POSITION TRACKING PERFORMANCE OF AC SERVOMOTOR BASED ON NEW MODIFIED REPETITIVE CONTROL STRATEGY

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2 simulink tool of MATLAB platform directly and it provides a multifunction, high speed analog to digital converter (ADC) and digital to analog converter (DAC). Figure 1. Experimental setup Figure 2. Closed loop hardware configuration of AC servo motor 3. IDENTIFICATION OF MODEL PARAMETERS AND CONTROLLERSETTINGS 3.1 AC Servo Motor Dynamics The model of the system consists of a motor coupled to a gear box and an inertia load rigidly fixed to output shaft. The control torque (T c ) for the two phase AC servo motor is described as T C =k 1 E(t) k 2 θ (t) (1) Where T C = Control torque (Nm) k 1 & k 2 = motor constants (Nm/V, Nm/rad/s) - identified parameters from experimental test. θ = angular velocity of the AC servo motor (rad/s) E = rated input voltage (v) The dynamic equation of the mechanical system is given by T C =Jθ Bθ T L (2) 120

3 Where = angular position of the AC servo motor (rad) θ = angular acceleration of the AC servo motor (rad/s 2 ) B = Friction coefficient J = Moment of inertia (Kg.cm 2 ) By equating (1) and (2) Jθ Bθ T L = k 1 E(t) k 2 θ (t) (3) Taking laplace transform the above equations becomes K 1 E(s) k 2 sθ(s) = Js 2 θ(s) Bsθ(s) T L (s) (4) The transfer function between θ(s) and E(s) is obtained by putting T L (s) = 0 θ(s) E(s) = K 1 Js 2 K 2 sbs = K m s(τ m s1) WhereK m = K 1 K 2 B Km = Motor gain constant τ m = Motor time constant The specifications of AC servo system, which has considered for real-time study, are given in table.1.by using equation (5) and considering the numerical values in Table.1, the identified transfer function model for the AC servo system is given as and τ m = J K 2 B G(s) = 0.4 s(2.7763s 1) Table 1. AC servo motor Specifications Type GSM62AE Voltage 230V Power 100W Speed 50 rpm Moment of inertia (J) kg.cm 2 Friction coefficient (B) GB ratio 36 Radius of the output shaft m 3.2 PD Controller Design A proportional derivative (PD) controller is designed to control the position of AC servo system. The PD controller parameters (Kc and Kd) are tuned using signal constraint block of simulink optimization tool in MATLAB platform [16]. The signal constraint is a block where response signals can be graphically constrained and model parameters are automatically optimized to get the performance requirements (refer table.2). Based on the model parameters and performance requirements, the optimized PD controller settings are identified as Kc = and Kd = Table 2. Performance specification for PD control system Rise time (t r ) 20 Settling time (t s ) 22.2 Over shoot (Mp) 20% 4. REPETITIVE CONTROL STRATEGY (RCS) Repetitive control strategy [17] is designed especially for tracking a periodic reference signal and rejecting a periodic load signal. The design of repetitive control strategy (RCS) is based on the Internal Model Principle (IMP) and it is proposed by Wonham and Francis [18]. The IMP states that if any exogenous signal can be regarded as the output of an autonomous system, the inclusion of the model of the signal in a stable closed-loop system can assure perfect tracking or complete rejection of the signal. Ls e The RCS includes the factor which has poles at jk 2π, k = 0, 1,.., (corresponding to the harmonic Ls L 1 e and sub harmonics of the basic period L), the controller can track any periodic signal and reject any disturbance of (5) 121

4 period L. Based on this concept, RCS is constructed with a model of structure is given in Figure 3. e 1 e Ls Ls. The basic Repetitive control Periodic disturbance Periodic reference Trajectory - Error of the current run e -L s Integrated Error of the previous run G (S) Figure 3. Repetitive Control Strategy 5. NEW MODIFIED REPETITIVE CONTROL STRATEGY (NMRCS) For high frequency signals, certain uncertainty is present in the model of AC servo motor system. Due to this uncertainty, noise has a great influence on the response, which intern affects the stability of the system. To trounce this problem, a low-pass filter, Q(s) is added to the existing RCS control loop and to ensure system stability. This modified structure is known as Modified Repetitive Control Strategy (MRCS) as proposed by Hara et al [17]. For further enhancement of stability in MRCS, a New Modified Repetitive Control Strategy is proposed in this work and the proposed structure is given in Figure 4. Since the stability is directly related to sensitivity, the sensitivity function is considered in this proposed structure. In addition, a rational factor is also incorporated in this new structure. Periodic disturbance Periodic reference Trajectory - Error of the current run e -Ls Integrated Error of the previous run Q(s) C(s) G(s) V Figure 4. New Modified Repetitive Control Strategy 5.1 Sensitivity From the above figure, the sensitivity function of the proposed scheme is derived as 5.2 Rational Factor By optimization technique, the stable rational factor (V) in equation (6) is identified by formulating minimum tracking error as objective function. The identified value of V for AC servo motor is 0.1. (6) 122

5 Phase (deg) Magnitude (db) IJRRAS 10 (1) January Low pass filter design A first order continuous time low pass filter is considered here. i.e Q(s) =,where ω c is the cut-off frequency in rad /sec. The cut-off frequency (0.3), is obtained from the Bode plot of AC servo motor system (Ref: Figure 5). 100 Bode Diagram Frequency (rad/sec) Figure 5. Bode plot of the AC servo motor system 6. RESULTS AND DISCUSSIONS 6.1 Real-Time Run An input reference periodic signal with known period (L = 62) and amplitude (V pp = 5) is generated and is applied to AC servo motor system with NMRCS based PD controller. The tracking response is recorded in Figure 6. In addition, an experimental runs of RCS based PD control strategy and conventional PD mode control strategy are carried out and responses are traced in Figure 7 and Figure 8. In all the cases the nominal operating point of 40% position angle is maintained. From the Figures 6-8, the tracking errors are calculated with respect to time and results are charted in Figure 9. It is observed that NMRCS in control loop is capable of tracking dynamic periodic reference trajectories with minimum error. To check the robustness of the NMRCS, a real-time runs of the AC servo motor system for a periodic input signal having different known periods and amplitude (L= 62,Vpp= 6) & (L= 45,Vpp = 5) are carried out. Figures (10 to 17) justify the robustness of NMRCS in AC servo motor system. Figure 6. Tracking response of periodic reference trajectories [Period (L) =62, amplitude (V pp ) =5, Operating point = 40%] with NMRCS based PD mode 123

6 Figure 7. Tracking response of periodic reference trajectories [Period (L) =62, amplitude (V pp ) =5, Operating point = 40%] with RCS based PD mode Figure 8. Tracking response of periodic reference trajectories [Period (L) =62, amplitude (V pp ) =5, Operating point = 40%] with Conventional PD mode Figure 9. Tracking error response for NMRCS, RCS and PD control strategies [Period (L) =62, amplitude (V pp ) =5, OP = 40%] 124

7 Figure 10. Tracking response of periodic reference trajectories [Period (L) =62, amplitude (V pp ) =6, Operating point = 40%] with NMRCS based PD mode Figure 11. Tracking response of periodic reference trajectories [Period (L) =62, amplitude (V pp ) =6, Operating point = 40%] with RCS based PD mode Figure 12. Tracking response of periodic reference trajectories [Period (L) =62, amplitude (V pp ) =6, Operating point = 40%] with Conventional PD mode 125

8 Figure 13. Tracking error response for NMRCS, RCS and PD control strategies [Period (L) =62, amplitude (V pp ) =6, OP = 40%] Figure 14. Tracking response of periodic reference trajectories [Period (L) =45, amplitude (V pp ) =5, Operating point = 40%] with NMRCS based PD mode Figure 15. Tracking response of periodic reference trajectories [Period (L) =45, amplitude (V pp ) =5, Operating point = 40%] with RCS based PD mode 126

9 Figure 16. Tracking response of periodic reference trajectories [Period (L) =45, amplitude (V pp ) =5, Operating point = 40%] with Conventional PD mode Figure 17. Tracking error response for NMRCS, RCS and PD control strategies [Period (L) =45, amplitude (V pp ) =5, OP = 40%] 6.2 Sensitivity Analysis Figure 18 shows the magnitude of sensitivity function for all the two control strategies such as RCS and NMRCS. It seems that the sensitivity at the period frequencies is smaller in NMRCS configuration as compared to RCS configuration. It clearly indicates that in NMRCS errors are minimized at period frequencies and shows the good tracking performance. 127

10 Phase (deg) Magnitude (db) IJRRAS 10 (1) January Proposed NMRCS Original RCS Frequency (Hz) Figure 18. Magnitude of the sensitivity function 7. CONCLUSION A new modified repetitive control strategy is proposed in this work for a AC servo motor system. Real-time implementation of the proposed strategy in AC servo motor system is done and tracking of periodic signal with this new control strategy is analysed. Performance analysis is identified in terms of tracking error. A comparative analysis with another control strategy (RCS) is also carried out. The result clearly shows the supremacy of the proposed NMRCS in Ac servo motor system. 8. ACKNOWLEDGEMENT We are cheerfully showering our heartfelt thanks to Prof.dr.ir.M.Steinbuch, Professor, Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands, for valuable suggestions. 9. REFERENCES [1]. Yoshitsugu, J.,Hiraki, E.,Nakaoka, M., Inoue, K. Active edge-resonant DC link snubber-assisted three phase soft switching inverter for AC servo drive, IEEE Confer Ind Electron Control Instrum, (2001). [2]. Huth, G. Permanent-magnet-excited AC servo motors in tooth-coil technology. IEEE Trans Energy Convers, 20(2), 300 7, (2005). [3]. Yoneya, A., Yoshimaru, K.,Togari, Y. Self-sensing control of AC-servo motor with DSP oriented observer. ProcAdv Motion Control, (2000). [4]. Yamaji, K., Mizuno, T., Ishii, N. The motor driving control of X Y Z table utilizing photoelectric device and optical pattern recognition, IECON, (1992). [5]. Chen, J Y. An integration design approach in PID controller, IPMM, (1999). [6]. Tang, K S., Kim, F M.,Guanrong, C.,Kwong, S. An optimal fuzzy PID controller. IEEE Trans Ind Electron,48(4), , (2001). [7]. Asano, M., Yamamoto, T., Oki, T.,Kaneda, M A. Design of neural-net based predictive PID controllers. IEEE SMC, 4, , (1999). [8]. Cuiyan,L.,Dongchun, Z.,Xianyi,Z. Theory and Applications of the Repetitive Control. SCIE Annual Conference, Sapporo, (2004). [9]. Yao,W S., Tsai, M C. Analysis and estimation of tracking errors of plug-in type repetitive control systems. IEEE Transactions on Automatical Control, 50(8), , (2005). [10]. Inoue,T.,Iwai,S.,Nakano,M. High accuracy control of a Proton synchrotron magnet power supply, in Proc 8 th IFAC WorldCongress, (1981). [11]. Inoue,T.,Nakano,M.,Iwai,S. High accuracy control of servo mechanism for repeated contouring, in Proc 10 th annual symposium on Incremental Motion, Control System and Devices, (1981). [12]. Fujimoto,H.;Hori,Y. High speed robust visual servoingbased onintersample estimation and multirate control, 7 th International Workshop on Advanced Motion Control, (2002). [13]. Rodriguez,H.,Pons,J L., Ceres, R A. ZPET-repetitive speed controller for ultrasonic motors, in Proc. leee Int. Conf. Robotics and Automation, (2000). [14]. Choi, G S., Lim, Y A.,Choi,G H. Tracking position control of piezoelectric actuators for periodic reference inputs. Mechatronics,5(12), , (2002). [15]. Fung, R F.,Huang, J S.,Chien, C C. Design and application of a continuous repetitive controller for rotating mechanisms. Int. Journal. of Mechanical Sciences, 42(9) , (2000). [16]. ManafeddinNamazov.,OnurBasturk. DC motor position control using fuzzy PD controllers with differenedefuzzyfication methods. Turkish journal of fuzzy systems, 1(36), 36-54, (2010). [17]. Hara, S., Yamamoto, Y.,Omata, T.,Nakano,M. Repetitive Control-System -A New Type Servo System for Periodic Exogenous Signals. IEEE Transactions on Automatic Control, 33, , (1998). [18]. Francis, B A.,Wonham, W M. Internal Model Principle for Linear Multivariable Regulators. Journal of Applied Mathematics and Optimization, , (1975). 128

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