Robust control with anti-windup compensation for LTI uncertain systems

This paper presents an approach for the synthesis of control systems with actuator saturation compensation. This technique is applied to linear time invariant (LTI) systems with polytopic uncertainties, considering a performance index that involves the difference between the actuator output signal and the controller output and its effect on the control signal. For the purpose of this paper, the actuator saturation is considered as a disturbance in the performance of the control signal action, which allows to establish functional indices for the design of the control law (static output feedback), and for the synthesis of a compensation gain for the windup problem. Thus, the method exhibits certain robustness properties when changes in the functioning of the actuators occur. For the synthesis of static output feedback and compensation gains, a method derived from the robust optimal control techniques in H₂/H_∞ for linear systems with polytopic uncertainties based on linear matrix inequalities is proposed here. In order to verify the properties of the proposed technique, a numerical example is presented in this paper.