Internal model control of MIMO discrete under-actuated systems with real parametric uncertainty

The synthesis of an internal model control (IMC) that is equable to the inverse of the model is extremely important in order to ensure perfect set-point tracking. This inversion presents the fundamental problem of the IMC structure for multivariable (MIMO) under-actuated systems with parametric uncertainty. However, the proposed IMC strategy is extended in the case of multi-input multi-output systems such that the number of control inputs is less than the outputs one. In the controller design procedure, a new method is presented to add to the model matrix underactuation a number of transfer function in order to make it a square matrix. Furthermore, the internal model control structure is changed in order to eliminate the excess control inputs by using the usual arithmetic operators. The problem of stability of controller is solved by applying a linear matrix inequality (LMI) approach, which can be easily solved using numerical standard software such as MATLAB. Robust stability of final closed control loops is tested using the value set concept and zero exclusion condition. In a set of experiments, the controlled system is approximated by a MIMO matrix with parametric uncertainty, the controllers are designed, the robust stability is verified, and the final control responses are tested and evaluated. Simulation results have proved the effectiveness and reliability of the proposed method.