Virtual torque and inertia loading of controlled electric drive

IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 1, FEBRUARY 2005 47 Virtual Torque and Inertia Loading of Controlled Electric Drive Alon Kuperman and Raul Rabinovici, Senior Member, IEEE Abstract—This paper presents a simple method to obtain effects similar to those obtained by real mechanical loading and real inertia variation but without any mechanical parts supplementary to the electric motor of the studied electric drive. The electric motor itself produces the load torque and the inertia variation using digital signal processing software. Therefore, the electric drive is virtually torque and inertia loaded, while its behavior is similar to that of the actual loaded drive. The present method could be used to test the implementation of control algorithms or for didactic purposes using motion control kits found on the market. The present method is used with laboratory works of the DSP Fundamentals in Power Electronics course at the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel. Index Terms—Digital control, load and inertia emulation. I. INTRODUCTION CONTROLLED electric drive consists principally of an electric motor supplied by a power electronics source and operated by a digital signal processor (DSP) with a suitable control algorithm [1]. However, the control algorithm and the electric drive as a whole should be tested in conditions of mechanical loading and inertia variation. A real mechanical load is quite difficult to implement even it is as simple as a constant torque one. The real mechanical loading becomes even more cumbersome when the load torque should change in time, e.g., a sinusoidal change. In addition, there are servo drive applications where the inertia has a large variation, e.g., in robotics the inertia range could be as wide as 1:10 [2]. Therefore, the system should be also tested under inertia variations. However, these changes are difficult to implement mechanically. The use of torque-controlled load dynamometers, which is common in engine test beds or in the testing of electrical machines [3]–[6], is often impossible in an educational laboratory because of the high price and complexity. Authors faced this problem teaching the DSP Fundamentals in Power Electronics course at the Ben-Gurion University of the Negev, Beer-Sheva, Israel. The course consists of three parts: DSPs for power electronics control, motion control, and control of power converters. Each part ends with laboratory work [13]. In order to implement a motor speed control system under load torque change, a load machine is needed. The method, proposed in this paper, was developed to allow emulating the effect of load torque without using a real load machine. A Manuscript received March 16, 2003; revised December 3, 2003. The authors are with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel. Digital Object Identifier 10.1109/TE.2004.832881 Fig. 1. BLDC speed control block diagram. DSPs have developed rapidly over the past years and have become an inseparable part of almost any motor drive system, performing real-time generation of space-vector modulated waveforms, online speed and current acquisitions, programmable soft-start, dynamic braking, and intelligent control. A DSP was used to emulate a mechanical load or inertia variation using a controlled motor set, as shown in this paper. Fields of electric drive and power engineering are generally considered by students as unattractive and old-fashioned. However, this present course and the laboratory attached to it seem able to change this situation. The DSP connection to power electronics and controlled electric drive attract a large number of students to these fields. For example, the first time the course was given, seven students were enrolled, while one year later, 20 students attended it. The students’ reactions to the course were extremely positive. They were fascinated by possibilities of introducing DSP features to the area of power engineering. The DSP seems to act as a temptation, attracting students familiar with signal processing and control to the field of power electronics. It is quite important to attract students with a background of signal processing and of computers and control in order to introduce their skills and knowledge to the area of motion control and power electronics. Furthermore, the presented approach of virtual loading and inertia change is used by students to validate experimentally different control algorithms in their senior projects. II. METHOD PRESENTATION A general closed-loop brushless dc (BLDC) motor speed control system, which consists of the motor itself and a proportional integral derivative (PID) controller, is shown in Fig. 1 [7], where is the reference speed, is the motor speed, is the speed is the PID controller output voltage, is the PID error, controller transfer function, is the motor voltage to speed transfer function, and is the Laplace operator. The motor speed is sensed and compared with a reference value. The difference is applied to the controller (usually implemented using DSP software), which outputs the voltage driving the motor. 0018-9359/$20.00 © 2005 IEEE 48 IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 1, FEBRUARY 2005 Then, by taking out of brackets and making a realistic assumption about the electrical time constant of the motor (7) the motor would react exactly as in the real torque loading case if a virtual voltage command of the following form is applied: Fig. 2. Block diagram model of BLDC motor. (8) A. Load Torque Emulating Using the motor block diagram shown in Fig. 2, the following transfer functions can be obtained: transfer function between the motor speed and the phase voltage, while one-phase model of the BLDC motor is used [7], [12] B. Inertia Variations Emulating According to Fig. 2, the following relation is true for a BLDC motor with a real inertia change: (9) (1) where and the transfer function between the motor speed and the load torque (10) (2) is the inertia change ratio from its nominal value . and is equal to the output of the PID The applied voltage controller where is the torque constant, is the back electromotive force (emf) constant, is phase inductance, is phase resisis tance, is rotor inertia, is the viscous friction constant, is real load torque. Equation the applied phase voltage, and (2) could be rearranged as (3) The goal is to obtain effects similar to those caused by the real mechanical loading and real inertia variation without any mechanical parts supplementary to the electric motor of the studied electric drive, using DSP software only. From the block diagram of the proposed model, shown in Fig. 3, this goal can be obtained , but without any real load torque applied to the motor added to the output of the PID conwith a virtual load signal troller [8]. Using the proposed diagram one can see that the transfer function between the motor speed and the phase voltage remains as in (1). The transfer function between the motor speed and the is virtual load signal (11) The authors propose the configuration shown in Fig. 3, where there is no change of inertia inside the motor ( is nominal), but the effect of inertia deviation from its nominal value is obtained instead of . by inserting a virtual inertia change signal The signal is added to the output of the PID controller. According to Figs. 2 and 3, the following relation is true for a BLDC motor with a virtual inertia change: (12) but now (13) To achieve the goal, the left-hand sides of (9) and (12) must be equal. Therefore, the following relation must be true, using (9)–(13): (14) (4) Then, by taking out of brackets and making another realistic assumption about the mechanical time constant of the motor which can be rearranged as (15) (5) To achieve the goal, the right-hand sides of (3) and (5) must be equal. To accomplish this step, the following relation must be true: (6) the following is obtained: (16) KUPERMAN AND RABINOVICI: CONTROLLED ELECTRIC DRIVE 49 Fig. 3. Virtually loaded BLDC speed control block diagram. Fig. 4. Load and inertia emulation system. or (17) From (17), can be found, as follows: (18) Therefore, by applying the virtual inertia change signal of (18), one obtains the same motor behavior as in the case of a real inertia change. III. SIMULATION AND EXPERIMENTAL RESULTS In order to simulate and implement the proposed method, a circuit called the Virtual Disturbance Generator (VDG) was developed using Simulink [9] and simulated together with the motor and PID controller models. The whole system is shown in Fig. 4. The VDG, which emulates both load torque and inertia , must be change, is shown in Fig. 5. Note that when normalized because the transfer function between motor speed and load torque depends on . The system simulation was performed for two cases: first, a real load torque and inertia variation were applied to the motor, and then the real load torque was set to zero, and the inertia was set to its nominal value. The simulation was performed using the VDG that emulated the variations applied in the first simulation case. Finally, the system was implemented using Technosoft’s MCK240 Motion Control Kit based on Texas Instruments’ 16-b fixed-point TMS320F240 Digital Signal Processor. The BLDC motor parameters are as follows [10]: phase resistance of 7.5 ; phase inductance of 480 uH; back emf constant of 2.1 v/1000 r/min; torque constant of 20 m/A; rotor inertia ; mechanical time constant of 8.6 ms; and of 4.6 Kgm encoder resolution of 2000 lines/revolution. Obviously, there is a good reason to make the assumptions of (7) and (15). Simulations and implementation were performed using the following data: sample time of 1 ms, reference speed of 100 lines/sample for 0.3 s; 100 lines/sample for 0.3 s, load torque of 10 e-3 for 0.07 s 0.18 s and 0.25 s 0.75 s; for 0.18 s 0.25 s; 0 for 0.07 s and 0.75 s; inertia 50 IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 1, FEBRUARY 2005 Fig. 5. Virtual Disturbance Generator model. Fig. 6. MCK240 Motion Control Kit block diagram [10], [11]. change ratio of 1 for 0.25 s; and 10 for 0.25 s. The PID controller parametersare as follows: , , and . The laboratory setup consists of a Technosoft’s MCK240 Motion Control Kit, shown in Fig. 6, connected to a PC via RS-232 serial port. The MCK240 [11] is a development kit for the Texas Instruments TMS320F240 DSP controller applied to digital motor-control applications. The MCK240 provides a complete set of tools in order to quickly develop, implement, and test digital motor-control algorithms. It includes high-level graphical programming tools and a DSP board equipped with a three-phase inverter and a BLDC motor with an incremental encoder. The MCK240 motion kit is also combined with the extended software package MCWIN, running on a PC connected to the kit, which includes a basic monitor for serial communication with download/upload functions and debug facilities and a Windows Integrated Development Environment for assistance on performance evaluation of motor-control applications. All these tools offer a user-friendly graphical interface, which facilitates the development, implementation, and testing of DSP motor-control applications. Ready-to-run examples of ac and dc brushless motor speed control are contained in the BLAC/BLDC packages. The dynamic behavior of the real-time system can be easily analyzed during run time through the data acquisition and graphical display of all the system variables, thus permitting a quick optimization of the control algorithms. The control algorithms contained in the packages can be modified or replaced by a user. Simulation and implementation results are shown in Fig. 7. Subplots a–c graphically show the applied reference speed, load torque, and inertia change ratio, accordingly. Subplot d presents the simulation result of real load torque and inertia change application, while subplot e presents a virtual load and inertia change effect. The implementation result of the virtual disturbance application is shown in subplot f. The effect of inertia change is much greater than the effect of load torque; therefore, subplots g and h, which are zoomed versions of e and f, accordingly, are presented. They show the effect of virtual load torque application more clearly. Implementation results accurately follow theoretical results and simulations. IV. CONCLUSION This paper has developed a strategy for dynamic emulation of both torque load and inertia change of a brushless dc motor without any mechanical parts supplementary to the electric motor of the studied electric drive. Using digital signal processing software, virtual load torque and inertia changes are KUPERMAN AND RABINOVICI: CONTROLLED ELECTRIC DRIVE 51 Fig. 7. Simulation and experimental results. a—Reference speed; b—load torque; c—inertia change ratio; d—motor speed, real conditions simulation; e—motor speed, virtual conditions simulation; f—motor speed, virtual conditions experimental implementation; g—motor speed, zoomed subplot e; h—motor speed, zoomed subplot f. created, forcing an electric motor to behave as in the real variation case. The emulation could, thus, be used for different motor-control algorithms testing. The proposed algorithm has been simulated using Simulink and tested on a Technosoft’s MCK240 Motion Control Kit based on Texas Instruments’ TMS320F240 Digital Signal Processor. Experimental results have shown excellent equivalence with simulations. The developed algorithm could be used by educational laboratories, where inertia and load torque changes are difficult to implement mechanically for various reasons. The proposed method is used with laboratory works of the DSP Fundamentals in Power Electronics course at the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev. The presented approach of virtual loading and inertia change is also used by students to validate experimentally different control algorithms in their senior projects. REFERENCES [1] B. K. Bose, Microcomputer Control of Power Electronics and Drives. New York: IEEE Press, 1987. [2] W. Leonhard, Control of Electric Drives. Berlin, Germany: SpringerVerlag, 1997. [3] C. R. Wasko, “A universal AC dynamometer for testing motor drive systems,” in Conf. Rec. IEEE Industry Applications Soc. Annu. Meeting, 1987, pp. 409–412. [4] E. R. Collins and Y. Huang, “A programmable dynamometer for testing rotating machinery using a three-phase induction machine,” IEEE Trans. Energy Conversion, vol. 9, pp. 521–527, Sep. 1994. [5] R. W. Newton, R. E. Betz, and H. B. Penfold, “Emulating dynamic load characteristics using a dynamic dynamometer,” in Proc. Int. Conf. Power Electronics Drive Systems, vol. 1, 1995, pp. 465–470. [6] Z. H. Akpolat, G. M. Asher, and J. C. Clare, “Experimental dynamometer emulation of nonlinear mechanical loads,” IEEE Trans. Ind. Applicat., vol. 35, pp. 1367–1373, Nov.–Dec. 1999. [7] R. C. Dorf and R. H. Bishop, Modern Control Systems, CA: AddisonWesley, 1998. 52 [8] R. Rabinovici and A. Kuperman, “Virtual loading of electric drive,” in International Conference on Electrical Machines (ICEM) 2002, Brugge, Belgium, Aug. 25–28. [9] The MathWorks Inc., SIMULINK Dynamic System Simulation for MATLAB: User’s Guide Version 2.1, 1997. [10] Technosoft DSP Motion Solutions, MCK240 v1.0 User Manual: , 2001. [11] [Online]. Available: http://www.technosoft.ch/B2000/AllPages/ MCK240.htm [12] J. Chen and F. Rodriguez, “SPICE modeling of a resolver-to-digital converter for closed loop simulations of brushless DC motors,” in Proc. of the 26th Intersociety Energy Conversion Engineering Conf. (IECEC), Boston, MA, Aug. 4–9, 1991. [13] [Online]. Available: http://www.ee.bgu.ac.il/~alonk/PowerDSP Alon Kuperman was born in Republika Moldova, in 1977. He received the B.Sc., M.Sc., and M.B.A. degrees from Ben-Gurion University of the Negev, Beer-Sheva, Israel, in 1999, 2001, and 2002, respectively. He is currently working toward the Ph.D. degree at the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev. He is a Fellow of the Marie Curie Control Training Site with the Control and Power Group of Imperial College, London, U.K. His fields of interest are digital signal processing and control algorithms applied to the field of power electronics and electric drives. IEEE TRANSACTIONS ON EDUCATION, VOL. 48, NO. 1, FEBRUARY 2005 Raul Rabinovici (M83–SM’97) was born in Romania in 1950. He received the electrical engineering degree from the Polytechnic Institute of Jassy, Jassy, Romania, in 1972 and the Ph.D. degree in electrical engineering from Ben-Gurion University of the Negev, Beer-Sheva, Israel, in 1987. He is currently an Associate Professor with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev. He is a Member of The Editorial Board of JEE, the Internet Journal on Electrical Engineering. Over the past ten years, his principal field of interest has been electric drives, including electric machines, power electronic drivers, digital signal processing operation, and control algorithms. Prof. Rabinovici is a Member of the International Steering Committee of the Optimization of Electrical and Electronic Equipment (OPTIM) Conference, Brasov, Romania. He was a Member of the Editorial Board of The IEEE TRANSACTIONS ON MAGNETICS between 1996 and 1998.