Optimal Design of Linear State Feedback Controller forTS-Fuzzy-Model-Based Systems via ChebyshevSeries and Genetic Algorithm

摘要

By use of the elegant operational properties of the shifted Chebyshev series (SCS), a directcomputational algorithm for solving the Takagi-Sugeno (TS) fuzzy-model-based feedback dynamicequations is first developed in this paper. The basic idea is that the state variables are expressed interms of the SCS. The new method simplifies the procedure of solving the TS-fuzzy-model-basedfeedback dynamic equations into the successive solution of a system of the recursive formulae takingonly two terms of the expansion coefficients. Based on the presented recursive formulae, thedeveloped computational algorithm only involves the straightforward algebraic computation. Then,the developed algorithm is integrated with the hybrid Taguchi-genetic algorithm (HTGA) to design thelinear state feedback controller of the TS-fuzzy-model-based control systems under the criterion ofminimizing a quadratic integral performance index, where the integral performance index is alsoconverted into the algebraic form by using the SCS approach (SCSA). The proposed new approach,which integrates the SCSA and the HTGA, is non-differential, non-integral, straightforward, and welladaptedto the computer implementation. The comp utational complexity can therefore be reducedremarkably. Thus, this proposed approach facilitates the design task of the optimal linear statefeedback controller for the TS-fuzzy-model-based control systems. A design example of the linear statefeedback controller for the translational oscillator system with an eccentric rotational proof massactuator is given to demonstrate the applicability of the proposed approach.