Chapter 6 Design of Fuzzy-neural Controllers for DC Servo motors Using
6.3 The Hardware Structure and Experimental Results
The MT22R2-24 DC servomotor system shown in Fig.6-8 was made by SME Company. The module output of this motor and the output of motor are
shown in Fig.6-9. The output voltage of the control module is 10V and the output voltage of the motor is 75V (3000RPM). The specification of MT22R2-24 is shown in Table 6-1.
Fig.6-8 The MT22R2-24 DC servomotor
The control modules output (V)
The control modules output (V)
Fig.6-9 Relationship of the control modules input and output
Table 6-1 The specifications of MT22R2-24.
ITEM SPECIFICATION UNIT
Max. Voltage(V) 120 Volts Max. Speed(RPM) 5000 RPM Armature Moment of inertia(J) 0.0006 Kg-m^2
Torque Constant(Kt) 0.23 N-m/Amp Voltage Constant(Kb) 0.23 Volts-sec/Rad Resistance(R) 3.11809 Ohm Peak Stall Torque 8.0 N-m Acceleration at Peak Torque 13300 Rad/sec^2 Mechanical Time Constant 16 Milliseconds
B 0.00203 N-m-s/rad Motor Weight 4.1 Kg
The block diagram of hardware implementation is shown in Fig. 6-10.
The hardware structure is composed of a person computer, USB I/O 24 module, microcontroller (82G516), switching DC-DC converter and DC servo motor system. The proposed method is implemented by using the person computer with 5-ms sampling interval, and the servo driver motor system is controlled by Pulse-Width Modulation (PWM) method where switch-duty ratio D∈[-1,1] is varied to adjust the output of the Buck DC-DC converter.
The control input voltage in PC needs to be transformed into the switch duty ratio D, and then the servo driver motor system is controlled by the output voltage of the converter. The duty ratio of PWM is described as
u
1 , 75
Fig.6-10 The block diagram of hardware implementation Fig.6-10 The block diagram of hardware implementation
The experimental control system block diagram is shown in Fig. 6-11.
According to initial states, design parameters and reference signals, two experimental cases are given to test the performance of the controlled systems.
The experimental control system block diagram is shown in Fig. 6-11.
According to initial states, design parameters and reference signals, two experimental cases are given to test the performance of the controlled systems.
Fig. 6-11. Control system block diagram
The membership functions, the initial states and the adjustable parameters wf of ˆf are the same as section 6-2. In the case 1, the reference signal is set
as . The design parameters are set as , .
The tracking response is shown in Fig.6-12, Fig.6-13, and Fig.6-14. In the case 2, the desired reference signal is set as . The design parameters are set as ,
( 60sin(0.1 )
y td )= t c1 =15
0e−t
2 10
c =
( ) 60 10 y td = −
1 15
c = c2 =10. The tracking response is shown in Fig.6-15, Fig.6-16, and Fig. 6-17.
Fig. 6-12 The system output x1 and bounded reference r(case1)
Fig. 6-13. The tracking error e(case1)
Fig. 6-14. The control input u(t)(case1)
Fig. 6-15 The system output x1 and bounded reference r(case2)
Fig. 6-16. The tracking error e(case2)
Fig. 6-17. The control input u(t) (case2)
6.4 Conclusions
In this chapter, the RBAFC have been used in DC servo motor through simulation and experiment. Compare with experiment results, it is obvious that performance in simulation is better than in experiment with the same conditions. That results from the temperature of motor, the signal disturbance, the damage of component or equipment, the preciseness of circuits design and so on. However, the RBAFC still achieves the desired effect in position tracking of the servo motor experiment.
Chapter 7
Summaries and Suggestions for Future Research
7.1 Summaries
In general, the universal approximators are trained via gradient-based methods, which may only find a local minimum solution during the learning process. Therefore, in Chapter 2 of this thesis, we proposed a reduced simulated annealing optimization algorithm (RSAOA) to adjust the weightings of fuzzy-neural networks. From the off-line simulation results, a suited way of learning for the fuzzy-neural network is provided.
In Chapter 3, the RSA-based indirect adaptive fuzzy-neural controller (RIAFC) for uncertain nonlinear systems has been proposed by using a reduced simulated annealing algorithm (RSA). The weighting factors of the adaptive fuzzy-neural controller are tuned on-line via the RSA approach. For the purpose of on-line tuning these parameters and evaluating the stability of the closed-loop system, a cost function is included in the RSA approach. In addition, in order to guarantee that the system states are confined to the safe region, a supervisory controller is incorporated into the proposed method.
Simulation results have shown that the proposed RSA-based indirect adaptive fuzzy-neural controller (RIAFC) scheme can rapidly learn the unknown system dynamics, and achieve favorable tracking performance.
The RSAOA-based fuzzy neural backstepping control scheme has been proposed to control a class of SISO and MIMO nonlinear systems in Chapter 4 and Chapter 5, respectively. The control scheme incorporates the backstepping design technique with a fuzzy neural network. The weighting factors of the fuzzy neural controller are tuned on-line via the RSAOA approach. The free parameters of the fuzzy-neural controller can be successfully tuned on-line via
the RSAOA approach with a special evaluation mechanism. In order to guarantee that the system states are confined to the safe region, a supervisory controller is incorporated into the RSAOA-based fuzzy neural backstepping controller. Simulation results have shown that the proposed RSAO-based fuzzy neural backstepping control scheme can rapidly learn the unknown system dynamics, and achieve favorable tracking performance.
Experimental results are shown in Chapter 6. The RSAOA-based fuzzy neural backstepping control scheme has been used to control the MT22R2-24 DC servo motor. Experimental results verify the control scheme can achieve the desired effect in tracking.
7.2 Suggestions for Future Research
In this thesis, we only discuss with the affine nonlinear systems. The future research is recommended to work toward more general nonlinear systems.
References
[1] K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators, ” Neural Networks, no. 2, pp.
359-366, 1989.
[2] L. X. Wang, Adaptive Fuzzy Systems and Control, Prentice Hall, 1994.
[3] C. H. Wang, W. Y. Wang, T. T. Lee, and P. S. Tseng, “Fuzzy B-spline membership function (BMF) and its applications in fuzzy-neural control, ” IEEE Transactions on Systems Man and Cybernetics, Vol. 25, No. 5, pp. 841-851, May 1995.
[4] W. Y. Wang, Y.H. Chien, and I.H. Li, “ An On-Line Robust and Adaptive T-S Fuzzy-Neural Controller for More General Unknown Systems,”
International Journal of Fuzzy Systems, vol. 10, no. 1, pp. 33-43, 2008.
[5] C. T. Lin, and L. Siana, “An Efficient Human Detection System Using Adaptive Neural Fuzzy Networks,” International Journal of Fuzzy Systems, vol. 10, no. 3, pp. 150-160, 2008.
[6] S. Wu, M. J. Er, and Y. Gao, “A fast approach for automatic generation of fuzzy rules by generalized dynamic fuzzy neural networks,” IEEE Transactions on Fuzzy Systems, Vol. 9, pp.578-594, 2001.
[7] Y. G. Leu, W. Y. Wang, and T. T. Lee, “Robust Adaptive Fuzzy-Neural Controllers for Uncertain Nonlinear Systems,” IEEE Transactions On Robotics and Automation, Vol. 15, No. 5, pp. 805-817, October 1999.
[8] Y. G. Leu, T. T. Lee, and W. Y. Wang, “On-line tuning of fuzzy neural network for adaptive control of nonlinear dynamic systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 27, pp.
1034–1043, Dec. 1997.
[9] T. Y. Kim and J. H. Han, “Edge representation with fuzzy sets in blurred images,” Fuzzy Sets Syst., vol. 100, pp. 77–87, 1998.
[10] Z. Yang, T. Hachino, and T. Tsuji, “Model reduction with time delay combining the least-squares method with the genetic algorithm, ” IEE Proc. Control Theorem Appl., vol. 143, no. 3, 1996.
[11] W.Y. Wang, Y.G. Leu, and T.T. Lee, "Output-feedback control of nonlinear systems using direct adaptive fuzzy-neural controller,” Fuzzy Sets and Systems 140, pp. 341-358, 2003.
[12] W. Y. Wang, M. L. Chan, T. T. Lee, and C. H. Liu, “Recursive Back-stepping Design of Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems,” Asian Journal of Control, Vol. 4, No.3, Sept. 2002.
[13] W. Y. Wang, M. L. Chan, C. C. Hsu, and T. T. Lee, “H∞ Tracking-Based Sliding Mode Control for Uncertain Nonlinear Systems via an Adaptive Fuzzy-Neural Approach,” IEEE Trans. on System Man and Cybernetics-Part B, Vol. 32, No.4, pp.483-492. 2002.
[14] L. X. Wang, “A Supervisory Controller for Fuzzy Control Systems that Guarantees Stability,” IEEE Trans. On Automatic Control, Vol. 39, No. 9, pp.1845-1847, 1994.
[15] Y.G. Leu, T.T. Lee, and W.Y. Wang, "Observer-based Adaptive Fuzzy-Neural Control for Unknown Nonlinear Dynamical Systems,"
IEEE Trans. Syst. Man, Cyber. Part B: Cybernetics, vol. 29, no. 5, pp.583-591, Oct., 1999.
[16] C.H. Wang, H.L. Liu, T.C. Lin, “Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems,” IEEE Transactions on Fuzzy Systems, vol. 10, no.1, pp.39-49, 2002.
[17] K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Networks, no. 2, pp.
359-366, 1989.
[18] Li-Xin Wang, Adaptive Fuzzy Systems and Control, Prentice Hall, 1994.
[19] 感應機向量控制驅動器之PID控制器調適 王進力 淡江大學 電機工 程學系
[20] S Kirkpatrick, CD Gelatt Jr, MP Vecchi, “Optimization by Simulated Annealing,” Science Vol. 220. no. 4598, pp. 671 – 680, 1983
[21] J. Sheild, ‘”Partitioning concurrent VLSI simulation programs onto a multiprocessor by simulated annealing,”IEE PROCEEDINGS, vol.134, Pt.E,NO.1,JANURAY 1987.
[22] K. Kurbel, B. Schneider, and K. Singh, “Solving Optimization Problems by Parallel Recombinative Simulated Annealing on a Parallel Computer-An Application to Standard Cell Placement in VLSI Design, ” IEEE Transactions on Systems, MAN, AND CYBERNETICS-PART B:
CYBERNETICS, vol. 28, on,3, pp. 454-461, JUNE 1998.
[23] M. Gao, and J. Tian, “Path Planning for Mobile Robot Based on Improved Simulatded Annealing Artificial Neural Network,” Third International Conference on Natural Computation, 2007.
[24] P. Lucidarme, and A. Liegeois, “Learning Reactive Neuroconrtollers using Simulated Annealing for Mobile Robots,” Intf. Conference on Intelligent Robots and Systems, Oct. 2003.
[25] Y. Wang, W. Yan, and G. Zhang, “Adaptive Simulated Annealing for the optimal of Electromagnetic Devices,” IEEE Transactions on MAGNETICS, vol. 32, no.3, pp.1214–1217, May 1996.
[26] A. F. Atiya, A. G. Parlos, and L. Ingber, ”A Reinforcement Learning Method Based on Adaptive Simulated Annealing,” IEEE Circuits and Systems , vol. 1, pp.121–124, Dec. 2003.
[27] L. Ingber “Very fast simulated re-annealing,” Mathematical Computer Modelling, vol.12, no.8, pp. 967-973, 1989.
[28] S. J. Ho, L. S. Shu, and S. Y. Ho, “Optimizing Fuzzy Neural Networks for Tuning PID Controllers Using an Orthogonal Simulated Annealing Algorithm OSA,” IEEE Tranactions on Fuzzy Systems,vol.14,no.3,JUNE 2006.
[29] W.K. Ho, C.C.Hang,and J. Zhou,“Self-tuning PID control of a plant with under-dampd response with specifications on gain and phase margins, ”IEEE Trans. Control Syst. Technol .,vol.5, no.4, pp.446-452, Jul.1997.
[30] S. J.Ho, S. Y. Ho, and L.S. Shu, “OSA:orthogonal simulated annealing algorithm and its application to designing mixed H2/ H∞ optimal controllers,” IEEE Trans.Syst.,Man,Cybern.A,Syst. Humans, vol. 34, no.
5, pp.588-600,Sep.2004.
[31] S. Y. Ho, S.J.Ho,Y.k.Lin and C.C.W.Chu, “An orthogonal simulated annealing algorithm for large floorplanning problems,” IEEE Trans. Very Large Scale(VLSI)Syst., vol. 12, no. 8, pp.874-876,Aug. 2004.
[32] W. Y. Wnag, and Y. H. Li, “Evolutionary learning of BMF fuzzy-neural networks using a reduced-form genetic algorithm,” IEEE Trans. on Systems, Man and Cybernetics ,part B vol. 33, pp.966-976, 2003.
[33] R.A. Krohling, and J.P. Ray, “Design of optimal disturbance rejection PID controllers using genetic algorithms,” IEEE Trans. Evol.Comput., vol. 5, no. 1, pp.78-82,Feb. 2001.
[34] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth,A. H. Teller,and E.
Teller,“Equation of state calculations by fast computing machines,”
J.Chem.Phys., vol. 21, no. 6, pp.1087-1092,1953.
[35] T. Renyuan, S.Jianzhong, and L.Yan,”Optimization of electromagnetic devices by using intelligent simulated annealing algorithm,” IEEE Trans.
Magn.,vol.34,no.5,pp.2992-2995,Sep.1998.
[36] H. Szu and R. Hartley, “Fast simulated annealing,”Phys.Lett.,vol.122,pp.
157-162,1987.
[37] S.Yang, J.M.Machado,G.Ni,S.L.Ho,and P.Zhou,”A self-learning simulated annealing algorithm for global optimizations of electromagnetic devices,”IEEE Trans. Magn.,vol.36,no.7,pp.1004-1008,Jul.2000.
[38] M. Zhaung and D. P. Atherton, “Automatic tuning of optimal PID controllers,” Proc. Inst. Elect. Eng.,D, vol. 140, pp. 216-224, 1993.
[39] Y. S. Ahmed, S. Tomonobu, M. Tsukasa, U. Naomitsu, and F.
Toshihisa, ”Fuzzy Unit Commitment Scheduling Using Absolutely Stochastic Simulated Annealing,” IEEE Transactions on power systems, vol. 21, no. 2, May 2006.
[40] T. Satoh, and K. Nara, “Maintenance scheduling by using simulated annealing method [for power plants ,” IEEE Trans. Power Syst., vol. 6, no.2, pp. 850-857, May 1991.
[41] S. Y. W. Wang, “An enhanced simulated annealing approach to unit commitment,” Elect. Power Energy Syst., vol. 20, pp. 359-368, May 1998.
[42] F. Zhuang and F. D. Galiana, ”Unit commitment by simulated annealing,”
IEEE Trans. Power Syst., vol. 5, no.1, pp. 311-318, Feb. 1990.
[43] A. H. Mantawy, Y. L. Abel-Mogid, and S.Z. Selim, “A simulated annealing algorithm for unit commitment,” IEEE Trans. Power Syst., vol.
13, no.1, pp. 197-204, Feb. 1998.
[44] C. P. Cheng, C. W. Liu and C.C. Liu,” Unit commitment by simulated annealing algorithms,” Elect. Power Energy Syst., Vol. 24, PP. 149 –158, 2000.
[45] M. M. El-Saadawi, M. A. Tantawi, and E. Tawfik, “A fuzzy optimization based approach to large scale thermal unit commitment,” Elect. Power Syst. Res.,Vol. 72, pp.245–252, 2004.
[46] D. W. Jeffrey,” A simulated annealing algorithm for optimizing RF power efficiency in coupled-cavity traveling-wave tubes,” IEEE Transactions onelectron devices, Vol. 44, No. 12, Dec. 1997.
[47] S. Kirkpatrick, C. D. Gelatt Jr.,and M. P. Vecchi,”Optimization by simulated annealing,”Science, Vol.220, pp. 671-680, May 1983.
[48] E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines.New York: Wiley, 1989, pp. 88-91.
[49] A. Isidori, Nonlinear Control System. New York: Springer-Verlag, 1989.
[50] M. Krstic, I. Kanellakopoulos, and P.V.Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
[51] I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “Systematic design of adaptive controller for feedback linearizable system,” IEEE Transactions Automat. Contr., vol. 36, pp. 1241–1253, 1991.
[52] C. Kwan and F. L. Lewis, “Robust backstepping control of nonlinear systems using neural networks,” IEEE Transactions Syst., Man, Cybern.
A, vol. 30, pp. 753–765, 2000.
[53] T. Knohl and H. Unbehauen, “ANNNAC—extension of adaptive backstepping algorithm with artificial neural networks,” Inst. Elect. Eng.
Proc. Contr. Theory Appl., vol. 147, pp. 177–183, 2000.
[54] C. M. Kwan and F. L. Lewis, “Robust backstepping control of induction motors using neural networks,” IEEE Transactions Neural Networks, vol.
11, pp. 1178–1187, 2000.
[55] J. Y. Choi and J. A. Farrell, “Adaptive observer backstepping control using neural networks,” IEEE Transactions Neural Networks, vol. 12, pp.
1103–1112, 2001.
[56] Y. Zhang, P.Y. Peng, and Z.P. Jiang, “Stable Neural Controller Design for Unknown Nonlinear Systems Using Backstepping,” IEEE Transactions on Neural Networks, vol. 11, no. 6, November 2000.
[57] C.F. Hsu, C.M. Lin, and T.T. Lee, “Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems,” IEEE Transactions on Neural Networks, vol. 17, no. 5, September 2006.
[58] S. S. Sastry and A. Isidori, “Adaptive control of linearization systems,”
IEEE Transactions Automat. Contr., vol. 34, pp. 1123–1131, 1989.
[59] R. Marino and P. Tomei, “Globally adaptive output-feedback control of nonlinear systems, part I: Linear parameterization,” IEEE Transactions Automat. Contr., vol. 38, pp. 17–32, Jan. 1993.
[60] R. Marino and P. Tomei, “Globally adaptive output-feedback control of nonlinear systems, part II: Nonlinear parameterization,” IEEE Transactions Automat. Contr., vol. 38, pp. 33–48, Jan. 1993.
[61] I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “Systematic design of adaptive controllers for feedback linearizable systems,” IEEE Transactions Automat. Contr., vol. 36, pp. 1241–1253, Nov. 1991.
[62] W. Y. Wang, M. L. Chan, T. T. Lee, and C. H. Liu, “Recursive
Back-stepping Design of Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems,” Asian Journal of Control, Vol. 4, No.3, Sept. 2002.
[63] L. X. Wang, “A Supervisory Controller for Fuzzy Control Systems that Guarantees Stability,” IEEE Trans. On Automatic Control, Vol. 39, No. 9, pp.1845-1847, 1994.
[64] Y.G. Leu, T.T. Lee, and W.Y. Wang, "Observer-based Adaptive Fuzzy-Neural Control for Unknown Nonlinear Dynamical Systems,"
IEEE Transactions on Systems, Man, and Cybernetics. Part B:
Cybernetics, vol. 29, no. 5, pp.583-591, Oct., 1999.
[65] C.H. Wang, H.L. Liu, T.C. Lin, “Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems,” IEEE Transactions on Fuzzy Systems, vol. 10, no.1, pp.39-49, 2002.
[66] W. Y. Wang, C. Y. Cheng, and Y. G. Leu, “An online GA-based output-feedback direct adaptive fuzzy-neural controller for nonlinear systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 34, pp.334-345, February. 2004.
[67] 結合基因演算法和模擬退火法在機組排程決策之應用 張振松 南開技 術學院資管系
[68] J. E. Slotine and W. Li, Applied Nonlinear Control. Englewood Cliffs, NJ:
Prentice-Hall, Inc., 1991.
[69] S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness, Englewood Cliffs, NJ: Prentice-Hall, 1989.
[70] Y. Tang, M. Tomizuka, G. Guerrero, and G. Montemayor, “Decentralized robust control of mechanical systems,” IEEE Trans. Automat.Contr.,vol.
45, pp. 771-776, Apr.2000.