CARMA-model-based j-step-ahead prediction for MIMO systems

Abstract

The single-input single-output (SISO) j-step-ahead predictor for generalized predictive control (GPC) controllers was traditionally derived using the polynomial approach through the Diophantine equations. An equivalent version of the predictor in a state-space form is available in the literature. In this paper, a z-domain analysis of the multiple input multiple output (MIMO) extension of the state-space predictor is carried out, and then an MIMO j-step-ahead predictor in polynomial form based on the controlled autoregressive moving average model is derived. The predictor enables us to simplify the GPC algorithm design for multivariable systems. In the SISO case the predictor is just the traditional GPC predictor, therefore this paper gives rigorous proof of the equivalence between the traditional GPC predictor and the state-space predictor.