On the design of single-loop single-input-output feedback control systems in the complex-frequency domain

Abstract

This paper is concerned with single-loop, single-input-output, feedback control systems consisting of a plant, controller, and feedback sensor each modeled by a rational transfer function. The plant can be unstable, nonminimum phase, and even improper. The objective is the determination of the controller transfer function for which the system is asymptotically stable and design objectives are met. This has always been the goal in feedback system design. What is novel about the approach presented here is that the family of all stabilizing controller transfer functions is parameterized in terms of a rational function K (s) . The design method allows for complete freedom in the selection of all closed-loop system poles (except those associated with hidden modes). This is accomplished through the choice of the denominator polynomial for K (s) . The remaining design freedom lies in the selection of the numerator of K (s) . This freedom is utilized to shape the system sensitivity function and to achieve specified steady-state error coefficients. A numerical example in which the plant is unstable and nonminimum phase is presented to illustrate the above points. The final design is compared with alternative designs and the tradeoffs are clearly displayed.