Robust multimodel control for uncertain nonlinear MIMO systems based on ARX-Laguerre multimodel and LSDP approach

Abstract

In this paper, we propose a new alternative for the robust control of nonlinear MIMO (multiple-input multiple-output) systems based on the multimodel approach and LSDP (Loop-Shaping Design Procedure)approach in the discrete case. First, the multimodel approach is exploited by representing each linear sub-model in the form of the recent linear MIMO ARX (Auto-Regressive with eXogenous inputs) -Laguerre model which guarantees a significant parameters number reduction compared with the MIMO ARX model. Thus, the resulting multivariable multimodel, entitled MIMO ARX-Laguerre multimodel, ensures a reduction of the parametric complexity with a simple recursive vector representation. However, this reduction is conditioned by an optimal choice of the pole characterising each Laguerre base. To deal with this, we propose the identification, using the genetic algorithm, of the Laguerre poles as well as the weighting function parameters of the MIMO ARX-Laguerre multimodel. This latter allows to generate a set of linear MIMO ARX-Laguerre sub-models which are exploited to propose a robust multimodel control for uncertain nonlinear MIMO systems. In fact, for each identified sub-model, we combine the LSDP approach and the RGA (Relative Gain Array) theory to develop a local robust controller. Then, a multivariable roust multimodel control algorithm is developed where the overall control strategy by multimodel approach amounts to incorporating the same weighting functions used in the considered multivariable multimodel in order to interpolate the control laws calculated from each local robust controller. The optimisation of Laguerre poles and weighting functions parameters as well as the proposed multivariable robust multimodel control algorithm are validated on the experimental prototype Quanser Aero system.