ROSSMPC: A New Way of Representing and Analysing Predictive Controllers

There is an increasing tendency towards the use of a lesser number of controllers in industry. This is so as the inclusion of an economical optimization layer becomes simpler. However, a reduced number of controllers means that they are large ones. These must be adequately tuned, which can be accomplished through their state space representation. Several ideas for obtaining a state space representation of the class of model predictive controllers (MPC) have appeared in the literature like the approach of Li et al . 1 Nevertheless, most of them lead to a system with thousands of states if the controller becomes large. As a consequence, the computation of eigenvalues or singular values to evaluate the stability of the system becomes prohibitive. In this paper a new state space representation of the MPC controllers is introduced based on the continuous step response of the system given by a transfer function. The idea is to represent the step response in a parametric form. The number of states of this representation is of the same order as the identified transfer function however large the optimization horizon of the chosen predictive controller might be. The method includes integrating and open loop unstable processes. Besides that the model time delay appears explicitly and is independent of other parameters. The computation work involved in the closed loop analysis is thus minimized. Also, this new representation can be used to robustly tune the MPC controllers without the use of extensive simulations.