A unified procedure for continuous-time and discrete-time root locus and bode design

Abstract

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 independent of the form of the 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.