Graphical computation of gain and phase margin specifications-oriented robust PID controllers for uncertain systems with time-varying delay

In this paper, a novel graphical method is proposed for computing all feasible gain and phase margin specifications-oriented robust PID controllers to stabilize uncertain systems with time-varying delay. A virtual gain phase margin tester compensator is incorporated. The coefficient values of the characteristic equation of the considered system are overbounded and eight vertex Kharitonov polynomials are obtained. The stability equation method accompanied with parameter plane analysis is carried out to portray the constant gain margin and phase margin boundaries. The feasible controllers which stabilize every one of the eight vertex polynomials are identified. The union region of the useful specifications-oriented parameter region of each vertex polynomial is the Kharitonov region which represents all of the admissible specifications-oriented robust PID controller gains set. A computer simulation is provided to demonstrate the effectiveness and confirm validity of the proposed controller.