PID controller design satisfying multiple performance indices for linear discrete-time systems with time delay

A method to design digital PID controller satisfying multiple performance indices is proposed for arbitrary-order linear discrete-time systems with time delay. The design idea of this method is first to present the control parameter set which stabilizes the closed-loop control system by adopting Tchebyshev representation and roots distribution conditions, and then to determine the corresponding parameter region satisfying each performance index on the basis of the resultant stabilizing set of the control parameters. Thus, the parameter values in the intersection of these regions must be the ones which can simultaneously satisfy multiple performance indices according to the demand of control system. The advantage of this approach lies in that it can accurately present the digital PID control parameters meeting multiple performance indices in an intuitive way so that it could be easy for engineers to understand. Finally, a numerical example is presented to show the validity of the proposed method.