134 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007 Vector Control Drive of Permanent Magnet Synchronous Motor Using Resolver Sensor Weera Kaewjinda 1 and Mongkol Konghirun 2, Non-members ABSTRACT The rotor position is necessary to achieve the vector control drive system of Permanent Magnet Synchronous Motor (PMSM). In this paper, the resolver sensor detecting the rotor position of PMSM is focused. The outstanding features of this sensor are its robust structure and noise insensitivity. The resolver algorithm is proposed and implemented in the vector control drive system of PMSM. The proposed scheme has been verified by both simulation and experiment using MATLAB/Simulink and the TMS320F2812 based digital controller, respectively. Keywords: PMSM, Resolver, Vector control drive 1. INTRODUCTION Permanent magnet synchronous motor (PMSM) used in servo-mechanical systems is generally called brushless servomotor or brushless AC servomotor. The power density of a PMSM is higher than one of induction motor with the same ratings due to the no stator power dedicated to the magnetic field production. Nowadays, PMSM is designed not only to be more powerful but also with lower mass and lower moment of inertia. Due to its high power density and smaller size, PMSM has in recent years evolved as the preferred solution for speed and position control drives on machine tools and robots. In vector control drive, the highly accurate position from position sensor is required to transform the abc variables to the dq variable in the synchronously rotating reference frame aligned with the rotor flux linkage vector. Resolver is the one of position sensors that can measure the initial rotor position at standstill. This feature is important to gain the maximum starting torque in such drive system. The resolver is also the most reliable and robust sensor for severe environments such as high temperature. Its signals are not degraded through the long cables. The concept of resolver is actually similar to transformer operation. There are one rotating coil as the primary winding and two stationary coils as the Manuscript received on August 1, 2006 ; revised on October 25, 2006. 1,2 The authors are with department of Electrical Engineering, King Mongkut s University of Technology Thonburi, Bangkok 10140, E-mail: aody2k@hotmail.com and Mongkol.Kon@kmutt.ac.th. secondary windings. The primary coil is applied by the high-frequency sinusoidal voltage in an order of khz. Two secondary coils are placed in the stator by 90 differences. Once the rotor is rotated, the induced voltages would be produced in the secondary coils. The amplitudes of these induced sinusoidal voltages are modulated with the rotor position. The demodulation technique must be designed to extract the rotor position. This demodulation process could be implemented on the R/D converter IC [1]. This chip is designed to calculate the error between actual angle and computed angle. This angle error is controlled to zero, resulting in the computed angle converges to the actual one. However, the resolver algorithm is implemented by special IC chip which increases the overall cost. In [2], the calculated rotor angle is obtained by the similar method. However, the calculation requires the resolver parameters, resulting in the complicated equations of the rotor angle. The phase lock loop demodulating method is presented in [3]. This scheme employs the additional analog circuit that requires the parameter adjustments due to the drift problems. In [4], the calculated position is basically obtained by a closed loop operation. The digital 16th-order FIR band-pass filters (to limit the signal bandwidth) and downsamplers (to reduce the sampling rate) are incorporated in their proposed algorithm. Obviously, the phase lag due to the filters is noticed in the system. The angle is needed to be compensated when implementing in the vector control drive of PMSM. Also, the computation time of these filters is significantly long because of their high order structure. This may not be practical when the low-cost fixed-point digital controller is used. In this paper, the computed rotor angle is computed by means of the feedback loop control. The error signal is introduced by the difference of the cross product of modulated signals and measured excitation signal. Then, this error would be controlled by PI controller. The computed rotor angle is guaranteed to be the actual one once the error becomes zero without usage of filters. Thus, the delay effects due to filters are eliminated. The proposed resolver algorithm is successfully implemented in the vector control drive of PMSM.
Vector Control Drive of Permanent Magnet Synchronous Motor Using Resolver Sensor 135 2. THEORY AND OPERATION 2. 1 Dynamic model of PMSM The mathematical model of the non-salient PMSM in the synchronously rotating reference frame aligned with the rotor flux linkage can be expressed as follows. V d = r s i d ω r λ q + pλ d (1) T e = V q = r s i q ω r λ d + pλ q (2) λ d = L s i d + λ m (3) λ q = L s i q (4) ( ) ( ) 3 P (λ d i q λ q i d ) 2 2 (5) where V d and V q = the stator voltages in dq-axis; i d and i q = the stator currents in dq-axis; λ d and λ q = the stator flux linkages in dq-axis; λ m = the permanent-magnet flux linkage; T e = the electromagnetic torque; ω r = the angular velocity of rotor; r s = the stator resistance; L s = the stator self inductance; P = the number of poles; p = d dt. Substituting equations (3) and (4) into the stator voltage equations (1) and (2), the stator current dynamic equations in the state-space form can be derived as follows. di d dt = γi d + ω r i q + βv d (6) di q dt = γi q + ω r i d + βω r λ m + pv q (7) where β = 1 L s and γ = rs L s. When the i d current is controlled to be zero, the stator flux linkages and torque equations (3) and (5) become. λ d = λ m (8) ( ) ( ) 3 P T e = (λ m i q ) (9) 2 2 As a result, the electromagnetic torque is controlled merely by the current i q, similarly to the DC motor operation. 2. 2 The Resolver sensor Resolver is a type of sensor that uses in servo system. The schematic of resolver is shown in Fig.1. Three signals (i.e., excitation, sine and cosine signals) are obtained from the resolver. The sinusoidal excitation signal (U 0 ) is applied to the rotor winding. The resolver outputs (stator windings) consist of two sinusoidal signals whose amplitudes are modulated according to the sine and cosine (U 1 and U 2 ) of the rotor position (φ). Fig.1: Schematic and signals of resolver sensor The relevant equations of rotor winding (U 0 ) and stator windings (U 1 and U 2 ) are summarized as follow. U 0 (t) = Û 0 sin ω ref t (10) U 1 (φ, t) = Û 0 k sin φ sin ω ref t (11) U 2 (φ, t) = Û 0 k cos φ sin ω ref t (12) k = turn ratio of the resolver. Û 0 = is the peak value ω ref = frequency (rad/sec) of the excitation signal φ = rotor position (rad.) Fig.2 shows the block diagram of the vector controlled drive system of PMSM using resolver sensor on a Digital Signal Processor (DSP) based controller. In this system, two line currents and three resolver signals are fed thru the on-chip ADCs of DSP. The controller implements the vector control algorithm and space-vector PWM generation as well as the resolver algorithms such as demodulation, speed calculation, etc. 3. CALCULATIONS OF ROTOR SPEED AND POSITION FROM THE RESOLVER SIGNALS Fig. 3 shows the block diagram of resolver algorithm, including the demodulation and speed/position calculation. The algorithm attempts to minimize the error between the actual rotor angle φ the computed angle θ, using a feedback loop. The error calculation is formulated basing on the following trigonometric identity. err = (Û 0 sin ω ref t cos θ)(û 0 k sin φ sin ω ref t) (Û 0 sin ω ref t sin θ)(û 0 k cos φ sin ω ref t) (13) err = Û 0(t) (Û 0 k sin ω ref t)[sin φ cos θ cos φ sin θ] (14) err = A [sin(φ θ)] (15) A = U 0 (t) (Û 0 k sin ω ref t) (16)
136 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007 Fig.2: Vector controlled drive system of PMSM using resolver sensor This error is controlled to zero by PI controller. The integrator is used to increase the resolution of computed angle. Once this control loop is accomplished (i.e., err = 0), then the computed angle θ, which is limited within 0 2π rad, is equal the actual rotor angle φ. Matlab/Simulink models of resolver algo- Fig.4: rithm Fig.3: Block diagram of resolver algorithm 4. SIMULATION RESULTS The overall system seen in Fig. 3 is created in the Matlab/Simulink blocks as shown in Fig.4. The excitation signal generator feeds the high frequency excitation signal to the resolver. When the rotor is rotated, the resolver would induce the two modulated sinusoidal signals. To obtain the rotor position from the resolver, these modulated signals have to be demodulated. The error signal shown in Eq. 14 is introduced and controlled by PI controller. The output of PI would be the rotor speed, ω m. Finally, the mechanical angle, θ m is obtained by the integration of the rotor speed. The simulation results can be seen in Figs. 5 and 6. Fig. 5 shows the modulated sine and cosine signals from resolver sensor are demodulated by the proposed algorithm. In Fig.6 the top trace is the rotor speed, the middle trace is the error in Eq. 14. The mechanical angle is shown in the bottom trace. Fig.5: Simulation results: modulated sine and cosine signals and their demodulated signals at 600 rpm
Vector Control Drive of Permanent Magnet Synchronous Motor Using Resolver Sensor 137 Fig.6: Simulation results: rotor speed, error and mechanical angle at 600 rpm 5. EXPERIMENTAL RESULTS To validate the proposed method, the algorithm is implemented on a 32-bit fixed point TMS320F2812 DSP. The speed controlled system shown in Fig. 2 is implemented to verify the proposed resolver algorithm. The ISR/PWM frequency is 10 khz. The frequency of sinusoidal excitation signal is 1 khz. During experiment, the PMSM is driven at a constant speed of 600 rpm. The experimental results can be seen in Fig. 7, the demodulated signals and computed mechanical angle by using the proposed algorithm are successfully obtained corresponding to the simulation results. In Fig.8, the top trace shows the speed response for a gradual change of speed from 0.1 p.u. (- 600 rpm) to 0.1 p.u. (600 rpm). Obviously, the speed response can be successfully tracked the speed command and the computed mechanical angle is shown in the lowest trace. In the middle trace, the error in Eq. 14 is controlled within the ±0.1 p.u. (±36 ) during transient. However, this error could be less if the PI controller in resolver algorithm is further tuned to obtain the optimal tracking of angle over a wide range of operation. Fig.7: Experimental results: modulated sine and cosine signals and their demodulated signals at 600 rpm Fig.8: Experimental results: rotor speed, resolver error and mechanical angle at 600 rpm
138 ECTI TRANSACTIONS ON ELECTRICAL ENG., ELECTRONICS, AND COMMUNICATIONS VOL.5, NO.1 February 2007 6. CONCLUSIONS In this paper, the proposed resolver algorithm has been verified in the current controlled drive system of PMSM. Both simulation and experimental results are presented. According to these results, the resolver algorithm can force the angle error to zero. Thus, the computed angle can eventually match with the actual rotor angle. Then, the correct rotor speed computation is guaranteed. In the future works, this algorithm will be extensively tested in the speed controlled drive system of PMSM. 7. APPENDIX The motor parameters and PI gains used in the system are summarized below: d-axis current loop: Kp = 0.5, Ki = 0.1 q-axis current loop: Kp = 0.5, Ki = 0.05 Speed loop: Kp =40, Ki = 0.2 Resolver algorithm : Kp = 0.00015,Ki = 0.0008 Weera Kaewjinda received a bachelor s degree in Electrical Engineering from King Mongkut s University of Technology Thonburi, Thailand. Nowadays he is pursuing a Master degree in Department of Electrical Engineering, King Mongkut s University of Technology Thonburi, Thailand. His ongoing research is the sensor drive system of permanent magnet synchronous motors. Mongkol Konghirun received a B.Eng. Electrical from King Mongkut s University of Technology Thonburi, Thailand in 1995. And he received M.Sc. and Ph.D. degrees in electrical engineering from the Ohio State University, USA in 1999 and 2003, respectively. Presently, he is working in Electrical Engineering department at King Mongkut s University of Technology Thonburi, Thailand. His research interests include electrical machine drives, and real-time control using digital signal processors. Table 1: Parameters of the PMSM motor Stator resistance 2.2Ω Stator inductance 0.0029 mh Number of poles 4 Base voltage 179.629 V Base current 10 A Base flux linkage 1 volt.sec/rad Base electric frequency 200 Hz Base Speed 6000 rpm References [1] B. Murray, Hare, and A. Hirao, Resolver Position Sensing System With Integrated Fault Detection for Automotive Applications, IEEE Proceedings in Sensors, Vol. 2, pp. 864-869, 2002. [2] Wan Jiuqing, Li Xingshan, and Guo Hong, The analysis and design of high-speed brushless resolver plus R/D converter shaft-angle measurement system, IEEE Conference Electrical Machines and Systems, Volume 1, pp. 289-292, 2001. [3] D. Hanselman, Resolver signal requirements for high accuracy resolver-to-digital conversion, IEEE Conference Industrial Electronics Society, Vol.2, pp. 486-493,1989. [4] A.O.Di Tommaso, and R.Miceli, A new high accuracy software based resolver-to-digital converter, IEEE Conference Industrial Electronics Society, Vol.3, pp. 2435-2440, 2003.