Multivariable PID controller design using online generalised predictive control optimisation

A novel multivariable state-space predictive PID optimal control law is proposed which is mathematically equivalent to generalised predictive control (GPC). The theoretical problem to be considered is to obtain the causal, stabilising, controllers of pre-specified PID structure, such that the individual PID controllers satisfy a multivariable predictive criterion and hence collectively perform as a multivariate GPC controller. The underlying practical problem and aim of this work is to obtain and develop an online optimisation method for tuning PID controllers so that they can operate either as classical PID controllers or in unison as a multivariable GPC controller. It is shown that such an approach leads to a dual mode controller which is the ability to switch the multivariable PID between operating either as a classical PID controller or a GPC controller.