Design of mixed H∞ and optimal controller for three-phase PWM rectifiers

The mathematic model of three-phase pulse-width modulated (PWM) voltage rectifiers is nonlinear, strong coupling. And the mathematic model error, time-varying uncertainties and external disturbance will influence the performance of the system. This paper presents a linear quadratic regulator (LQR) for the inner current loop control without decoupling, and a robust H∞ control method for the outer voltage loop. For the inner current loop, a Riccati equation is solved and a constant value adjoint matrix is calculated to derive the designed controller. For the outer voltage loop, the state equations are established and the suitable weighting functions are selected. And then, the Riccati inequality is solved to derive the H∞ controller. The simulation results show that the designed controller can achieve unit power factor control, and has faster response and better external disturbance rejection capabilities compared with the conventional PI controller.