Internal Model Control Design for Nonlinear Systems Based on Inverse Dynamic Takagi–Sugeno Fuzzy Model

In recent years, applications of inverse model-based control techniques have experienced significant growth in popularity and have been widely used in engineering applications, mainly in nonlinear control system design problems. In this study, a novel fuzzy internal model control (IMC) structure is presented for single-input-single-output (SISO) nonlinear systems. The proposed structure uses the forward and inverse dynamic Takagi–Sugeno (D-TS) fuzzy models of the nonlinear system within the IMC framework for the first time in literature. The proposed fuzzy IMC is obtained in a two-step procedure. A SISO nonlinear system is first approximated using a D-TS fuzzy system, of which the rule consequents are linearized subsystems derived from the nonlinear system. A novel approach is used to achieve the exact inversion of the SISO D-TS fuzzy model, which is then utilized as a control element within the IMC framework. In this way, the control design problem is simplified to the inversion problem of the SISO D-TS fuzzy system. The provided simulation examples illustrate the efficacy of the proposed control method. It is observed that SISO nonlinear systems effectively track the desired output trajectories and exhibit significant disturbance rejection performance by using the proposed control approach. Additionally, the results are compared with those of the proportional-integral-derivative control (PID) method, and it is shown that the proposed method exhibits better performance than the classical PID controller.