Design nonlinear model reference with fuzzy controller for nonlinear SISO second order systems

Model reference controller is considering as one of the most useful controller to specific performance of systems where the desired output is produced for a given input. This system used the difference between the outputs of the plant and the desired model by comparing them to produce the signals of the control. This paper focus on design a model reference controller (MRC) combined with (type-1 and interval type-2) fuzzy control scheme for single input-single output (SISO) systems under uncertainty and external disturbance. The model reference controller is designed firstly without fuzzy scheme based on an optimal desired model and Lyapunov stability theory. Then a (type-1 and Interval type-2) fuzzy controller Takagi-Sugeno type is combine with the suggested MRC in order to enhance the performer of it, the common parts between the two fuzzy systems such as: fuzzifier, inference engine, fuzzy rule-base and defuzzifier are illustrated. In this paper the proposed controller is applied to controla (SISO) inverted pendulum sustem and the Matlab R2015 software is used to carry out two simulation cases for the overall controlled scheme. The obtained results for the two cases show that the proposed MRC with both fuzzy control schemes have acceptable performance, but it have better performance with the interval type-2 fuzzy scheme.