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This paper presents a disturbance-rejection method for a modified repetitive control system with a nonlinearity. Taking advantage of stable inversion, an improved equivalent-input-disturbance (EID) estimator that is more relaxed for system design is developed to estimate and cancel out the influence of the disturbance and nonlinearity in the low-frequency domain. The high-frequency influence is filtered owning to the low-pass nature of the linear part of the closed-loop system. To avoid the restrictive commutative condition and choose a Lyapunov function of a more general form, a new design algorithm, which takes into account the relation between the feedback control gains and the observer and improved EID estimator gains, is developed for the nonlinear system. Furthermore, comparisons with the generalized extended-state observer (GESO) and conventional EID methods are conducted. A clear relation between the developed estimator and the GESO is also clarified. Finally, simulations show the effectiveness and the advantage of the developed method.

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A new configuration of a modified repetitive-control system has been devised for a class of strictly proper plants that suppresses exogenous disturbances and uncertainties in the dynamics of the plant. It extends the applicability of the control system. The system consists of four parts: a two-dimensional augmented model of the plant, which takes into account the difference in characteristics between continuous control and discrete learning in repetitive control; an equivalent-input-disturbance estimator; a state observer; and a state-feedback controller. A robust-stability condition expressed in terms of a linear matrix equality is used to determine the gains of the observer and the controller. Finally, a comparison of our method with repetitive control based on linear active disturbance rejection control (LADRC) shows how effective our method is and that it is superior to LADRC-based repetitive control.

This paper concerns a repetitive-control system with an input-dead-zone (IDZ) nonlinearity. First, the expression for the IDZ is decomposed into a linear term and a disturbance-like one that depends on the parameters of the dead zone. A function of the system-state error is used to approximate the combination of the disturbancelike term and an exogenous disturbance. The estimate is used to compensate for the overall effect of the IDZ and the exogenous disturbance. Next, the state-feedback gains are obtained from a linear matrix inequality that contains two tuning parameters for adjusting control performance; and the pole assignment method is employed to design the gain of a state observer. Then, two stability criteria are used to test the stability of the closed-loop system. The method is simple, employing neither an inverse model of the plant nor an adaptive control technique. It is also robust with regard to the different parameters of the IDZ, uncertainties in the plant, and the exogenous disturbance. Finally, two numerical examples demonstrate the effectiveness of this method and its advantages over others.

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