A comparative study on existing and new methods to design internal model controllers for non-square systems

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.