A novel model predictive control for a piecewise affine class of hybrid system with repetitive disturbance

Abstract

The present investigation addresses an innovative method based on explicit form of the model predictive control (EMPC) for a constrained Piecewise affine (PWA) class of hybrid systems, considering repetitive disturbance. This model of hybrid systems is investigated due to the fact that PWA modeling structure can approximate nonlinear systems via various operating points, and also because the simulation of PWA models are easy. With EMPC, the problem of optimization is solved in an offline way only once. Unlike conventional EMPC, the process information of the past and the data which are predicted are applied in the proposed strategy. This is the first time that in this study, the investigators adopt an approach in which these predicted data are weighted by another optimization problem (OP) and this weighted predicted sequence along with the past information of the process as an updating control input formula. In fact, two separate OPs are solved simultaneously at each step of proposed EMPC. The first one is linked with calculating the control input from the constrained cost function of EMPC algorithm and the second one concerns finding the optimal weighting factors in order to minimize the error signal, i.e. the difference between the reference path and the output signal at each optimization step of EMPC strategy. The precision of the proposed method is extremely dependent on the accuracy of the process model, so iterative learning control (ILC) algorithm is applied to protecting the process model against the periodic disturbances. These mathematical analyses are proven and validated by simulation results.

Keywords: Explicit model predictive control; Iterative learning algorithm; Optimal weighting factors; Past information; Repetitive disturbances.