Two degrees of freedom control and B-spline functions as tools for a reduced complexity approach to MPC

Abstract

The purpose of this paper is to simplify the treatment of the major issues of Model Predictive Control (MPC): stability, feasibility and complexity of the on line optimization procedure. To this purpose new MPC policy is developed using two Degrees of Freedom (2DoF) control scheme where the output r(k) of the feedforward Input Estimator (IE) is used as input forcing the closed-loop system Σ f . This latter is the feedback connection of an LTI plant Σ p with an LTI feedback controller Σ g . The task of Σ g is to guarantee the stability of Σ f , as well as the fulfillment of hard constraints on some physical variables for any input r(k) satisfying an a priori determined admissibility condition. The input r(k) is computed by the feedforward IE through the on-line minimization of suitably definite finite-horizon quadratic cost functional and is applied to σ F according to the usual receding horizon strategy. To simplify the constrained optimization problem, r(k) is assumed to be given by B-spline function. This greatly decreases the number of decision variables of the on-line optimization procedure. It is shown that stability and recursive feasibility of the adopted MPC strategy are guaranteed in advance, regardless the chosen prediction horizon.