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Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 9, pp. 617—622
DOI: 10.17587/mau.18.617622
Synthesis of the Optimal Fuzzy TS Controller for the Mobile Robot System Using the Chaos Theory
S. M. Jafarov, jafarovsm@gmail.com, Azerbaijan State Oil and Industry University, Baku, AZ1010, Azerbaijan, P. S. Jafarov, jafarovsm@gmail.com, A. M. Mustafayeva, aida.mustafayeva.1981@mail.ru, Azerbaijan National Academy of Sciences. Institute of Control Systems, Baku, Az1141, Azerbaijan

Corresponding author: Jafarov Saetdin M., D. Sc., Professor, Azerbaijan State Oil and Industry University, Baku, AZ1010, Azerbaijan,
email: jafarovsm@gmail.com
Received on February 21, 2017
Accepted on February 28, 2017
There are a series of nonlinear dynamic objects (or systems), which is chaoticnonregular [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 TS controller, which provides the optimal quality of the vector criterion. The control object is a mobile robot that moves in all directions (omnidirectionalOD), 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 x_{3}(t) is about Mi. Then u(t) = K_{j}x(t) + G_{i}e(t), where e(t) — is threedimensional vector error, x(t) — is threedimensional vector state of OD mobile robot. According to the phase variables and error, as well as the parameters M_{i}^{opt} of the term fuzzy sets of linguistic rules,
it is required to determine such optimal matrices K_{i}^{opt}, G_{i}^{opt} of fuzzy TS regulators which, while transferring of the systems from the initial state x_{0}, y_{0} to the final state x_{f}, y_{f} would assure optimality of the vector quality criterion, i. e. the minimum of integral square error — J_{1}[K, G, M], high damping degree of the oscillations — J_{2}[K, G, M] and minimum overshoot transient — J_{3}[K, G, M] in the CS. In order to solve the abovementioned problem, synthesis of the parameters of fuzzy controllers K_{i}, G_{i} can be implemented on the basis of chaos theory according to the vector criterion. The synthesis of controller parameters K_{i}, G_{i} and fuzzy term sets M_{i} are carried out by iterative procedure in accordance with system of automatic synthesis parameters
(ASP) of fuzzy TS regulators. Then, according to systems of simulation experiments it is determined Giopt, Kioptand Miopt, 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 wellknown 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 %.
Keywords: omnidirectional mobile robot, chaos theory, fuzzy TS controller, overshoot, integral square error, damping degree

For citation:
Jafarov S. M., Jafarov P. S., Mustafayeva A. M. Synthesis of the Optimal Fuzzy TS Controller for the Mobile Robot System Using the Chaos Theory, Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 9, pp. 617—622.
DOI: 10.17587/mau.18.617622
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