Optimal error governor for PID controllers

Error Governor (EG) deals with the problem of dynamically modifying the feedback error driving a controller having bounded control signals, for preventing controller or actuators saturation, avoiding integrator and/or slow dynamics windup and preserving the nominal linear controller behaviour. In this paper, an optimisation-based EG scheme is proposed for discrete-time Proportional-Integral-Derivative (PID) controllers driving Single-Input Single-Output (SISO) plants. The PID controller is considered in state-space form, and this formulation is used to pose the EG problem as a constrained quadratic programme (QP). Because the QP problem is subject to inequality constraints related to controller saturation, in order to use the proposed scheme in real-world applications, it should be necessary to consider appropriate algorithms for efficiently solving the optimisation problem. An efficient way to efficiently compute the solution of the EG problem is presented, reducing the computational effort required to solve the EG QP for using the proposed scheme in real control loops with high sampling rate. An analysis of control performance and computational burden is provided, comparing in simulation studies the optimal EG scheme performance with respect to control results provided by saturated PID with and without anti-windup action.