Classical state feedback controller for nonlinear systems using mean value theorem: closed loop-FOC of PMSM motor application

Abstract

The problem of state feedback controllers for a class of Takagi-Sugeno (T-S) Lipschitz nonlinear systems is investigated. A simple systematic and useful synthesis method is proposed 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 linear parameter varying (LPV) systems. Using the Lyapunov theory, stability conditions are obtained and expressed in terms of linear matrix inequalities (LMIs). The controller gains are then obtained by solving linear matrix inequalities. The effectiveness of the proposed approach for closed loop-field oriented control (CL-FOC) of permanent magnet synchronous machine (PMSM) 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.

Keywords

Takagi-Sugeno (T-S) fuzzy systems / sector nonlinearity / nonlinear controller / linear matrix inequality (LMI) approach / differential mean value theorem (DMVT) / field oriented control (FOC) / linear parameter varying (LPV)

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