Abstract
This paper presents a novel design and tuning technique of fuzzy PID (FPID) controllers for multivariable process systems. The inference mechanism of the FPID system follows the Standard Additive Model (SAM)-based fuzzy rule structure. The proposed design method can be used for any n×n dimensional multiinput– multi-output (MIMO) process system and guarantees closed-loop stability. In general the design of FPID for MIMO systems is challenging, mainly due to the existence of loop interactions. To address this issue a static decoupler is implemented which has the capacity to remove steady-state loop interactions. The each control loop is assigned with a FPID system. Two types of FPID configurations are considered. The first FPID system follows the Mamdani-type rule structure, where error and error rates are directly used in the input space to derive fuzzy rules. The second FPID configuration consists decoupled fuzzy rules where three decoupled rule bases are assigned to follow individual PID actions. The tuning is achieved while using the two-level tuning principle as described in [1]. The low-level tuning is dedicated to devise linear gain parameters in the FPID system where as the high-level tuning is dedicated to adjust the fuzzy rule base parameters. The low-level tuning method adopts a novel linear tuning scheme for general decoupled PID controllers and the high-level tuning adopts a heuristic-based method to change the nonlinearity in the fuzzy output. For robust implementation, a stability analysis is performed using Nyquist array and Gershgorin band. The stability properties provides the hard limits allowed for fuzzy rule parameters and also guarantees to operate within a given gain phase margin limits. The performance and the design criterion is finally evaluated using several control simulations.
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References
George K.I. Mann, Bao-Gang Hu and Raymond G. Gosine. Two-Level Tuning of Fuzzy PID Controllers. IEEE Transactions on Systems, Man and Cybernetics, Part B, 31(2), pp. 263-269, Apr 2001.
2. Jiawen Dong and Coleman B. Brosilow. Design of Robust Multivariable PID controllers via IMC. Proceedings of the American Control Conference, 5, pp. 3380-3384, June 4-6, 1997.
S. Yamamoto and I. Hashimoto. Present status and future needs: The view of from Japanese industry. Proceedings of the 4th International Conference on Chemical Process Control. in I. Arkun and I. Ray, Eds., New York: AIChe, 1991.
J.G. Ziegler and N.B. Nichols. Optimum settings for automatic controllers. Trans. ASME, 64, pp. 759-768, 1942.
A. Niederlinski. A Heuristic Approach to the Deisgn of Linear Multivariable Interactiing Con-trol Systems.. Automatica, 7, pp. 691-701, 1971.
William L. Luyben. Simple Method for Tuning SISO Controllers in Multivariable Systems. Ind. Eng. Chem. Process Des. Dev, 25(3), pp. 654-660, July 1986.
D. Chen and D.E. Seborg. Multiloop PI/PID controller design based on Gershgorin bands. Proceedings of the American Control Conference, 5, pp. 4122-4127, June 25-27, 2001.
M. Witcher and T.J. McAvoy. Interacting Control Systems: Steady State and Dynamic Mea-surement of Interaction. ISA Transactions, 16(3), pp. 35-41, 1977.
Karl Johan Astrom, Karl Henrik Johansson and Qing-Guo Wang. Design of decoupled PID controllers for MIMO systems. Proceedings of the American Control Conference, 3, pp. 2015-2020, June 2001.
Jietae Lee and Thomas F. Edgar. Interaction measure for decentralized control of multivari-able processes. Proceedings of the American Control Conference, Anchorage, AK, United States, 1, pp. 454-458, May 2002.
M.H. Moradi, M.R. Katebi and M.A. Johnson. The MIMO Predictive PID Controller Design. Asian Journal of Control, 4(4), pp. 452-463, Dec 2002.
D.E. Rivera, S.M. Morari and S. Skogestad. Internal Model Control 4. PID Controller Design. Ind. Eng. Chem. Proc. Des. Dev., 25(1), pp. 252-265, Jan 1986.
J. Lieslehto, J.T. Tanttu and H.N. Koivo. An Expert System for Multivariable Controller Design. Automatica, 29(4), pp. 953-968, 1993.
R. Sehab, M. Remy and C. Renotte. An approach to design fuzzy PI supervisor for a nonlinear system. IFSA World Congress and 20th NAFIPS International Conference, 2001. Joint 9th, 2, pp. 894-899, July 25-28, 2001.
A. Selk Ghafari and A. Alasty. Design and real-time experimental implementation of gain scheduling PID fuzzy controller for hybrid stepper motor in micro-step operation. Proceedings of the IEEE International Conference on Mechatronics ICM ’04., pp. 421-426, June 2004.
E.H Mamdani. Application of fuzzy algorithms for control of simple dynamic plant. Proceed-ings of the Institution of Electrical Engineers, 121(12), pp. 1585-1588, 1974.
F.L. Lewis and Kai Liu. Towards a paradigm for fuzzy logic control. Automatica, 32(2), pp. 167-181, Feb 1996.
A. Rahmati, F. Rashidi and Rashidi M. A hybrid fuzzy logic and PID controller for control of nonlinear HVAC systems. IEEE Transactions on Systems, Man and Cybernetics, 3, pp. 2249-2254, Oct 2003.
D. Dubois and H. Prade. Fuzzy Sets and Systems: Theory and Applications. Academic Press, 1980.
M. Sugeno. Industrial Application of Fuzzy Control. North-Holland, Amsterdam, The Netherlands. 1985.
Han Xiong Li and Shaocheng Tong. A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems. Fuzzy Systems, IEEE Transactions on, 11(1), pp. 24-34, Feb 2003.
Timothy J. Ross. Fuzzy Logic with Engineering Applications. Wiley, Chichester, UK, 2nd edition, 2004.
G.I. Eduardo and M.R. Hiram. Fuzzy multivariable control of a class of a biotechnology process. Proceedings of the IEEE International Symposium on Industrial Electronics, 1, pp. 419-424, July 1999.
Chieh-Li Chen and Pey-Chung Chen. Application of fuzzy logic controllers in single-loop tuning of multivariable system design. Computers in Industry, 17(1), pp. 33-41, 1991.
B. Wayne Bequette. Process Control Modeling, Design and Simulation. Prentice-Hall of India, 2003.
Shaoyuan Li, Hongbo Liu, Wen-Jian Cai, Yeng-Chai Soh and Li-Hua Xie. A new coordinated control strategy for boiler-turbine system of coal-fired power plant. IEEE Transactions on Control Systems Technology, 13(6), pp. 943-954, Nov 2005.
Hassan B. Kazemian. The SOF-PID controller for the control of a MIMO robot arm. IEEE Transactions on Fuzzy Systems, 10(4), pp. 523-532, Aug 2002.
Bart Kosko. Fuzzy Engineering. Prentice-Hall, Simon & Schuster/A Viacom Company Upper Saddle River, New Jersey, 1997.
H.A. Malki and D. Misir. Determination of the control gains of a fuzzy PID controller using neural networks. Fuzzy Systems, Proceedings of the Fifth IEEE International Conference on, 2, pp. 1303-1307, Sept 1996.
Yu Yongquan, Huang Ying, Wang Minghui, Zeng Bi and Zhong Guokun. Fuzzy neural PID controller and Ftuning its weight factors using genetic algorithm based on different location crossover. Systems, Man and Cybernetics, 2004 IEEE International Conference on, 4, pp. 3709-3713, Oct 10-13 2004.
J.-X. Xu, C. Liu and C.C. Hang. Tuning of fuzzy PI controllers based on gain/phase margin specifications and ITAE index. ISA Transactions, 35(1), pp. 59-91, May 1996.
J.-X. Xu, C. Liu and C.C. Hang. Designing a stable fuzzy PI control system using extended circle criterion. Int. J. of Intelligent Control and Systems, 1, pp. 355-366, 1996.
S. Hayashi. Auto-tuning fuzzy PI Controller. Proceedings of the Intn’l Fuzzy Systems Associ-ation Conference, pp. 41-44, 1991.
H.-X. Li and H.B. Gatland. A new methodology for designing a fuzzy logic controller. IEEE Transactions on Systems, Man and Cybernetics, 25(3), pp. 505-512, Mar 1995.
K.J. Astrom and T. Hagglund. PID Controllers: Theory, Design and Tuning. Instrument Soci-ety of America, Research Triangle Park, 2nd edition, NC, 1995.
C.W. Reynolds. Flocks, Herds, and Schools: A Distributed Behavioral Model. Computer Graphics, 21(4), pp. 25-45, July 1987.
J.P. Martino. Technological Forecasting for Decisionmaking. Elsevier, 8(1), 1972.
Baogang Hu, George K.I. Mann and Raymond G. Gosine. New methodology for analytical and optimal design of fuzzy PID controllers. IEEE Transactions on Fuzzy Systems, 7(5), pp. 521-539, Oct 1999.
H.H. Rosenbrock. State -Space and Multivariable Theory. Nelson, London, 1970.
J.M. Maciejowski. Multivariable Feedback Design. Addison-Wesley, 1989.
K. Ho Weng and H. Lee Tong, and Oon P. Gan. Tuning of Multiloop Proportional-Intergral-Derivative Controllers Based on Gain and Phase Margin Specifications. Ind. Eng. Chem. Res., 36, pp. 2231-2238, 1997.
Weng Khuen Ho, Tong Heng Lee, Wen Xu, Jinrong R. Zhou and Ee Beng Tay. Direct Nyquist array design of PID controllers. IEEE Transactions on Industrial Electronics, 47(1), pp 175-185, Feb 2000.
P.K. Roy and G. Mann and B.C. Hawlader. Fuzzy rule-adaptive model predictive control for a multi-variable heating system. IEEE Conference on Control Applications., pp. 260-265, Aug 2005.
E.F. Camacho and C. Bordons. Model Predictive Control. Springer-Verlag, London, 1999.
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Mann, G.K.I., Harinath, E. (2008). Two-Level Tuning of Fuzzy PID Controllers for Multivariable Process Systems. In: Lowen, R., Verschoren, A. (eds) Foundations of Generic Optimization. Mathematical Modelling: Theory and Applications, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6668-9_9
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