm the effectiveness of the antiwindup scheme. The operating speed is 500 r/min, and no load is applied. In this case, neither the proposed methods for torque limiting nor the FW is applied. A large torque overshoot appears when antiwindup is not applied. In contrast, the torque overshoot becomes small when antiwindup is applied. This is because voltage saturation increases the angular difference θ ε and, thus, the gain variation γ i decreases. This confirms that the antiwindup scheme proposed in Section IV is effective for the torque controller of the RFVC DTC system. C. Acceleration Characteristics To confirm the effectiveness of the torque limiting and the FW control proposed in Section III-C and D, respectively,

5 974 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 3, MAY/JUNE 2012 Fig. 7. Comparison of torque step response (operating conditions: 500 r/min and no load). the acceleration characteristics are investigated. In this section, antiwindup is applied to the torque controller. Fig. 8 shows the speed response characteristics when the rotor speed is increased from 500 to 3500 r/min when no load is applied. The results in Fig. 8(a) show that the rotor speed increases stably. When torque limiting and FW are applied, the proposed scheme satisfies the limiting values of the voltage and current, as shown in Fig. 8(a) and (b). Fig. 8(c) shows that the M-axis current decreases as the rotor speed increases during FW. Fig. 9 shows the torque trajectory for the same operating conditions as those in Fig. 8. Torque limiting is applied between points B and D, and FW control is applied between points C and E. These results confirm that the proposed system achieves maximum power operation and stable control. Fig. 10 shows the acceleration characteristics when the rotor speed is increased from 500 to 2500 r/min when no load is applied. In Fig. 10(a), the trajectory moves from the FW region to the MTPA region at the operating point E. The proposed system can change smoothly between control methods. Fig. 10(b) shows that the armature voltage is below its limiting value after point E. In the proposed system, both torque limiting and FW are achieved by the limiter. Thus, it is unnecessary to calculate the rotor speed when the control method changes. In the conventional method, the limiting torque is calculated based on the PMSM model in the d q frame 6]. In the MTPA control region, the maximum torque is constant. In the FW control region, the limiting torque is variable and is a function of the rotor speed. Therefore, an approximate value of the limiting torque T lim is given by (17), shown at the bottom of the page, which is an example of the conventional method, where T lim MTPA is the limiting torque calculated using the PMSM model and K tl4, K tl3, K tl2, K tl1, and K tl0 are the coefficients of the approximating polynomial. In this case, Fig. 8. Acceleration characteristics (ωm = 500 to 3500 r/min; no load). (a) Rotor speed, torque, and stator flux linkage. (b) Armature voltage and current. (c) M- andt -axis currents. motor parameters such as the inductance and magnet flux are required. When the PMSM model has the parameters shown in Table I, T lim MTPA is 1.9 N m. The coefficients K tl4, K tl3, K tl2, K tl1, and K tl0 are , , , , and 2.670, respectively. Fig. 11 shows the armature voltage and current for the conventional method, where the limiting torque is given by { Tlim MTPA, for MTPA control region T lim = K tl4 ω 4 + K tl3 ω 3 + K tl2 ω 2 + K tl1 ω + K tl0, for FW control region (17)

6 INOUE et al.: CONTROL METHOD SUITABLE FOR DTC-BASED MOTOR DRIVE SYSTEM 975 Fig. 9. Torque trajectory in torque/rotor speed plane (ωm = 500 to 3500 r/min; no load). Fig. 11. Armature voltage and current for torque limiting based on motor model in the d q frame (acceleration characteristics: ωm = 500 to 3500 r/min andnoload). Fig. 10. Acceleration characteristics (ωm = 500 to 2500 r/min; no load). (a) Torque trajectory in torque/rotor speed plane. (b) Armature voltage and current. (17). The plots exhibit almost the same characteristics as those shown in Fig. 8(b) for which the proposed method was applied. However, calculating torque limiting based on the motor model in the d q frame is complicated. In addition, when parameter variation (e.g., variation in the inductance due to magnetic saturation) is considered, parameters should be determined for several operating conditions. Therefore, the proposed control laws have several advantages, including insensitivity to parameter variation and simplicity of calculation. D. Transient Performance of Torque Limiting Fig. 12 shows the transient characteristics of the proposed torque limiting. Fig. 12(a) shows that, when antiwindup is not applied, the estimated torque does not follow the reference torque. Fig. 12(b) reveals that good torque control performance is achieved when antiwindup is applied. Consequently, the Fig. 12. Effect of torque response improvement on current limitation (operating condition: 500 r/min and no load). (a) Torque response without antiwindup. (b) Torque response with antiwindup. (c) Comparison of armature current. armature current is maintained at the limiting value for both steady and transient states, as shown in Fig. 12(c). Fig. 13 shows the transient performance of the torque limiting when the parameter error exists. In this case, the resistance value used in the proposed controller is 0.4 Ω, which is about 50% of the nominal value, and thus, the estimation error occurs. However, in the proposed method for the FW and the torque limiting, the flux estimation error does not affect the voltage and current limitations as long as the torque follows the reference value. This is because both the proposed method and the DTC

7 976 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 48, NO. 3, MAY/JUNE 2012 weakening, IEEE Trans. Ind. Appl., vol. 34, no. 6, pp , Nov./Dec ] L. Tang, L. Zhong, M. F. Rahman, and Y. Hu, A novel direct torque controlled interior permanent magnet synchronous machine drive with low ripple in flux and torque and fixed switching frequency, IEEE Trans. Power Electron., vol. 19, no. 2, pp , Mar ] J. Faiz and S. H. Mohseni-Zonoozi, A novel technique for estimation and control of stator flux of a salient-pole PMSM in DTC method based on MTPF, IEEE Trans. Ind. Electron., vol. 50, no. 2, pp , Apr ] T. Nakano, H. Ohsawa, and K. Endoh, A high-performance cycloconverter-fed synchronous machine drive system, IEEE Trans. Ind. Appl., vol. IA-20, no. 5, pp , Sep ] G. Pellegrino, E. Armando, and P. Guglielmi, Optimal exploitation of the constant power region of IPM drives based on field oriented control, in Conf. Rec. IEEE IAS Annu. Meeting, Sep. 2007, pp ] Y. Inoue, S. Morimoto, and M. Sanada, Control method for direct torque controlled PMSG in wind power generation system, in Proc. IEEE IEMDC, May 2009, pp ] Y. Inoue, S. Morimoto, and M. Sanada, A novel method of maximumpower operation for IPMSMs in DTC system, in Proc. 13th EPE, Sep. 2009, pp ] Y. Inoue, S. Morimoto, and M. Sanada, Examination and linearization of torque control system for direct torque controlled IPMSM, IEEE Trans. Ind. Appl., vol. 46, no. 1, pp , Jan./Feb Fig. 13. Transient characteristic of the torque limiting under the parameter variation. (The resistance error is 50% of the nominal value, and antiwindup is applied. Operating condition is the same as that in Fig. 12.) (a) Torque response. (b) Armature current. are based on the same mathematical model, as shown in (4) and (5). Hence, the errors of the estimated and the reference values are canceled out. VI. CONCLUSION In this paper, control laws for torque limiting and FW suitable for a DTC system have been proposed. Experiments confirm that the proposed method for the FW and the torque limiting can accomplish maximum power operation satisfying the limitations of the voltage and the current without the need to determine any motor parameters except for the resistance. In addition, the proposed antiwindup scheme for the torque controller was applied, and it was confirmed that the proposed torque-limiting method is valid for both steady and transient states. Consequently, the proposed system has several advantages, including insensitivity to parameter variation, simplicity of calculation, and stable control. REFERENCES 1] I. Takahashi and T. Noguchi, A new quick-response and highefficiency control strategy of an induction motor, IEEE Trans. Ind. Appl., vol. IA-22, no. 5, pp , Sep./Oct ] G. S. Buja and M. P. Kazmierkowski, Direct torque control of PWM inverter-fed AC motors A survey, IEEE Trans. Ind. Electron., vol. 51, no. 4, pp , Aug ] L. Tang, L. Zhong, M. F. Rahman, and Y. Hu, A novel direct torque control for interior permanent-magnet synchronous machine drive with low ripple in torque and flux A speed-sensorless approach, IEEE Trans. Ind. Appl., vol. 39, no. 6, pp , Nov./Dec ] M. Fu and L. Xu, A sensorless direct torque control technique for permanent magnet synchronous motors, in Conf. Rec. IEEE Ind. Appl. Soc. Annu. Meeting, Oct. 1999, vol. 1, pp ] S. Morimoto, M. Sanada, and Y. Takeda, Wide-speed operation of interior permanent magnet synchronous motors with high-performance current regulator, IEEE Trans. Ind. Appl., vol. 30, no. 4, pp , Jul./Aug ] M. F. Rahman, L. Zhong, and K. W. Lim, A direct torque-controlled interior permanent magnet synchronous motor drive incorporating field Yukinori Inoue (S 07 M 10) was born in Japan in He received the B.E., M.E., and Ph.D. degrees from Osaka Prefecture University, Sakai, Japan, in 2005, 2007, and 2010, respectively. Since 2010, he has been with the Graduate School of Engineering, Osaka Prefecture University, where he is currently an Assistant Professor. His research interests include control of electrical drives, particularly the direct torque control of permanent-magnet synchronous motors and position-sensorless control of these motors. Dr. Inoue is a member of the Institute of Electrical Engineers of Japan and the Japan Institute of Power Electronics. Shigeo Morimoto (M 93) was born in Japan in He received the B.E., M.E., and Ph.D. degrees from Osaka Prefecture University, Sakai, Japan, in 1982, 1984, and 1990, respectively. In 1984, he joined Mitsubishi Electric Corporation, Tokyo, Japan. Since 1988, he has been with the Graduate School of Engineering, Osaka Prefecture University, where he is currently a Professor. His main areas of research interest are permanentmagnet synchronous machines, reluctance machines, and their control systems. Dr. Morimoto is a member of the Institute of Electrical Engineers of Japan, the Society of Instrument and Control Engineers of Japan, the Institute of Systems, Control and Information Engineers, and the Japan Institute of Power Electronics. Masayuki Sanada (M 94) was born in Japan in He received the B.E., M.E., and Ph.D. degrees from Osaka Prefecture University, Sakai, Japan, in 1989, 1991, and 1994, respectively. Since 1994, he has been with the Graduate School of Engineering, Osaka Prefecture University, where he is currently an Associate Professor. His main areas of research interest are permanent-magnet motors for direct-drive applications, their control systems, and magnetic field analysis. Dr. Sanada is a member of the Institute of Electrical Engineers of Japan, the Japan Institute of Power Electronics, and the Japan Society of Applied Electromagnetics and Mechanics.