Multivariable generalized predictive control with new multiple reference model: a robust stability analysis

In this paper, it is presented the polynomial form of multivariable generalized predictive control with multiple reference model (MIMO GPC⧸MRM). A new choice of the reference model is given which allows to obtain decoupled and smooth nominal output responses. Then the equivalent polynomial controller is obtained and the analysis by means of non structured singular values is introduced. Lastly the method is applied to a flexible arm: simulations results display the decoupling efficiency and a comparison with the traditional choice of the reference model is done. The analysis of robustness in stability in terms of the ‘tuning knobs’ of GPC⧸MRM is dealt with and used to give a guideline as regards the final choice of ‘tuning knobs’ with preservation of robust performance. This is verified by means of time responses on a mismatched model.