Internal model control of discrete non-minimum phase over-actuated systems with multiple time delays and uncertain parameters

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.