Nonlinear Control with Integral Compensation via the SOS Method for Output Voltage of Boost Converters Based on a Discretized Bilinear Model

Abstract

This paper investigates the nonlinear control with integral compensation for the output voltage of boost converters through their discretized bilinear model and the Sum of Squares (SOS) method. We first obtain a discretized bilinear model of an actual boost converter through identification. Subsequently, for this discretized bilinear system, we initially design two control laws via the SOS method: one is a nonlinear state feedback stabilizing controller, and the other is a nonlinear state feedback control law maximizing the Lyapunov function decrement in each switching instant. Each of the control laws is applied together with a state observer for a bilinear system. These controllers are effective in an ideal setting without variations in the load resistance and the input voltage, but result in the steady-state errors when they vary. To circumvent the problem, we design the second type controller with integral compensation incorprated through the SOS method. Finally, we carry out control experiments to confirm the effectiveness with the proposed control law.