Modified Kharitonov Theorem Based Optimal PID Controller Design for MIMO Systems

This work proposes a design methodology for a robust optimum proportional integral derivative (PID) controller based on modified Kharitonov theorem. A modification in Kharitonov theorem is suggested in this work to examine robustness criteria of uncertain systems for the sake of implementation. In the conventional Kharitonov theorem, robust stability is inspected by satisfying the routh hurwitz (RH) stability criteria of four Kharitonov polynomials which is quite tedious, whereas in the proposed method sufficient conditions for stability are determined by simply inspecting few maximum and minimum bounds of Kharitonov polynomial, which is not, found in any earlier literature. Through the modified Kharitonov theorem, ranges of the controller parameters towards robust PID controller are obtained which is further optimally tuned by teaching learning based optimization (TLBO). The designed controller is implemented to different types of multi input multi output (MIMO) systems. Robustness of the compensated system is verified in presence of output disturbances as well as with input output gain and phase variations. Simulation results exhibit much-improved performance compared to the results available in the previous literature.