Comparative Analysis of Evolutionary Computation Based Gain Scheduling Control for Ball and Plate Stabilization System

Abstract

The platform stabilization systems used in marine, airborne or land vehicle applications are controlled with very different control methods basically including linear, nonlinear and artificial intelligence-based design techniques. Nowadays, evolutionary computation based optimization algorithms also provide new opportunities to engineers in order to design a gain scheduling controller. In this study, an evolutionary computation based gain scheduling controller is proposed for a ball and plate system so as to examine its control performances on a stabilization system. For this purpose, the swarm intelligence based Particle Swarm Optimization (PSO) and evolutionary algorithm based Differential Evolution (DE) algorithms are chosen due to their better performance than the other evolutionary computation algorithms. The results are comparatively investigated by using time domain and frequency domain analysis methods. Additionally, the robustness analysis is also applied to examine the tuning performances of these controllers in case of changing system parameters in the range of ±50%.

Keywords

• Platform stabilization,Ball and plate system,Gain scheduling control,Evolutionary computation,Particle swarm optimization algorithm,Differential evolution algorithm

References

1. [1] S. Leghmizi, S. Liu, “A Survey of Fuzzy Control For Stabilized Platforms”, International Journal of Computer Science&Engineering Survey, vol.2, no.3, (2011).
2. [2] F.N. Barnes, “Stable Member Equations of Motion for a Three-Axis Gyro Stabilized Platform”, IEEE Transaction on Aerospace and Electronic Systems, vol.7, no.5, 1971, pp. 830-842.
3. [3] T.H. Lee, E.K. Koh, M.K. Loh, “Stable Adaptive Control of Multivariable Servomechanisms with Application to Passive Line-of-Sight Stabilization System,” IEEE Transactions on Industrial Electronics, vol. 43, no.1, 1996, pp. 98-10.
4. [4] J.A.R.K. Moorty, R. Marathe, “LQG/LTR Control Law for A Wideband Controller for Line of Sight Stabilization for Mobile Land Vehicles”, Proceedings International Conference on Electro-Optics, 1999, pp.729–735.
5. [5] J.A.R.K. Moorty, R. Marathe, V.R. Sule, “H∞ Control Law for Line-of-Sight Stabilization for Mobile Land Vehicles”, Society of Photo-Optical Instrumentation Engineers, Optical Engineering, vol.41, no.11, 2202, pp. 2935-2944.
6. [6] Y.J. Chen, S.H. Huang, W. Shanming, W. Fang, “DSP-Based Real-Time Implementation of A Neural Network Observer and Hybrid H∞ Adaptive Controller for Servo-Motor Drives”, Proceedings of the 27th Chinese Control Conference, China, 2008, pp.130-134.
7. [7] F.R. Rubio, “Application of Position and Inertial-Rate Control to A 2-DOF Gyroscopic Platform”, Robot Computer Integration Manufacturing, 2010, pp. 1-10.
8. [8] J.T. Spooner, K.M. Passino, “Stable Adaptive Control Using Fuzzy Systems and Neural Networks,” IEEE Transactions on Fuzzy Systems, vol.4, no.3, 1996, pp. 339-359.

9. [9] M.A. El-Sharkawi, T.C. Huang, A. El-Samahi, “Intelligent Control for High Performance Drives”, IEEE International Electric Machines and Drives Conference Record, no.18-21, 1997, pp. TA2/1.1-TA2/1.6.
10. [10] J.A.R.K. Moorty, R. Marathe, H. Babu, “Fuzzy Controller for Line-of-Sight Stabilization Systems”, Society of Photo-Optical Instrumentation Engineers, Optical Engineering, vol.43, no.6, 2004, pp. 1394-1400.
11. [11] W. Ji, Q. Li, B. Xu, “Design Study of Adaptive Fuzzy PID Controller for LOS Stabilized System”, IEEE Proceedings of the Sixth International Conference on Intelligent Systems Design and Applications, vol.1, 2006, pp. 336-341.
12. [12] P. Horacek, “Laboratory Experiments For Control Theory Courses: A Survey”, Annual Reviews in Control, vol.24, 2000, pp. 151-162.
13. [13] X. Fan, N. Zhang, S. Teng, “Trajectory Planning and Tracking of Ball And Plate System Sing Hierarchical Fuzzy Control Scheme”, Fuzzy Sets and Systems, vol.144, issue 2, 2004, pp. 297–312.
14. [14] M. Bai, H. Lu, J. Su, Y. Tian, “Motion Control of Ball and Plate System Using Supervisory Fuzzy Controller”, Proceedings of the 6th World Congress on Intelligent Control and Automation, China, 2006.
15. [15] W. Hongrui, T. Yantao, F. Siyan, S. Zhen, “Nonlinear Control for Output Regulation of Ball and Plate System”, Proceedings of the 27th Chinese Control Conference, China, 2008.
16. [16] M. Bai, Y. T. Tian, J. T. Su, “Position Control of Ball and Plate System Based on ANFIS”, Complex Systems and Applications, vol.1, 2008, pp.165.
17. [17] X. Dong, Z. Zhang, J. Tao, “Design of Fuzzy Neural Network Controller Optimized by GA for Ball and Plate System”, Proceedings of the Sixth International Conference on Fuzzy Systems and Knowledge Discovery,Vol.4, 2009, pp. 81-85.
18. [18] X. Dong, Z. Zhang, C. Chen, “Applying Genetic Algorithm to On-Line Updated PID Neural Network Controllers for Ball and Plate System”, Fourth International Conference on Innovative Computing, Information and Control, 2009, pp.751-755.
19. [19] D. Casagrande, A. Astolfi, T. Parisini, “Switching-Driving Lyapunov Function and the Stabilization of the Ball-and-Plate System”, IEEE Transactions on Automatic Control, vol.54, no.8, 2009, pp.1881-1886.
20. [20] M.A. Moreno-Armend´ariz, E. Rubio, C.A. P´erez-Olvera, “Design and Implementation of a Visual Fuzzy Control in FPGA for the Ball and Plate System”, International Conference on Reconfigurable Computing, 2010, pp.85-90.
21. [21] X. Dong, Y. Zhao, Y. Xu, Z. Zhang, P. Shi, “Design of PSO Fuzzy Neural Network Control for Ball and Plate System”, International Journal of Innovative Computing, Information and Control, vol.7, issue.12, 2011, pp. 7091-7103.
22. [22] K. Han, Y. Tian, Y. Kong, J. Li, Y. Zhang, “Tracking Control of Ball and Plate System Using An Improved PSO On-Line Training PID Neural Network”, IEEE ICMA International Conference on Mechatronics and Automation, 2012, pp. 2297-2302.
23. [23] S. Mochizuki, H. Ichihara, “I-PD Controller Design based on Generalized KYP Lemma for Ball and Plate System”, European Control Conference (ECC), Switzerland, 2013, pp.2855-2860.
24. [24] P. Roy, B. Kar, I. Hussain, ”Trajectroy Control of a Ball In A Ball and Plate System Using Cascaded PD Controllers Tuned By PSO”, Proceedings of Fourth International Conference On Soft Computing For Problem Solving, vol.2, 2014, pp.53.
25. [25] Y. Zhao, Y. Ge, “The Controller of Ball And Plate System Designed Based On FNN”, Journal of Chemical and Pharmaceutical Research, vol.6, issue.6, 2014, pp. 1347-1352.
26. [26] K.W. Han, Y.T. Tian, Y.S. Kong, B.H. Zhao, C. Li, “Fuzzy Indirect Adaptive Control For Ball And Plate System”, Kongzhi yu Juece/Control and Decision, vol.30, issue.2, 2015, pp. 303-310.
27. [27] M., Oravec, A. Jadlovska, “Model Predictive Control of a Ball and Plate laboratory Model”, SAMI 2015 - IEEE 13th International Symposium on Applied Machine Intelligence and Informatics, 2015, pp. 165-170.
28. [28] A., Negash, N.P. Singh, “Position Control And Tracking Of Ball And Plate System Using Fuzzy Sliding Mode Controller”, Advances in Intelligent Systems and Computing, vol.334, 2015, pp. 123-132.
29. [29] J. Xiao, G. Buttazzo, “Adaptive Embedded Control for a Ball and Plate System”, Proceedings of The Eighth International Conference on Adaptive and Self-Adaptive Systems and Applications IARIA, 2016, pp. 40-45.
30. [30] Quanser Inc., “2-DOF Ball Balancer Experiment for MATLAB/Simulink Users (Student Workbook)”, 2013.
31. [31] Quanser Inc., “Rotary Servo Base Unit Workbook (Student Workbook)”, 2011.
32. [32] D.J. Leith, W.E. Leithead, “Survey of Gain-Scheduling Analysis Design”, International Journal of Control, vol.73, 1999, pp. 1001-1025.
33. [33] S.G. Anavatti, F. Santoso, M.A. Garratt, “Progress in Adaptive Control Systems: Past, Present, and Future”, International Conference on Advanced Mechatronics, Intelligent Manufacture, and Industrial Automation (ICAMIMIA), 2015.
34. [34] J. Kennedy, R.C. Eberhart, “Particles Swarm Optimization”, IEEE International Conference on Neural Networks, 1995, pp.1942–1948
35. [35] R. Storn, "On the Usage of Differential Evolution for Function Optimization", Proceedings Fuzzy Information Processing Society, Biennial Conference of the North American, 1996.
36. [36] S. Das, P.N. Suganthan, “Differential Evolution: A Survey of the State-of-the-Art”, IEEE Transactions on Evolutionary Computation, vol.15, issue.1, 2011, pp. 4-31.
37. [37] K.J. Aström, T. Hagglund, ”PID Controllers”, Instrument Society of America, USA, 1995.
38. [38] K. Ogata, “Modern Control Engineering”, Fourth edition, Prentice-Hall Inc., USA, 2002.
39. [39] QUANSER Inc., Quarc Real Time Control Software, 2015.