Synthesis of the Optimal Fuzzy T-S Controller for the Mobile Robot System Using the Chaos Theory

Abstract

There are a series of non-linear dynamic objects (or systems), which is chaotic-nonregular [1-3]. In such systems dynamic chaotic processes (irregular movement), that is the phenomenon can be characteriZed as "desirable " (positive) or "undesirable" (negative) [1, 3]. In the present work, it has been proposed the method of designing automatic synthesis problem of intellectual control system (CS) with using of the elements of chaos theory, i. e. tuning parameters of knowledge base T-S controller, which provides the optimal quality of the vector criterion. The control object is a mobile robot that moves in all directions (omni-directional-OD), a mathematical model, of which is described by nonlinear differential equation [6]. For nonlinear object - OD mobile robot the control law is chosen in the intelligent controllers class with two elastic feedback: If X3(t) is about Mi. Then u(t) = KjX(t) + Gfi(t), where e(t) - is three-dimensional vector error, x(t) - is three-dimensional vector state of OD mobile robot. According to the phase variables and error, as well as the parameters Miopt of the term fuZZy sets of linguistic rules, it is required to determine such optimal matrices K°pt, G°pt of fuZZy T-S regulators which, while transferring of the systems from the initial state Xo, yo to the final state Xf, yf would assure optimality of the vector quality criterion, i. e. the minimum of integral square error - JJK, G, M], high damping degree of the oscillations - J^K, G, M] and minimum overshoot transient - J3[K, G, M] in the CS. In order to solve the above-mentioned problem, synthesis of the parameters of fuZZy controllers K, Gi can be implemented on the basis of chaos theory according to the vector criterion. The synthesis of controller parameters Ki, Gi and fuZZy term sets Mi are carried out by iterative procedure in accordance with system of automatic synthesis parameters (ASP) of fuZZy T-S regulators. Then, according to systems of simulation experiments it is determined G°pt, K°pt and M°pt, that provides the optimal values on CS vector of the quality criterion. The experimental results showed that the synthesiZed CS mobile robot is relatively efficient than synthesiZed system by well-known paper [1, 4, 6]. Since the total integral quadratic error of the control system synthesiZed by a known method [1, 6] was 0,2605 and above at 0,2113 the proposed method, i.e., quality is improved by about 18,8 %.