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This article provides a comparative analysis of two common control configurations used to control the side-stream distillation used to separate benzene, toluene and xylene as suggested by Doukas and Lyben. Their under-actuated model has been considered as the model of distillation column and the internal model controller is designed considering a Singular Value Decomposition (SVD) and Virtual Inputs (VI) techniques. An internal controller design based on VI is proposed in this article for this kind of underactuated systems. This design is used to control in parallel the distillation process and its model in real time. The proposed controller design is simple and systematic in relation with the desired closed loop specifications of the internal model control structure. Furthermore, the controller obtained ensure robustness to process variations. The SVD technique can realize the decoupling of under-actuated processes and wipe out unrealizable factors by introducing compensation terms, affecting the dynamic of the system. The aim of this article is to make a comparison between our proposed VI controller and the SVD approach. The results we obtained confirmed the potentials of the proposed controller based on VI considering the set point tracking and its robustness. [ABSTRACT FROM AUTHOR]

Internal model control (IMC) is an established technique in continuous time linear control, but it is less used for discrete-time systems. Most of the existing solutions do not cover all the situations and, in any case, they lead to complex procedures to design the controller. In this paper, a IMC technique able to control over-actuated systems is used to deal with a discrete-time Non-Minimum-Phase (NMP) process with multiple time delays and uncertain parameters. The proposed IMC control scheme is based on the system augmentation with a suitable number of virtual outputs to the model matrix, in order to create a square matrix, so that the realization of an approximate inverse of the model plant is possible. Robust stability analysis is provided via combination of the value set concept and the zero exclusion conditions. Internal stability is verified using Linear Matrix Inequalities (LMI). Simulations are reported to demonstrate the suitability of the proposed design, as regards robust stability, performance, parametric uncertainties and load disturbances. [ABSTRACT FROM AUTHOR]