Controller Design for Nonlinear Systems using Takagi Sugeno Model: Closed Loop-FOC of IM Motor Application
This note, we investigate the problem of state feedback controllers for a class of Takagi-Sugeno (TS) Lipschitz nonlinear systems. A simple systematic and useful synthesis method is proposed which based on the use of the Differential Mean Value Theorem (DMVT) and convex theory. The proposed design approach is based on the mean value theorem (MVT) to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients as LPV systems. Using the Lyapunov theory, stability conditions are obtained and expressed in term of Linear Matrix Inequalities (LMI). The controller gains are then obtained by solving linear matrix inequalities. The effectiveness of the proposed approach for Field Oriented Control of Induction Motor (FOC-IM) drives is demonstrated through an illustrative simulation for the proof of these approaches. Furthermore, an extension for controller design with parameter uncertainties and perturbation performance is discussed.