A hybrid anti-windup scheme for output saturated SISO linear closed loops

We give a formal definition of the anti-windup problem for a SISO linear control system with output saturation. We address the problem by relying on a hybrid modification of the linear closed loop which employs a suitable logic variable to activate/deactivate various components of a control scheme. The above scheme relies on a finite-time observation law, an open-loop observer and an open-loop input generator which is capable of driving the plant output within the saturation limits. Then the control scheme is based on suitable (hybrid) resetting laws allowing the controller to operate on the artificial output signal generated by the open-loop observer when the actual plant output is outside the saturation limits. We provide a formal proof of the effectiveness of the scheme in terms of the usual local preservation and global recovery, peculiar of anti-windup schemes. We also illustrate the proposed technique on an example study.