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This paper focuses on a challenging problem in the internal model control (IMC) strategy: the model inversion to design the IMC controller for non-square systems. Several existing approaches for the synthesis of a specific inversion of the identified model will be presented in this paper to deal with the differences between the system's inputs and outputs numbers. The non-square effective relative gain is firstly presented. It consists of the measurement of interactions between the loops of the system in order to square the system and make it invertible. The equivalent transfer function method is presented as well. It is based on tuning the pseudo-inverse of the process to design the internal model controller. These methods are then compared with a novel proposed model inversion approach based on virtual outputs method. Virtual adding is considered in order to obtain an invertible square transfer matrix to design the internal model controller. This simple yet effective method ensures robust control performance. Its efficiency and availability, as compared with other presented methods, is illustrated through simulations on an overactuated system with three inputs/two outputs. [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]

This paper deals with the synthesis of a novel internal multimodel control designed for nonlinear overactuated systems. The multimodel approach is proposed to deal with system nonlinearity. A base of linear models is considered to describe the nonlinear system in the whole operating domain and then squared by adding virtual outputs. An internal model controller, obtained by a specific inversion method, is proposed for each model of the base. Thus, the global system control parameters are deduced through fusion of the elementary controller parameters by means of two techniques: commutation or residual approach. The case of three inputs/two outputs system is studied to illustrate the ability of both techniques to satisfy a tolerance interval for position error values, overshoot, settling time specifications and robustness requirement. [ABSTRACT FROM AUTHOR]