Improving disturbance-rejection performance in a modified repetitive-control system based on equivalent-input-disturbance approach

This paper presents a method to actively reject aperiodic disturbances and to suppress uncertainties in a modified repetitive-control (RC) system, based on an equivalent-input-disturbance (EID) approach. The influences of aperiodic disturbances and uncertainties on the input channel are estimated by an EID estimates and then rejected by incorporating the estimation into a repetitive control law. First, how to construct an EID-based modified repetitive-control system is described, in which a correction is introduced to the amount of the delay of the repetitive controller to enhance the steady-state tracking performance. Next, a linear-matrix-inequality-(LMI)-based stability criterion is derived by employing the Lyapunov functional method. Two tuning parameters introduced in the LMI can manipulate the preferential adjustment of the robust stability and learning efficiency and thus improve both transient and steady-state performances. Then, an optimisation algorithm is presented to produce optimal controller gains. Finally, simulations exhibit the design procedure in detail, and the superiority of the proposed method in this paper is demonstrated through comparisons with some conventional RC and $H_\infty $H∞ RC methods.