Takagi‐Sugeno exact model and linear matrix inequalities for an active power filter control

Abstract

In order to take advantage of the capabilities of a shunt active power filter (SAPF), the design of an adequate control scheme must be developed; generally, the SAPF control scheme corresponds to a cascade control composed of an inner loop and an outer loop. This article approaches the design of an inner loop control based on linear matrix inequalities (LMIs) for a SAPF with LCL coupling filter. The control design begins with the system rewriting in exact Takagi-Sugeno (TS) models, in the sequel, through the use of a quadratic energy function, and considering the closed-loop system, the Lyapunov direct method to establish LMI conditions is used. This proposal of inner loop control is called TSLMI, and in conjunction with a PI control, a PI-TSLMI cascade control scheme is configured. The SAPF objectives are the reduction of the total harmonic distortion (THD) in the mains current, the power factor (PF) correction, and facing load changes. The results show a correct performance of the proposed PI-TSLMI for both simulation and experimental tests.