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This paper deals with modelling and robust control of linear multivariable uncertain systems based on the new linear multivariable ARX (Auto-Regressive with eXogenous input)-Laguerre model and the loop-shaping design procedure with the relative gain array theory. In fact, to guarantee significant parameter number reduction of the multivariable ARX-Laguerre model compared with the classic multivariable ARX model, we propose the optimization of the Laguerre poles of the model using the genetic algorithm where the Fourier coefficients are identified using the recursive least square method. Later, the optimized multivariable ARX-Laguerre model is exploited to propose a robust control algorithm for linear multivariable uncertain systems. Indeed, we propose to combine the loop-shaping design procedure approach and the relative gain array theory to develop a simplified final robust controller guaranteeing reference tracking and robust stability against parametric uncertainties. This proposition aims for the simplification of the control’s scheme by adjusting the weighting matrix and the final robust controller calculated from the loop-shaping design procedure for a simpler and more experimentally applicable control scheme. The identification of Fourier coefficients and Laguerre poles as well as the robust multivariable control algorithm are experimentally validated on a laboratory coupled two-tank system showing good results in terms of modelling and attending desired control performances.

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The present work focuses on the control of the nonlinear system, the PT326 blower, using the LSDP (Loop Shaping Design Procedure) approach in the discrete case and the gain scheduling technique. First, the system’s behavior is described by defining two operating points. In each of these latter the system is described using the linear ARX (Auto Regressive model with Xternal inputs) model which we propose to identify its parameters using the least squares method. Then, for each operating point the LSDP approach is exploited to synthesize a local robust controller. Later, the global robust controller resulting from switching between the local robust controllers by exploiting the gain scheduling technique is used to control the nonlinear PT326 blower.