An adaptive fuzzy PID controller with gain scheduling is proposed in this paper. The structure of the proposed gain scheduled fuzzy PID (GS_FPID) controller consists of both fuzzy PI-like controller and fuzzy PD-like controller. Both of fuzzy PI-like and PD-like controllers are weighted through adaptive gain scheduling, which are also determined by fuzzy logic inference. A modified genetic algorithm called accumulated genetic algorithm is designed to learn the parameters of fuzzy inference system. In order to learn the number of fuzzy rules required for the TSK model, the fuzzy rules are learned in an accumulated way. In other words, the parameters learned in the previous rules are accumulated and updated along with the parameters in the current rule. It will be shown that the proposed GS_FPID controllers learned by the accumulated GA perform well for not only the regular linear systems but also the higher order and time-delayed systems.
[1] J. G. Ziegler and N. B. Nichols, ''Optimum settings for automatic controller,'' ASME Trans., Vol. 64, pp. 756-768, Jun. 1942.[2] A. Datta, M. T. Ho and S. P. Bhattacharyya, Structure and Synthesis of PID Controllers, London, U.K.:Springer-Verlag, 2000.[3] L. A. Zadeh, ''Fuzzy sets,'' Inform. Contr., Vol. 8, pp. 338-353, June. 1965.[4] E. H. Mamdani, Application of fuzzy algorithms for simple dynamic plant,'' Proc. Inst. Elect. Eng., Vol. D-122, pp. 1585-1588, 1974.[5] E. H. Mamdani and S. Assilian, ''An experiment in linguistic synthesis with a fuzzy logic controller,'' Int. J. Man-Math. Stud., Vol. 7, pp. 1-13, 1975.[6] G. K. I. Mann, B. G. Hu and R. G. Gosine, ''Analysis of direct action fuzzy PID controller structures,'' IEEE Trans. SMC. '' Pt. B, Vol. 29, pp. 371-388,Jun. 1999.[7] G. K. I. Mann, B. G. Hu and R. G. Gosine, ''A systematic study of fuzzy PID controllers - function-based evaluation approach,'' IEEE Trans. Fuzzy Sys., Vol. 9, pp. 699-712, Oct. 2001.[8] Z.-Y. Zhao, M. Tomizuka and S. Isaka, ''Fuzzy gain scheduling of PID controllers,'' IEEE Trans. Syst., Man, Cybern., Vol. 23, pp. 1392-1398,1993.[9] S. G. Tzafestas and N. P. Papanikolopoulos, ''Incremental fuzzy expert PID control,'' IEEE Trans. Ind. Electron., Vol. 37, No. 5, pp. 365-371, 1990.[10] S.-Z. He, S. Tan and F.-L. Xu, ''Fuzzy self-tuning of PID controllers,''Fuzz Sets Syst., pp. 37-46, 1993.[11] A. Visioli, ''Fuzzy logic based set-point weighting for PID controllers,''IEEE Trans. Syst. Man, Cybern.,- Pt. A, Vol. 29, pp. 587-592, 1999.[12] M. Maeda and S. Murakami, ''Fuzzy gain scheduling of PID controllers,''Fuzzy Sets Syst., Vol. 51, pp. 29-40, 1992.[13] C.-L. Chen, P.-C. Chen and C. K. Chen, ''Analysis and design of fuzzy control systems,'' Fuzzy Sets Syst., Vol. 57, pp. 125-140, 1993.[14] W. Li, ''Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller,'' IEEE. Trans. Fuzzy Syst., Vol. 6, No. 4, pp.449-463, 1998.[15] B. Armstrong, ''FLC design for bounded separable functions with linear input-output relations as a special case,'' IEEE Trans. Fuzzy Syst., Vol. 4, pp. 72-79, 1996.[16] H. A. Malki, D. Misir, D. Feigenspan and G. Chen, ''Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads,''IEEE Trans. Contr. Syst. Technol., Vol. 5, pp. 371-378, 1997.[17] D. Misir, H. A. Malki and G. Chen, ''Design and analysis of a fuzzy proportional integral derivative controller,'' Fuzzy Sets Syst., Vol. 79, pp.297-314, 1996.[18] S. J. qin and G. Borders, ''A multiregion fuzzy logic controller for nonlinear process control,'' IEEE Trans. Fuzzy Syst., Vol. 2, pp. 74-81,1994.[19] A. Visioli, ''Tuning of PID controllers with fuzzy logic,'' IEE Proc.-Control Theory Appl., Vol. 148, No. 1, pp. 1-8, 2001.[20] M. J. Er and Y. L. Sun, ''Hybrid fuzzy proportional-integral plus conventional derivative control of linear and nonlinear systems,'' IEEE Trans. Ind. Elect., Vol. 48, No. 6, pp.1109-1117, Dec. 2001.[21] K. S. Tang, K. F. Man, G. Chen and S. Kwong, ''An optimal fuzzy PID controller,'' IEEE Trans. Ind. Electrn., Vol. 48, No. 4, pp. 757-765, Aug.2001.[22] K. S. Tang, K. F. Man, G. Chen and S. Kwong, ''A GA-optimized fuzzy PD+I controller for nonlinear systems,'' in Proc. IEEE IECON?01, Denver,Colorado, Nov. 29-Dec. 2, 2001, pp. 718-723.[23] B. Hu, G. K. I. Mann and R. G. Gosine, ''New methodology for analytical and optimal design of fuzzy PID controllers,'' IEEE Trans. Fuzzy Syst., Vol. 7, No. 5, pp. 521-539, Oct. 1999.
[1] J. G. Ziegler and N. B. Nichols, ''Optimum settings for automatic controller,'' ASME Trans., Vol. 64, pp. 756-768, Jun. 1942.[2] A. Datta, M. T. Ho and S. P. Bhattacharyya, Structure and Synthesis of PID Controllers, London, U.K.:Springer-Verlag, 2000.[3] L. A. Zadeh, ''Fuzzy sets,'' Inform. Contr., Vol. 8, pp. 338-353, June. 1965.[4] E. H. Mamdani, Application of fuzzy algorithms for simple dynamic plant,'' Proc. Inst. Elect. Eng., Vol. D-122, pp. 1585-1588, 1974.[5] E. H. Mamdani and S. Assilian, ''An experiment in linguistic synthesis with a fuzzy logic controller,'' Int. J. Man-Math. Stud., Vol. 7, pp. 1-13, 1975.[6] G. K. I. Mann, B. G. Hu and R. G. Gosine, ''Analysis of direct action fuzzy PID controller structures,'' IEEE Trans. SMC. '' Pt. B, Vol. 29, pp. 371-388,Jun. 1999.[7] G. K. I. Mann, B. G. Hu and R. G. Gosine, ''A systematic study of fuzzy PID controllers - function-based evaluation approach,'' IEEE Trans. Fuzzy Sys., Vol. 9, pp. 699-712, Oct. 2001.[8] Z.-Y. Zhao, M. Tomizuka and S. Isaka, ''Fuzzy gain scheduling of PID controllers,'' IEEE Trans. Syst., Man, Cybern., Vol. 23, pp. 1392-1398,1993.[9] S. G. Tzafestas and N. P. Papanikolopoulos, ''Incremental fuzzy expert PID control,'' IEEE Trans. Ind. Electron., Vol. 37, No. 5, pp. 365-371, 1990.[10] S.-Z. He, S. Tan and F.-L. Xu, ''Fuzzy self-tuning of PID controllers,''Fuzz Sets Syst., pp. 37-46, 1993.[11] A. Visioli, ''Fuzzy logic based set-point weighting for PID controllers,''IEEE Trans. Syst. Man, Cybern.,- Pt. A, Vol. 29, pp. 587-592, 1999.[12] M. Maeda and S. Murakami, ''Fuzzy gain scheduling of PID controllers,''Fuzzy Sets Syst., Vol. 51, pp. 29-40, 1992.[13] C.-L. Chen, P.-C. Chen and C. K. Chen, ''Analysis and design of fuzzy control systems,'' Fuzzy Sets Syst., Vol. 57, pp. 125-140, 1993.[14] W. Li, ''Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller,'' IEEE. Trans. Fuzzy Syst., Vol. 6, No. 4, pp.449-463, 1998.[15] B. Armstrong, ''FLC design for bounded separable functions with linear input-output relations as a special case,'' IEEE Trans. Fuzzy Syst., Vol. 4, pp. 72-79, 1996.[16] H. A. Malki, D. Misir, D. Feigenspan and G. Chen, ''Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads,''IEEE Trans. Contr. Syst. Technol., Vol. 5, pp. 371-378, 1997.[17] D. Misir, H. A. Malki and G. Chen, ''Design and analysis of a fuzzy proportional integral derivative controller,'' Fuzzy Sets Syst., Vol. 79, pp.297-314, 1996.[18] S. J. qin and G. Borders, ''A multiregion fuzzy logic controller for nonlinear process control,'' IEEE Trans. Fuzzy Syst., Vol. 2, pp. 74-81,1994.[19] A. Visioli, ''Tuning of PID controllers with fuzzy logic,'' IEE Proc.-Control Theory Appl., Vol. 148, No. 1, pp. 1-8, 2001.[20] M. J. Er and Y. L. Sun, ''Hybrid fuzzy proportional-integral plus conventional derivative control of linear and nonlinear systems,'' IEEE Trans. Ind. Elect., Vol. 48, No. 6, pp.1109-1117, Dec. 2001.[21] K. S. Tang, K. F. Man, G. Chen and S. Kwong, ''An optimal fuzzy PID controller,'' IEEE Trans. Ind. Electrn., Vol. 48, No. 4, pp. 757-765, Aug.2001.[22] K. S. Tang, K. F. Man, G. Chen and S. Kwong, ''A GA-optimized fuzzy PD+I controller for nonlinear systems,'' in Proc. IEEE IECON?01, Denver,Colorado, Nov. 29-Dec. 2, 2001, pp. 718-723.[23] B. Hu, G. K. I. Mann and R. G. Gosine, ''New methodology for analytical and optimal design of fuzzy PID controllers,'' IEEE Trans. Fuzzy Syst., Vol. 7, No. 5, pp. 521-539, Oct. 1999.
@article{"International Journal of Electrical, Electronic and Communication Sciences:63519", author = "Leehter Yao and Chin-Chin Lin", title = "Design of Gain Scheduled Fuzzy PID Controller ", abstract = "An adaptive fuzzy PID controller with gain scheduling is proposed in this paper. The structure of the proposed gain scheduled fuzzy PID (GS_FPID) controller consists of both fuzzy PI-like controller and fuzzy PD-like controller. Both of fuzzy PI-like and PD-like controllers are weighted through adaptive gain scheduling, which are also determined by fuzzy logic inference. A modified genetic algorithm called accumulated genetic algorithm is designed to learn the parameters of fuzzy inference system. In order to learn the number of fuzzy rules required for the TSK model, the fuzzy rules are learned in an accumulated way. In other words, the parameters learned in the previous rules are accumulated and updated along with the parameters in the current rule. It will be shown that the proposed GS_FPID controllers learned by the accumulated GA perform well for not only the regular linear systems but also the higher order and time-delayed systems.
", keywords = "Gain scheduling, fuzzy PID controller, adaptive control, genetic algorithm.", volume = "1", number = "1", pages = "91-5", }
