A Unified Procedure for Continuous-Time and Discrete-time Root-Locus and Bode Design

As an alternative to the numerous distinct controller design algorithms in continuous-time and discrete-time classical control textbooks, a simple, unified design approach is presented for all standard continuous-time and discrete-time, classical compensators that is independent of the form of the linear system information. This approach is based on a simple root locus design procedure for a proportional-derivative (PD) compensator. From this procedure, design procedures for unified notation lead, proportional-integral (PI), proportional-integral-derivative (PID), and Pi-lead compensator are developed. The delta operator, which serves as a link between the continuous-time and discrete-time procedures, offers improved numerical properties to the traditional discrete - time shift operator. With this proposed approach, designers can concentrate on the larger control system design issues, such as compensator selection and closed-loop performance, rather than the intricacies of a particular design procedure.