Adaptive Predictive PID Controller Based on Elman Neural Network with Hierarchical BP Algorithm

基於Elman類神經網路與Hierarchical演繹法之適應預估PID控制器

10.29548/BGYY.201109.0010

呂奇璜(Chi-Huang Lu)；呂奇明(Chi-Ming Lu)；常元海(Yuan-Hai Charng)

Elman類神經網路 ； Hierarchical演繹法 ； 模型預估控制 ； PID控制器 ； Elman neural network ； hierarchical BP algorithm ； model predictive control ； PID controller

修平學報

23期（2011 / 09 / 01）

175 - 188

英文

本論文提出以Elman類神經網路(ENN)做為非線性系統之預估比例－微分－積分(PID)控制器。ENN具備有及時學習與好的近似能力，是用來估測受控系統的非線性函數。ENN辨識器係以Hierarchical演繹法與與適應學習率來學習ENN的權重值，適應學習率可確保ENN辨識器收斂。這預估PID控制器是藉由預估性能指標來推導，適應最佳率可確保所提PID控制器收斂；而閉迴路控制系統由離散Lyapunov穩定準則來進行穩定分析。數值模擬指出所提控制策略具備了滿意的設定點追蹤與擾動排除的性能。

This paper presents a predictive proportional-integral-derivative (PID) controller based on Elman neural network (ENN) for a class of nonlinear systems. The ENN with both online learning and well approximation capability is employed to estimate the nonlinear function of the controlled system. The weights of the ENN identifier are trained by the hierarchical backpropagation algorithm with the adaptive learning rate, the adaptive learning rate is suitable for the ENN identifier can be convergent. The predictive PID controller is derived via a predictive performance criterion and the adaptive optimal rate for guaranteeing the convergence of the proposed PID controller. The stability analysis of the closed-loop control system is presented by the discrete Lyapunov stability theorem. Numerical simulations reveal that the proposed control law gives satisfactory tracking and disturbance rejection performances.

1. Adetona, O.,Garcia, E.,Keel, L. H.(2000).A new method for the control of discrete nonlinear systems using neural networks.IEEE Transactions on Neural Networks,11(1),102-109.
2. Allgöwer, F.,Zheng, A.(2000).Nonlinear Model Predictive Control.Birkhäuser Verlag.
3. Camacho, E. F.,Bordons, C.(1999).Model Predictive Control.Springer-Verlag.
4. Clarke, D. W.,Mohtadi, C.(1989).Properties of generalized predictive control.Automatica,25(6),859-857.
5. Ge, S. S.,Zhang, J.,Lee, T. H.(2004).Adaptive neural network control for a class of MIMO nonlinear systems with disturbances in discrete-time.IEEE Transactions on Systems, Man, Cybernetics B,34,1630-1645.
6. Granado, E.,Colmenares, W.,Bernussou, J.,García, G.(2003).Linear matrix inequality based model predictive controller.IEE Proc. Control Theory Appl,150,528-533.
7. He, P.,Jagannathan, S.(2007).Reinforcement learning neural-network-based controller for nonlinear discrete-time systems with input constraints.IEEE Transactions on Systems, Man, Cybernetics B,37(2),425-436.
8. He, P.,Jagannathan, S.(2007).Reinforcement learning neuralnetwork-based controller for nonlinear discrete-time systems with input constraints.IEEE Transactions on Systems, Man, Cybernetics B.,37(2),425-436.
9. Huang, S.,Tan, K. K.,Lee, T. H.(2002).Applied Predictive Control.Springer-Verlag.
10. Kouvaritakis, B.,Cannon, M.(2001).Nonlinear Predictive Control - Theory and Practice.London:IEE.
11. Kremer, S. C.(1995).On the computational power of Elman-style recurrent networks.IEEE Transactions on Neural Networks,6,1000-1004.
12. Kwiatkowski, A.,Werner, H.,Blath, J. P.,Ali, A.,Schultalbers, M.(2009).Linear parameter varying PID controller design for charge control of a spark-ignited engine.Control Engineering Practice
13. Lee, C. C.,Lee, Y. H.,Teng, C. C.(2002).A novel robust PID controller design by fuzzy neural network.Asian Journal of Control,4(4),433-438.
14. Lin, F. J.,Hung, Y. C.,Chen, S. Y.(2009).FPGA-based computed force control system using Elman neural network for linear ultrasonic motor.IEEE Transactions on Industrial Electronics,56,1238-1253.
15. Lu, C. H.,Tsai, C. C.(2008).Adaptive predictive control with recurrent neural network for industrial processes: an application to temperature control of a variable-frequency oil-cooling machine.IEEE Transactions on Industrial Electronics,55(3),1-10.
16. Lu, C. H.,Tsai, C. C.(2007).Generalized predictive control using recurrent fuzzy neural networks for industrial processes.Journal of Process Control,17,83-92.
17. Maciejowski, J. M.(2002).Predictive Control with Constraints.Prentice Hall.
18. Narendra, K. S.,Parthasarathy, K.(1990).Identification and control of dynamical systems using neural networks.IEEE Transactions on Neural Networks,1,4-27.
19. Potocink, P.,Grabec, I.(2002).Nonlinear model predictive control of a cutting process.Neurocomputing,43,107-126.
20. Rawlings, J. B.(2000).Tutorial overview of model predictive control.IEEE Control Systems Magazine,20(4),38-52.
21. Sales, K. R.,Billings, S. A.(1999).Self-tuning control of nonlinear ARMAX model.International Journal of Control,51,753-769.
22. Wai, R. J.,Lin, F. J.(2001).Adaptive recurrent-neural-network control for linear induction motor.IEEE Transactions of Aerospace
23. Woo, T. K.(2001).Fast hierarchical least mean square algorithm.IEEE Signal Processing Letters,8(11),289-2914.
24. Yang, S. S.,Ho. C. L.,Lee, C. M.(2006).HBP: improvement in BP algorithm for an adaptive MLP decision feedback equalizer.IEEE Transactions on Circuits and Systems II,53(3),240-244.
25. Yoo, S.J.,Choi, Y. H.,Park, J. B.(2006).Generalized predictive control based on self-recurrent wavelet neural network for stable path tracking of mobile robots: adaptive learning rates approach.IEEE Transactions on Circuits and Systems I,53(6),1381-1394.
26. Zheng, J. M.,Zhao, S. D.,Wei, S.G.(2009).Application of self-tuning fuzzy PID controller for a SRM direct drive volume control hydraulic press 2009.Control Engineering Practice
27. Ziegler, J. G., & Nichols, N. B. (1942). Optimum settings for automatic controller. Transactions on ASME, 62, 759-768.