Robust Optimal Controller Design for MIMO Systems on the Basis of Modified Discrete Kharitonov Theorem

In this paper, a modification in the Kharitonov theorem is proposed to fix the robustness criteria of the discrete time systems. This proposed method is noble and quite simpler than the existing method of the Kharitonov theorem for discrete time plants. In this method, to ensure robust stability, there is no need to check the stability of all four Kharitonov interval polynomials, whether it can be calculated through the much simpler conditions by only knowing the polynomials' maximum and lowest limits up to fourth order polynomials. The proposed method is derived and verified for the different orders of the plants. Further, the proposed method is implemented as a physical example of a four tank MIMO system. A PID controller is designed in this work on this proposed method to find the robust gains, which are further fine-tuned by the TLBO algorithm. Tests of the multi-channel input output gain change, delay variation, and output disturbance to the plant are used to assess the robustness of the developed controller.