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In this paper, new Takagi–Sugeno proportional–integral-fuzzy controllers (PI-FCs) to control a class of servosystems are proposed. The controlled plants in these control systems (CSs) are of integral type. In the first phase, there are designed linear PI controllers tuned in terms of the extended symmetrical optimum method to ensure the imposed overshoot and settling time with respect to the set point and to three possible types of load disturbance inputs. The connections between the two design parameters of the linear controllers and the desired maximum sensitivity and complementary sensitivity considering one of the disturbance inputs are derived. Then, accepting the approximate equivalence between the fuzzy controllers and the linear ones in certain conditions and using the modal equivalence principle, an attractive design method for the PI-FCs is proposed. With this respect, the design method guarantees maximum imposed sensitivity and complementary sensitivity for the CSs and, therefore, good responses with respect to modifications of the set point and of the disturbance inputs, and robustness with respect to model uncertainties. An application in speed control of a nonlinear servosystem with variable load, accompanied by experimental results, is provided to validate the new results, the fuzzy controllers, and a design method.
Precup et al. (Mon,) studied this question.