Predictive PID controller design

A novel polynomial predictive optimal control problem is discussed for the discrete time system where the structure of the controller is assumed to be limited to discrete PID controller. The theoretical problem to be considered is to obtain the causal, stabilising, controller of the pre-specified PID form that minimises a generalised Predictive Control criterion and is equivalent to a GPC control law. The underlying practical problem and aim of this work is to obtain the optimal PID controller coefficients that provide the required closed loop performance over a range of operating conditions and working points.