Novel_Robust_Control_Algorithm_of_DC_Motors

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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/228336566 Novel Robust Control Algorithm of DC Motors Article · January 2009 CITATIONS 2 READS 1,865 3 authors , including: Some of the authors of this publication are also working on these related projects: A Study on Life Cycle of Twisted String Actuators View project Nonlinear Control of Soft Growing Robots View project Jee-Hwan Ryu Korea Advanced Institute of Science and Technology 201 PUBLICATIONS 5,283 CITATIONS SEE PROFILE All content following this page was uploaded by Jee-Hwan Ryu on 11 August 2014. The user has requested enhancement of the downloaded file.

Novel Robust Control Algorithm of DC M otors Ba-Hai Nguyen Korea University of Technology and Education nguyenbahai@hocdelam.org Hai-Bac Ngo Korea University of Technology and Education ngohaibac@hocdelam.org Jee-Hwan Ryu Korea University of Technology and Education jhryu@kut.ac.kr Abstract - In this paper, a novel speed control algorithm of DC motors is presented. The key contribution here is a simple speed controller only with speed feedback and without an inner current control loop. This is possible by adjusting the reference speed based on a certain rule. Therefore, the proposed speed controller here becomes simpler while maintaining the control performance. Moreover, with the proposed controller, the system response can be tuned with less complexity. This proposed control method is investigated both mathematically and experimentally. Keywords - DC motor control, speed control of motor, robust control of DC motor, angular velocity control. 1. I NTROD U CTION Direct current (DC) motors are widely used in industrial applications including mechatronics, automobile, robotics, and aerospace systems [1, 2]. In those applications, speed control is one of the most essential aspects. It includes the speed control of mobile robots, CD-ROM, electrical screw driver, computer hard-disk, and so on. In general, an accurate speed control scheme requires two closed-loops, an inner current control loop [1,3] and an outer speed control loop. In this paper, a novel robust control method of DC motors is presented. Our proposed speed control algorithms for DC motors need only a simple PWM signal. The current control loop can be removed while the performance of the system is maintained. Moreover, after this method is developed, a simpler controller as well as a less complex tuning method is possible. 2. G E N E RA L SP EE DC ONTRO L M E T H OD O F DC M OTORS 2.1 DC motor modeling The electrical diagram of the permanent magnet DC motor is shown as Fig. 1. According to the Kirchhoff law, the electrical equation of DC motors can be expressed as in Equation (1). Fig. 1. Electrical diagram of permanent magnet DC motors By applying the Newton's law and Kirchhoff's law to the DC motor system, we come up with mathematical equation (1) and (2) of DC motors. Ea Ri dt di L V . . (1) m b J W 4 . 4 x x x (2) Where, V is the supply voltage, i the armature current, Ea is the back-emf (electromotive force). L and R are the electric inductance, and electric resistance respectively. J is the moment of inertia of the rotor, b is the damping ratio of the mechanical part. The motor torque, m W , is related to the armature current, i , by a constant factor t k (In SI units, t k (armature/torque constant) is equal to e k (motor/speed constant)). The back emf, E is related to the rotational speed by the equation (3). i k t m . W (3) 2.2 Typical speed control structure for DC motors Figure 2 illustrates a typical speed control structure of DC motor [4-6]. Fig. 2. A typical speed control structure for DC motor The control scheme consists of an inner current control loop and an outer speed control loop. The output signal of speed controller is the input of the current controller. Those two controllers can be designed independently because the mechanical dynamics of the system is usually much slower than the dynamics of the armature circuit. Reference speed ref Z is the desired speed which the motor should be achieved after a designed time. The controller found in typical industrial systems is PID control algorithm. It can also be included fuzzy, neural network, or adaptive controllers. The current sensor and 119 The 6th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2009)

encoder are usually used as feedback devices in the system. The general equation of a PID controller can be seen in [7-8]. ) ( t U is the output signal of PID controller which is the summation of proportional term, integral term, and derivative term. dt t de K dt t e K t e K t U d t i p ) ( ) ( ) ( ) ( 0 . ³ . . With a large proportional gain ) ( p K , the system enhances faster response and causes a larger error. An excessively large proportional gain will lead to instability and oscillation of the system. With a larger integral gain ( i K ), the steady state errors of system are reduced more quickly. With a larger derivative gain ( d K ), the overshoot of system can be reduced. But the derivative gain also plays as a damper of the system. In addition, the noise amplification in the differentiation of the error may make the system unstable. There are several methods to calculate these three terms. The reference [8] provides the detail of all tuning methods. 3. N O VEL R O BU ST SP EE DC ONTRO L A LG ORIT HM S 3.1 Overvie w of proposed speed control algorithms To simplify the speed control of DC motors, we have proposed a new control scheme shown in Fig. 3. The novel concept here which is the original reference speed is multiplied by the gain m . The modified reference now becomes the reference input of the controller. With this modification, the current control loop can be removed in the control scheme while steady-state error can be converged to zero. The detail analysis of steady-state error and the method to find the exact value of m are presented in session 3.2. Fig. 3. Proposed scheme for motor speed control 3.2 M athematical analysis of the proposed algorithm Let consider a P controller for speed control loop in typical control scheme in Fig. 3. The closed loop system can be described as: ref DCM p DCM p m G K G K Z Z . 1 Where, B Js G DCM . 1 and s d ref : Z s B Js K m K d p p : . . ¡o ¡ Z B Js K m K s s p d p s s ss . . : " 0 " 0 lim ] ). ( [ lim 0 0 Z Z . B K m K p d p . : . p p d ss K B K m . ¡o m : Z Where, B represents the effective damping [9]. This analysis means that the steady state speed is equal to d : when m is equal to p p K B K / ) ( . . In other word, if a p K is given, it is always possible to find a value of m which make the steady state speed the same as the reference speed. However, p K must not be equal to zero. Let consider the system with PD controller shown as in Fig. 4. Fig. 4. Proposed control algorithm with PD control The output speed of motor Z will be: . ) ( ) ( s B Js s K K m s K K d d p d p : . . . . ¡o ¡ Z B Js s K K m s K K s s d p d d p s s ss . . . : . " 0 " 0 ) ( ) ( lim ] ). ( [ lim 0 0 Z Z . B K m K p d p . : . p p d ss K B K m . ¡o m : Z This means if a p K is given, it is always possible to find a value of m which make the steady state speed the same as the reference speed. In other words, the proposed control algorithm is not affected by the derivative term. 4. E X P E RI ME NT AND R E S UL T 4.1 E xperimental setup The experiment was set as in Fig. 5. A DC maxon motor was used. The encoder had 4096 pulse/revolution. An PCI board (NI PCI 7356) was used to connect the DC motor with a user interface developed in LabVIEW environment. Kp G DCM + - m ref Z Z Kp G DCM + - Kd.de/dt + + m ref Z Z 120 The 6th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2009)

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Fig. 5. Proposed scheme for motor speed control In the PID control experiment, a Maxon motor driver is used. The Maxon motor driver has current mode control. Therefore, the current loop control can be easily implemented. In the experiment based on the proposed method, a simple H-bridge motor driver is used. The PWM signal is generated using LabVIEW function. In addition, the proposed control algorithm and a graphical the user interface (GUI) are programmed in LabVIEW environment shown in Fig. 6. The GUI allows users to set the reference speed, and observe the acquired data. User may change two control modes, PID control and robust control by swiching a button. Fig. 6. The proposed control algorithm and graphical user interface are developed. 4.2 E xperimental result The first experiment was conducted with conventional PID control of motor speed. The Z iegler–Nichols method was used to tune the PID controller. In Fig. 7, the result of this experiment showed noise behavior due to the change in sign of error. To explain this more clearly, it is important to notice the difference between position control technique and speed control. In position control, once the position error reaches zero the control signal should be zero. However, the control signal must remain at a stable value when speed error approaches zero. Fig. 7. Experimental result of conventional PID control The second experiment was carried out based on the proposed robust control algorithm. The system damping is found to be 4 . 41 . The gain Kp _robust was set to be equal 23. Therefore, m was calculated as follows: 8 . 2 23 4 . 41 23 _ _ . . roboust p roboust p K B K m . The detail of how to calculate B is provided in [9]. With a certain value of Kp , m will have approximate value. The result of this experiment is shown in Fig. 8. Fig. 8. Experimental result of proposed control method with 23 Kp , and m=2.8. To demonstrate the tuning technique, the experiment was conducted with the second set of Kp and m , and the result is shown in Fig. 9. The steady state speed can follow the reference speed set. Fig. 9. Experimental result of proposed control method with 5 1 Kp , and m=3.76. GUI NI PCI 7356 Encoder Maxon Motor Motor Driver 121 The 6th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2009)

Figure 10 shows the experimental result of varying reference speed. The measured speed follows reference speed with error 4%, and setting time is 30 ms. Fig. 10. Experimental result of proposed control method with 5 1 Kp , and m=3.76. Figure 11 shows the comparison of the noise behaviour of the conventional PID controller and the proposed controller. With the proposed control algorithm, the noise was reduced about 25% compared with the PID controller. During the experiment, it was evaluated that the proposed controller made the motor run smoother and more quite. Fig. 11. Comparison of noise in PID controller and proposed controller. The comparison of the conventional PID control and the proposed robust control algorithm is provided in [Table 1]. With the proposed method, noise behavior can be reduced and the tuning technique is very simple because there is no requirement of finding Ki and Kd. Table 1 Comparison of conventional PID controller and the proposed robust controller F ACTORS TO BE CO M PAR E D PID SP EE D CONTRO LLE R RO BU ST SP EE D CONTRO LLE R PERFORMANCE Noise Less Noise IMPLEMENTATION Complex Tuning Technique Easy Tuning technique 5 . C ONC LU SION In this research, a novel and simple robust control algorithm of motor’s speed was proposed. The proposed method has an advantage in both noise reduction and simple tuning method. Moreover, this controller does not require an inner loop current control. The feasibility of the proposed method was demonstrated with mathematical analysis and experimental results. A CKNO WLE D GEME NT This research was financially supported by the Ministry of Education, Science Technology (MEST) and Korea Industrial Technology Foundation (KOTEF) through the Human Resource Training Project for Regional Innovation. R EFE R E NC E S [1] S. C. Won D. J. Lim D. H. Chyung, “D-C motor driven robotic manipulator control,” IEEE Decision and Control, Vol. 24, pp. 330-333, 1985. [2] Ba-Hai Nguyen, Jee-Hwan Ryu, “Direct Current Measurement Based Steer-By-Wire Systems for Realistic Driving Feeling,”, Proceedings of the IEEE International Symposium on Industrial Electronics, pp. 1023-1028, 2009. [3] Kenji KANEKO et al., “High Stiffness Torque Control for a Geared DC Motor Based on Acceleration Controller,” Industrial Electronics, Control and Instrumentation, 1991. Proceedings, vol.1, pp. 849 – 854, 1991. [4] Mohamed Abdelati, “FPGA-Based PID Controller Implementation,” The Islamic University of Gaza. [5] Y. F. Chan, M. Moallem, W. Wang, “Efficient implementation of PID control algorithm using FPGA technology,” Proceedings of the 43ed IEEE Conference on Decision and Control, V5, PP. 4885-4890, Bahamas 2004. [6] J. Tang, “PID controller using the TMS320C31 DSK with on-line parameter adjustment for real-time DC motor speed and position control,” IEEE International Symposium on Industrial Electronics, V2, PP 786-791, Pusan 2001. [7] Ang K., Chong G., Li Y., “PID control system analysis, design, and technology,” IEEE Trans. Control System Technology, vol. 13, p. 559 – 576, Jul. 2005. [8] Wikipedia.org/wiki/PID_controller. [9] Mark W. Spong, Seth Hutchinson, M. Vidyasagar, “Robot Modeling and Control,”, Wiley, 2006. PID CONTROLLER PROPOSED CONTROLLER 122 The 6th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2009) View publication stats