Predictive PID controller design

A polynomial predictive optimal control problem is discussed for the discrete time system where the structure of the controller is assumed to be limited to a 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 the 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.