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.
This paper concerns a Padé-approximation-based preview repetitive control (PRC) scheme for continuous-time linear systems. Firstly, the state space representation of the repetitive controller is transformed into a nondelayed one by Padé approximation. Then, an augmented dynamic system is constructed by using the nominal state equation with the error system and the state equation of a repetitive controller. Next, by using optimal control theory, a Padé-approximation-based PRC law is obtained. It consists of state feedback, error integral compensation, output integral of repetitive controller, and preview compensation. Finally, the effectiveness of the method is verified by a numerical simulation.
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