Computation of all robust PID controllers for two-input and two-output time delay control systems with gain margin and phase margin specifications

This paper presents a method to graphically compute all feasible gain margin (GM) and phase margin (PM) specifications-oriented PID controllers for two-input and two-output interactive and time delay (TITOTD) control systems. The considered TITOTD control system is first decomposed into two decoupled single input and single output time delay (SISOTD) systems. Two gain-phase margin testers are added in the forward parts of the two SISOTDs. The gain-phase margin tester method, the stability equation method, and the parameter plane method are exploited to perform GM and PM analysis in the parameter plane. Boundaries for stability and for pre-specified GM and PM can be portrayed in the parameter plane. All feasible GM and PM specifications-oriented PID controllers can be graphically computed. For validity verification, two independent PI/PID controllers are designed for each decoupled subsystem to achieve the desired GM and PM, and the performance is verified on the original interactive TITOTD control system. An illustrative example cited from the literature is given to show the effectiveness of the proposed method.