Controllers for linear systems with bounded actuators: Slab scheduling and anti-windup

For linear systems with bounded actuators, a continuous family of controllers is designed which avoids control saturation for a given worst case disturbance. The control law acts as a scheduling scheme which, at each time, based on the closed-loop behavior (i.e., the closed-loop state vector) out of the continuous family selects a controller that provides the best performance while avoiding saturation. Graphically, the resulting scheduling scheme relies on slab regions in phase plane. It is shown that the most aggressive controller can be set to be a nominal controller designed without any regard to the saturation bounds, resulting in an anti-windup scheme. Among advantages of this anti-windup protection scheme are its improved performance while the nominal controller is mildly saturated and its applicability to open-loop unstable plants. The benefits of the proposed technique are demonstrated through two numerical examples.