A New Method for Tuning PID-Type Fuzzy Controllers Using Particle Swarm Optimization
Soufiene Bouallègue, Joseph Haggège, Mohamed Benrejeb · InTech eBooks · 2012
Will-be-set-by-IN-TECH achieved based on a classical trials-errors procedure.Up to now, there is neither clear mor systematic method to guide such a choice.So, this tuning problem becomes more delicate and harder as the complexity of the controlled plant increases.Hence, the proposition of a systematic approach to tune the scaling factors of these particular PID-type FC structures is interesting.In this study, a new approach based on the Particle Swarm Optimization (PSO) meta-heuristic technique is proposed for systematically tuning the scaling factors of the PID-type FC, both with and without self-tuning mechanisms.This work can be considered as an extension of the results given in [11,12,16,26,31].The fuzzy control design is formulated as a constrained optimization problem which is efficiently solved based on a developed PSO algorithm.In order to specify more robustness and performance control objectives of the proposed PSO-tuned PID-type FC, different optimization criteria are considered and compared subject to several various control constraints defined in the time-domain framework.The remainder of this chapter is organized as follows.In Section 2, the proposed fuzzy PID-type FC structures, both with and without self-tuning scaling factors mechanisms, are presented and discussed within the discrete-time framework.Two adaptive mechanisms for scaling factors tuning are especially adopted.The optimization-based problems of the PID-type FC scaling factors tuning are formulated in Section 3. The developed constrained PSO algorithm, used in solving the formulated problems, is also described.An external static penalty technique is used to deal with optimization constraints.Theoretical conditions for convergence algorithm and parameters choice are established, based on the stability theory of dynamic systems.Section 4 is dedicated to apply the proposed fuzzy control approaches on an electrical DC drive benchmark and a thermal process within an experimental real-time framework based on an Advantech PCI-1710 multi-functions board associated with a PC computer and MATLAB/Simulink environment.Performances on convergence properties of the proposed PSO and the used GAO algorithm, are compared for the known Integral Absolute Error (IAE) and the Integral Square Error (ISE) criterion cases.The real-time fuzzy controllers are developed through the compilation and linking stage, in a form of a Dynamic Link Library (DLL) which is, then, loaded in memory and started-up. PID-type fuzzy control designIn this section, the considered PID-type FC structures are briefly described within the discrete-time framework based on [11,12,16,26,31]. Discrete-time PID-type FLCProposed by Qiao and Mizumoto in [26] within continuous-time formalism, this particular fuzzy controller structure, called PID-type FC, retains the characteristics similar to the conventional PID controller.This result remains valid while using a type of FC with triangular and uniformly distributed membership functions for the fuzzy inputs and a crisp output, a product-sum inference and a center of gravity defuzzification methods.Under these conditions, the equivalent proportional, integral and derivative control components of such a PID-type FC are given by αK e P + βK d D, βK e P,andαK d D, respectively, as shown in [16,26,31].In these expressions, P and D represent relative coefficients, K e , K d , 140 Fuzzy Controllers -Recent Advances in Theory and Applications