Robust PID controller design via LMI approach

In this paper, a method which allows explicit incorporation of the description of system uncertainties in the problem formulation for designing robust proportional-integal-derivative (PID) controller is presented. The multiple-model paradigm is employed to represent the uncertainties and provides the basis for the PID controller design. Using standard techniques, the robust PID controller design is reduced to a convex constraint problem which can be efficiently solved with linear matrix inequalities (LMIs) approach. Various practical specifications are considered simultaneously within this framework. Extension to system with time-delays, which follows naturally from the preceding development, is also discussed. Two examples are used to demonstrate the effectiveness of the proposed method and a comparison with the existing PID tuning methods is made.