Constrained MPC for a linear system to track time-varying reference signals

This paper presents a model predictive control algorithm under input and state constraints. The algorithm is designed to track time-varying reference signals and allows for offset-free tracking when the reference signal is a constant or ramp signal. A double integrator is inserted into the controller as a servo compensator, when the cost function is large, the state of the integrator can be reset at each sampling moment, thereby allowing the cost function to decrease rapidly to improve the system’s performance. While the cost function is sufficiently small, an integral action is employed to achieve offset-free tracking. The control algorithm is reduced to a convex optimization problem under linear matrix inequality constraints.