Repetitive Control System Design Based On Equivalent Input Disturbance

Repetitive control (RC) provides a simple and feasible solution to the high performance control of a class of periodic signals for many industrial systems since repetitive control can almost completely track or reject such periodic signals.In this dissertation, to cope with the non-periodic disturbance rejection problem in conventional RC systems, a novel equivalent input disturbance (EID) based repetitive control system has been developed. Simulation and experiment results demonstrate that the proposed EID-based RC system effectively rejects non-periodic disturbances.Firstly, an EID-based modified RC system is presented in continuous time domain, and then the function of each its composition is analyzed. By equivalently transforming, the system is transformed into an equivalent system which is composed by two subsystems connected in series; a sufficient stability criterion is obtained based on the small gain theorem respectively against the nominal plant and the uncertain plant, and then a system design algorithm is developed; the sensitivity function between reference input and tracking error and that between disturbance and tracking error are derived, and based on these sensitivity functions, relationship between the tracking and rejection performance and the parameters of the system are analyzed. Simulation results show the effectiveness of the proposed EID-based modified RC system.Secondly, in discrete time domain, an EID-based prototype repetitive control (PRC) system is developed as an extension of the proposed system above in continuous time domain. A sufficient stability criterion is obtained by applying the small gain theorem; and a system design algorithm is developed based on the stability criterion. Simulation results show the efficiency of the proposed system.Finally, the two proposed EID-based RC systems are implemented in DOS environment on a motor experiment platform for motor speed control against disturbances. Compared to the conventional RC system, experiment results show that the EID-based RC system obviously makes the motor rotate more smoothly and stably against non-periodic disturbances. Thus, the EID-based RC system is effective in rejecting non-periodic disturbances and feasible in practice.