Design of rank-one modification feedback controllers for second-order systems with time delay using frequency response methods

Abstract

In this note, a novel approach to design rank-one – single input – feedback controllers for second-order systems with time delay is presented. The versatile, well-known receptance modeling is combined with classical frequency response methods of control design, and the feedback gains are computed in order to achieve a given stability margin based on sensitivity specifications. The systems under study are assumed to be stable in open-loop. A heuristic optimization technique, namely, genetic algorithm is employed to impose a minimal distance from the Nyquist plot of the controlled system to the critical point, guaranteeing thereby a predefined margin of robust stability. In addition to the well known advantages of the receptance method in obtaining experimental models, the proposed design approach brings the possibility of considering time delay without approximations, by using frequency response calculations, avoiding thereby the drawbacks inherent to the a posteriori stability verification when pole assignment techniques are used. Numerical examples help to enlighten the merits of the proposed approach.