RTLinux Based Speed Control System of SPMSM with An Online Real Time Simulator
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1 Extended Summary pp RTLinux Based Speed Control System of SPMSM with An Online Real Time Simulator Tsuyoshi Hanamoto Member (Kyushu Institute of Technology) Ahmad Ghaderi Non-member (Kyushu Institute of Technology) Teruo Tsuji Member (Kyushu Institute of Technology) Keywords: digital speed control, online real time simulator, RTLinux, SPMSM In this paper we propose the new method to achieve the experimental system with an online simulator using a RTLinux based PC system. This system consists of mainly two functions. One is the simulation part, where a motor mathematical model based on the three phase stationary coordinate is solved using a fourth order Runge-Kutta method in real time. The motor model includes non-linear operation, such as, trigonometric functions, square waves generated by a PWM inverter, dead time, and limiter circuits, so on. The other is the motor control part where conventional PI controllers and de-coupling controllers are programmed. The system is able to realize the motor control in 200 µs period and achieves the online real time simulator simultaneously. The configuration of the experimental system which includes the online real time simulator is shown in Fig. 1. The outputs of the real time simulator can be used for the control, and these variable is also corrected and modified using the real values. All of these functions are implemented in the computer, so it is easy to select the data. The simulation time is about 23 µs and it takes about 33 µs forthe control in the system. From the results, it is enough to achieve the online real time simulation and the control at the same time. Figure 2 shows the experimental results of the control performance when the sampling interval of the pulse encoder is expanded. Here, the measured data is obtained by 20 ms period. While the output speed of the simulation is used in every 200 µs to the control instead of the measured value. Figure 2(a) shows the result when the speed is detected as an average values every 20 ms. The result of the step response is not desirable. On the other hand, Fig. 2(b) shows the result when the speed data of the online real time simulator is used for the control every 200 µs. And the simulation results is revised by the measured value only once in a hundred times. To compare these two results, Fig. 2(b) to be the satisfactory result. We proposed the online real time simulator using RTLinux based PC system and achieve both the speed control system of SPMSM and the real time simulation simultaneously in 200 µs control period. From the experimental results, it is clear that our model is valid and the system parameters are identified correctly. The proposed method is useful of the analysis and control design of the motor drive system and it has the possibility of more precise control and sensorless control. (a) step response when the sampling interval of the pulse encoder is expanded Fig. 1. Configuration of the proposed system (b) step response when the speed of the simulator is used for the control Fig. 2. experimental result when the sampling period of the speed detector is selected in 20 ms 12
2 Paper RTLinux based speed control system of SPMSM with an online real time simulator Tsuyoshi Hanamoto Ahmad Ghaderi Teruo Tsuji Member Non-member Member An online real time simulator for a RTLinux based speed control system of SPMSM (Surface Permanent Magnet Synchronous Motors) is proposed. For realization of the online real time simulator, a motor mathematical model based on the three phase stationary coordinate is solved using a fourth order Runge-Kutta algorithm in real time. The Runge-Kutta algorithm is required since the model includes non-linear operation, such as, trigonometric functions, square waves generated by a PWM inverter and limiter circuits, so on. The experimental system based on the RTLinux accomplishes both the motor control and the real time simulation at the same time in 200 µs control period. The online simulation results show considerable coincidence with the experimental results. Keywords: digital speed control, online real time simulator, RTLinux, SPMSM 1. Introduction Motor drive systems are widely used for the actuators in various industrial applications (1) (6). Especially, permanent magnet synchronous motors (PMSM) are frequently used because they have many advantages such as easy maintenance, small size and light weight structures. Recently more precise and high speed controls of the motor drive systems are requested. To achieve these requirements, not only the experimental apparatus but also the computer simulation technique, which simulate the system behavior precisely are important (7) since they both are necessary to tune up the high performance system. But it has been difficult to realize online real time simulators especially for non-linear systems. In this paper we propose the new method to realize the experimental system with an online real time simulator using a RTLinux (8). A typical application of the real time simulator is the real time analysis of the power systems (9) and hardwarein-the-loop-simulation of electric drives (10). In the other hand, we consider to control the real system by using the output of the simulator. That means that the motor control system and the simulator are coupled and driven simultaneously, so that the output of the simulator can be used for the motor control online. Then it is possible to develop a more precise and high performance sensorless or a reduced sensor control system when the proposed online real time simulator is realized. For example, when a precise waveform of output of a PWM inverter model which is included in the proposed simulator is used, the more precise speed sensorless control is realized even in low speed and light weight load conditions. In fact without the precise PWM inverter model, undesirable dead time affect are appeared. In addition the dead time affect appears in the current wave form and the harmonic Graduate school of life science & systems engineering, Kyushu Institute of Technology Wakamatsu-ku, Kitakyushu, Fukuoka , Japan components are increased. Even in that case, the proposed simulator output can simulate the motor current correctly and can keep the high performance control characteristics in the sensorless control. This system consists of mainly two functions. One is the simulation part, where a motor mathematical model based on the three phase stationary coordinate is solved using a fourth order Runge-Kutta method in real time. The motor model includes non-linear operation, such as, trigonometric functions, square waves generated by a PWM inverter, dead time, and limiter circuits, so on. The other is the motor control part where conventional PI controllers and de-coupling controllers are programmed. The system is able to realize the motor control in 200 µs period and achieves the online real time simulator simultaneously. 2. Configuration of a Speed Control System 2.1 Mathematical Model of SPMSM In this paper, we consider the Surface Permanent Magnet Synchronous Motor (SPMSM) which has no salient characteristic. Figure 1 shows the analytical model of SPMSM. A voltage equation of the model in the stationary uvw axes and a kinetic equation of the motor are described as follows. v u v v v w = R a + PL a R a + PL a R a + PL a i u i v i w + ω e Φ sin θ e ω e Φ sin(θ e 2 3 π) ω e Φ sin(θ e π) (1) J dω m = T e T L (2) dt where, v: armature voltage, i: armature current R a : armature resistance, L a : armature inductance, θ e : electrical angle of rotor from u axis, ω m : me- D
3 chanical angular speed, ω e : electrical angular speed (= pω e, p number of pole pairs), P: differential operator (= d dt ), T e: input torque, T L : load torque, and subscriptions u,v,w mean u,v,waxes components. The dq transformation is applied to the three phase model of SPMSM because the mathematical model by the dq system is convenient for the motor control. Equation (3) shows the dq system based on the rotational coordinate. [ ] [ ][ ] vd Ra + PL = a ω e L a id v q ω e L a R a + PL a i q [ ] 0 + (3) eq And from (2) J dω m = k t i q T L (4) dt where, k t is torque constant. As mentioned above, the motor control system is based on the rotational coordinate (dq-axis), and here the conventional PI (Proportional - Integral) type controllers are used for both the speed and the current control loop, and the de-coupling control are applied. Figure 2 shows the block diagram of the experimental system. 3. Online Real Time Simulator 3.1 Runge-Kutta Algorithm The linearized model of the state space observer has been frequently used to estimate the unknown state variables of the nonlinear system, because of the limitation of the calculation performance. In this paper we propose the new method to achieve the online real time simulation for such nonlinear system in the experimental system using RTLinux based PC system. Because the performance of the PC is extremely developed, it become possible to solve complex equations during the small sampling period. Here, the nonlinear motor equations described in (1) is solved directly using the well-known fourth order Runge-Kutta method (11). That is, the Runge-Kutta algorithm give us the numerical solutions of the nonlinear differential equation. For reference, the fourth order Runge-Kutta algorithm is shown below. Consider the nonlinear differential equation, d x = f (t, x) (5) dt Suppose that x n is the value of the variable at time t n. The Runge-Kutta formula takes x n and t n and calculates an approximation for x n+1 at a brief time later, t n + h. The formula is given by Fig. 1. Three phase model of SPMSM where, x n+1 = x n (k 1 + 2k 2 + 2k 3 + k 4 ) (6) k 1 = hf(t n, x n ) k 2 = hf(t n + h 2, x n + k 1 2 ) k 3 = hf(t n + h 2, x n + k 2 2 ) k 4 = hf(t n, x n + k 3 ) Fig. 2. Block diagram of the experimental system 454 IEEJ Trans. IA, Vol.126, No.4, 2006
4 RTLinux based online real time simulator Table 1. pattern of the PWM mode gate signal phase voltage MODE U V W U V W 0 L L L I U L L 2E/3 E/3 E/3 II U U L E/3 E/3 2E/3 III L U L E/3 2E/3 E/3 IV L U U 2E/3 E/3 E/3 V L L U E/3 E/3 2E/3 VI U L U E/3 2E/3 E/3 VII U U U E: inverter voltage, U: on signal adds to upper device, L: on signal adds to lower device Fig. 3. model of a PWM switching 3.2 PWM inverter model Here, the nonlinear PWM inverter model is considered to simulate the real system accurately. The waveform of the voltage source is modeled as square waves, which is generated by a PWM inverter. Table 1 shows a pattern of the PWM mode, and shows the state of each power device in the inverter. Each phase voltage value is determined from the pattern. For example, MODE III means the lower devices are ON at U and W phase, and upper device is ON at V phase, and the voltage of each phase is determined as follows. V u = E 3, V v = 2E 3, V w = E 3 (7) Figure 3 shows an example of the PWM switching in one sampling period. In the figure, u, v, w are the three phase voltage commands, respectively, and it shows the instant when u >v >w. G u, G v, G w shows the gate signal shown in Table 1. The PWM pattern shown in the Table 1 is determined from the relationship of the amplitude of the voltage commands of the each phase. Fig. 4. A switch pole of the voltage source inverter Each voltage command is compared with the carrier wave and the gate pulse is generated. In the simulator T 1 T 4 are calculated by the relationship between the voltage reference and the carrier wave. Then each phase voltage shown in the figure is computed from the PWM pattern. In order to save the computation time the Runge-Kutta algorithm is used only once during the one mode. This means that the width of time interval h is changed by the state of the Mode, and the Runge-Kutta algorithm is performed seven times in the every sampling period T s. The dead-time is also simulated in the PWM model because the output characteristic is affected a little by the deadtime. Fig. 4 shows the typical inverter switch pole with IGBT and free wheeling diodes (12) (13). The IGBTs are driven by gate signals which are delayed by the dead time from ideal PWM signal. Although the actual output voltage affected by dead time is depend on the polarity of the phase current i ac.such voltage deviation due to the dead-time results in undesirable harmonic component. For the precise control of motor derive system, it is important to consider the mathematical motor model which includes the PWM inverter model because the inverter outputs square waveforms (not sinusoidal wave) modulated PWM pulse, and in addition, dead time affect is exist. To analyses the dead time affect, ON condition of both of the IGBTs and the anti-parallel connected diodes must be considered. As shown in Fig. 3, the switching pattern are defined at the beginning of the sampling point. Dead time is inserted at the instant of the mode change, so that the affect the dead time depends on the direction of the phase current i ac described as follows. When the current flows the arrow direction in Fig. 4 and the ON signal is added to the S 1, phase current i ac flows through S 1. At the instant of the mode change, S 1 turns off,andthend 2 becomes active to keep the current flows. At this condition, when ON signal is applied to the S 2, the device cannot turn on because of the inverse bias. The dead time affect does not appear. On the other hand, when the phase current i ac flows the inverse direction even if the S 1 signal is ON, then, S 1 cannot be ON because of the inverse bias, and i ac flows through D 1. At the instant of the mode change, the OFF signal is applied to S 1, and after the dead time period, S 2 becomes ON. During this period, current is still flow into D 1, this makes the mode change timing delay. And this means the dead time affect. In addition, the limitation of the voltage and the current command, and the time delay of the calculation of the controller are considered in the simulator. Thus the proposed D
5 simulator can simulate the nonlinear behavior. 4. Experimental results 4.1 Experimental setup To apply the control theory to the motor control system, there is a need for an appropriate operating system that works in real time. The PC-based control offers great advantages such as a faster design cycle and increase of productivity. Here, we refer to the real time system based on the RTLinux (8). The RTLinux is a hard real time operating system that handles time-critical tasks and runs the normal Linux as its lowest priority execution thread. So the system includes the networking, GUI programming and several other function as conventional tools. The PCbased experimental setup is constructed shown in Fig. 5 (Linux RTLinux2.2), which includes not only the control program but also the user GUI, such as, data entry windows of the reference, controller gains and so on. Our experimental system consists of the SPMSM, RTLinux based PC, PWM inverter (15), and some other equipment. We require a speed detector, a position detector, the PWM pulse generator, and the interface circuit. In this paper, we designed the interface circuit which includes all of the above necessary functions. The interface board consists of the FPGA (Field Programmable Gate Array), 33 MHz system clock and an A/D converter. An Altera EP1S10 is selected for the FPGA device (14) and the circuit is designed using the VHDL which is one of the hardware description language. The speed detector with correction function and position detectors, clock generator for A/D converter and PCI interface circuit are designed in it. In the experimental system, the carrier frequency of the PWM inverter is 5 khz, and the control period is selected as 200 µs. As a pulse encoder is used to measure the speed and position detector and it has the resolution of 2500 ppr (pulse per revolution), sampling period of the speed detector is set to 2 ms. Table 2 shows the specification of the tested motor. The configuration of the experimental system which includes the online real time simulator is shown in Fig. 6. The outputs of the real time simulator can be used for the control, and these variable is also corrected and modified using the real values. All of these functions are implemented in the computer, so it is easy to select the data. An example of the control method using the online real time simulator enables to expand the sampling period of the pulse encoder greatly. This means that the lower limit of the speed detector decreases, on the other hand, the control performance is kept even if the pulse encoder with low resolution is mounted. By using the simulation output, the interval can be expanded to 20 ms. The controller uses the speed and position values by the simulator usually and the data are modified once in a hundred times. We can obtain the average speed from the encoder every 20 ms, then the error between the average speeds of the simulator and the real data are used to update the date of the simulator. 4.2 Experimental results First, Fig. 7 shows the calculation time of the experimental system. In the figure, (a) calculation time of the online real time simulator, (b) calculation time of the motor speed control algorithm (c) total calculation time are described. The simulation time is about 23 µs and it takes about 33 µs for the control. From the results, it is enough to achieve the online real time simulation and the control at the same time even if we use a consumer model of PC (CPU: Celeron 700 MHz). Next, a comparison between outputs of the simulation and the real motor system are represented in Fig The motor speeds and the q-axis currents are measured when the step change of the speed command is applied. Figure 8 shows the response where the speed command is changed from 250 Table 2. Specification of the motor items value rated power (W) 308 rated torque (Nm) 1.05 rated current (A) 3.0 inverter voltage (V) 50 armature resistance (Ω) 2.5 armature inductance (mh) 4.5 torque constant (Nm/A) number of pole pairs 3 Fig. 6. Configuration of the proposed system Fig. 5. PC based experimental system Fig. 7. (a) calculation time of the simulator (b) calculation time of the speed control (c) total calculation time calculation time of the experimental system 456 IEEJ Trans. IA, Vol.126, No.4, 2006
6 RTLinux based online real time simulator Fig. 8. comparison of the q-axis current in the step response (a) step response when the sampling interval of the pulse encoder is expanded (a) measured u-phase current Fig. 9. state (b) calculated u-phase current comparison of the u-phase current in the steady (b) step response when the speed of the simulator is used for the control Fig. 10. experimental result when the sampling period of the speed detector is selected in 20 ms to 750 min 1. In this experiment, as the controller gain are selected to relatively large values, so that the voltage commands are reached to limit. Since the simulator can deal with the non-linear operation, the output waveform of the simulation coincides well with the experimental result though the control and the simulation are executed independently. Figure 9 shows the phase current in the steady state. Here the initial values of the simulator is obtained from the real system at first, then the simulator is executed independently. From the figure it is clear that both wave forms correspond well, and the effect of the dead time in the phase current is simulated well by the real time simulator. At last, we show the control performance when the sampling interval of the pulse encoder is expanded. Here, the measured data is obtained by 20 ms period. This condition is equivalent that the resolution of the pulse encoder becomes 250 ppr from 2500 ppr. While the output speed of the simulationisusedinevery200µs to the control instead of the measured value. The results are shown in Fig. 10. Figure 10(a) shows the result when the speed is detected as an average values every 20 ms. The result of the step response is not desirable so that the measured speed changes every 20 ms. On the other hand, Fig. 10(b) shows the result when the speed data of the online real time simulator is used for the control every 200 µs. And the simulation results is revised by the measured value only once in a hundred times. To compare these two results, Fig. 10(b) to be the satisfactory result. 5. Conclusion We proposed the online real time simulator using RTLinux based PC system and achieve both the speed control system of SPMSM and the real time simulation simultaneously in 200 µs control period. From the experimental results, it is clear that our model is valid and the system parameters are identified correctly. The proposed method is useful of the analysis and control design of the motor drive system and it has the possibility of more precise control and sensorless control under very low speed and/or light weight load conditions. Now we consider to decrease the current sensors control system to adopt the simulation values to the real system. (Manuscript received May 9, 2005, revised Oct. 28, 2005) This paper was presented at IPEC-Niigata 2005, and approved for publication in the IEEJ Transactions on Industry Applications Society. D
7 References ( 1 ) Z. Chen, M. Tomita. S. Ichikawa, S. Doki, and S. Okuma: Sensorless control of interior permanent magnet synchronous motor by estimation of an extended electromotive force, IEEE IAS Annual Meeting, Vol.3, pp (2000) ( 2 ) S. Morimoto, K. Kawamoto, M. Sanada, and Y. Takeda: Sensorless control strategy for salient-pole PMSM based on extended EMF in rotating reference frame, IEEE Trans. IA, Vol.38, pp (2002) ( 3 ) T. Hanamoto, A. Ghaderi, T. Fukuzawa, and T. Tsuji: Sensorless control of synchronous reluctance motor using modified flux linkage observer with an estimation error correct function, Proc. of ICEM2004, CD-ROM (2004) ( 4 ) T. Hanamoto, T. Tsuji, and T. Mochizuki: Sensorless speed control of IPMSM using the modified flux linkage observer, Proc. of ICEM2002, Vol.334, CD-ROM (2002) ( 5 ) T. Hanamoto, T. Tsuji, and Y. Tanaka: Comparison of the control characteristics of sensorless speed control of based on the observer theory, Proc. of ICEM 2000, Vol.3, pp (2000) ( 6 ) T. Hanamoto, T. Tsuji, and Y. Tanaka: Sensorless speed control of cylindrical type PMSM using modified flux observer, IPEC-Tokyo 2000, pp (2000) ( 7 ) M. Harakawa, H. Yamasaki, T. Nagano, S. Abourida, C. Dufuor, and J. Belanger: Real-Time simulation of complete PMSM drive at 10 µs time step, IPEC-Niigata, pp (2005) ( 8 ) ( 9 ) V.R. Dinavahi, M.R. Iravani, and R. Bonert: Real-time digital simulation and experimental varifacation of a D-STATCOM interfaced with a digital controller, INT J of Electrical power and energy systems, Vol.26, No.9, pp (2004) (10) S. Abourida, C. Dufuor, and J. Belanger: Real-Time Hardware-In-The-Loop simulation of electric drives and power electronics: process, problems and solutions, IPEC-Niigata, pp (2005) ( 11) kutta.html (12) P.-T. Cheng, H.-C. Lin, and C.-C. Hou: An integrated pulse width modulatior/dead-time generator with improved output voltage precision, IPEC-Niigata, pp (2005) (13) N. Urasaki, T. Senju, T. Kinjo, and T. Funahashi, and H. Sekine: Adaptive dead-time compensation of voltage source inverter for variable speed drives, IPEC-Niigata, pp (2005) ( 14) (15) Tsuyoshi Hanamoto (Member) received his B.S. and M.S. from Kyushu Institute of Technology, Japan, in 1984 and 1986, respectively. In 1986 he joined Kobe works of Kobe Steel, Ltd. In 1990 he was engaged Center for Cooperative Research of Kyushu Institute of Technology. From 1997 to 2000 he was with the Department of Electrical Engineering. Since April 2000 he has been with the Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, where he is presently an Associate Professor. His research interests include motor control and power electronics. Ahamd Ghaderi (Non-member) received his B.S. from Shahed University and M.S. from Isfahan University of Technology, Iran in 1999 and 2002, respectively. From 2002 to 2003 he worked National Iranian Oil Refining and Distribution Company. He is currently a Ph.D. candidate student with the Graduate School of Life Science and Systems Engineering, Kyushu institute of technology. His research interests include motor control and power electronics. Teruo Tsuji (Member) received his B.S., M.S., and Dr. Eng. degrees in Electrical Engineering from Kyushu University, Japan, in 1963, 1965 and 1978 respectively. From 1968 to 2001 he was with the Department of Electrical Engineering, Kyushu Institute of Technology. Since 2001 he has been with the Graduate School of Life Science and Systems Engineering, Kyushu Institute of Technology, where he is presently a Professor. His research interests include control, identification, and control application to magnetic levitation system and power electronics systems. 458 IEEJ Trans. IA, Vol.126, No.4, 2006
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