A two-mass fuzzy control system is considered. For fuzzification process, classical both linear and nonlinear membership functions are used. To find optimal values of membership function’s parameters, genetic algorithm is used. To take into account values of both output and intermediate parameters of the system, a penalty function is considered. Research is conducted for the case of speed control system and displacement control system. Obtained results are compared with the case of the system with classical, crisp controller. 1. Introduction In the optimal controls synthesis, various approaches are used. Among them are: the method of analytical design of controllers [1], the Pontryagin maximum principle, and Bellman dynamic programming [2, 3], and also root finding methods. The disadvantages of these approaches are that they do not take into account changing conditions of the system, changes of the subject, and so forth. Nonlinear control theory, including feedback linearization [4], is not widely used due to complexity of determining the aggregate variables in technical systems. As well as method of geometric control theory [5] are rather not widespread. Application of fuzzy logic at synthesis of optimal control is frequently used. In particular, in [6], for each of the subsystems LQR, optimal control is synthesized. Switching between subsystems is done by means of the fuzzy sets theory. In the paper [7], fuzzy control in conjunction with genetic algorithms is used for the synthesis of optimal control for continuous stirred tank reactor. In [8], an optimal control algorithm for T-S fuzzy descriptor systems with time domain hard constraints including control input constraints and state constraints was proposed. Many studies are devoted to selecting the type of membership function (e.g., [9, 10]), that is, mapping between the set of operation error admissible values and the interval . However, in industrial problems standard types of membership functions, trapezoid, triangular sigmoid, and so forth (see, e.g., [11]), are often used. When one uses these functions there is a problem of choosing the parameters of membership function which would provide the desired transients in the system. One approach to solving this problem is the synthesis of control actions that ensure a minimum level of quality desired integral performance index. By means of genetic algorithms, it is possible to determine the unknown parameters of the membership functions. 2. Materials and Methods 2.1. Problem Statement Research was conducted for the case of two-mass dynamic system. In
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