The works presented in this book are focused on the control structure by internal model. It is a structure known as being robust and making it possible to consider the effects of modeling errors on the one hand and of external disturbances on the other. Its main advantages lie in the simplicity of synthesis of the corrector, its ease of implementation and the explicit adjustment of robustness. As for its disadvantages, they mainly concern its applicability reserved for systems and stable correctors. To achieve a perfect transfer between the reference and the output of the process, independently of the process to be controlled, the regulator used in this structure is chosen the inverse of the model. The controller thus synthesized achieves perfect tracking despite the disturbance. However, if the modeling error is significant, the control loop can be destabilized, hence the usefulness of filtering the return signal to ensure a certain robustness with respect to this modeling error.
The book is organized into three chapters as follows:
In chapter 1, we presented a first control structure by internal model which showed its effectiveness for the case of continuous linear multivariable systems with non-zero relative degree and minimum phase. Nevertheless, in the case of delay systems or with unstable zeros, the results were not satisfactory, especially from the point of view of precision.
A second approach of realizing the inverse of the multivariate model is proposed to improve the performance of delay systems. We have proposed a second command structure by internal model that is simple to design and implement. The application of the latter, to the different cases of multivariable systems: with non-zero relative degree, minimum phase, non-minimum phase or presenting a modeling delay, has given satisfactory results.
Chapter 2 is focused on the design of an internal model controller for discrete multivariable systems. This controller is designed for linear systems with delay or without delay at minimum phase or non-minimum phase. The first section of this chapter is devoted to the presentation of the different techniques of discretization since all physical systems have a continuous presentation. Then, the discretization techniques most used in the literature were detailed and the results of simulations were discussed to choose the most efficient technique. The third section was devoted to the presentation of the control by internal model of square multivariable systems by detailing its basic structure, its main properties, and the design phase of the controller specific to this control.
The results obtained are satisfactory and showed the robustness of the control by discrete internal model in the improvement of the performances the discrete multivariable linear systems.
Chapter 3 is focused on the exploration and proposal of new control structures by internal model for multivariable continuous overactuated and underactuated systems leading to the synthesis of robust numerical control systems. These proposed internal model control structures have proven through numerous applications their ability to guarantee increased performance while being simple to implement. These applications can be applied to industrial processes, linear or non-linear, such as underactuated system example 1, two tank cylindrical system and example 2, overatuated system, the mixing tank process.
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