Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

Abstract

This paper investigates the problem of preview repetitive control with equivalent‐input‐disturbance for a class of continuous‐time linear systems in the presence of unknown external disturbances. First, an augmented delay system is constructed by using the nominal state equation with error system and the state equation of a modified repetitive controller, which is then transformed into a non‐delayed one by state transformation. Next, by using optimal control theory, a preview repetitive control law is obtained. It is composed of state feedback, tracking error compensation, output of modified repetitive controller and preview compensation. Furthermore, in order to achieve a good disturbance estimation and attenuation performance, by applying the results of the standard equivalent‐input‐disturbance theory, a preview repetitive control law with equivalent‐input‐disturbance is offered for the uncertain system with unknown external disturbance. Finally, the numerical simulation example is provided to illustrate the effectiveness of the proposed method.

Estimation and rejection of periodic disturbance in a preview repetitive control system

“…As far as we know, the LQR-based PRC design method is used for continuous-time systems [39,40], which only applies to autonomous system. The proposed preview repetitive controller depends on the model.…”

“…Based on the optimal control theory, the optimal PRC design method was first obtained for continuous-time linear systems [39]. Subsequently, for continuous-time linear systems with relative degree greater than zero, the problem of PRC with equivalent input disturbance (EID) was discussed [40].…”