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A constructive derivation of repetitive control is obtained, through attempting to derive a control law for asymptotic rejection of periodic disturbances. This derivation not only reveals a close relationship between iterative operator inversion and repetitive control, but also suggests a unified design method for a learning control algorithm. Also, based on the observation, digital repetitive control can be generalized to reject periodic disturbance whose period is not exactly an integer multiple of the sampling interval. This study introduces a delay filter in the digital repetitive control law, which optimally interpolates the signal between samples, thus effectively reconstructing the signal of the previous period and making the learning process of repetitive control successful. The proposed optimal delay filter can be updated easily according to different signal periods. Thus it is specifically suitable for on-line tuning when the signal period is changing. Compared with the available tuning methods, the proposed tuning method has excellent steady-state performance while maintaining fast transient and system robustness. The simulations on active noise cancellation within a duct confirm the superiority of this tuning method. @DOI: 10.1115/1.1389309#

This paper presents an optimal repetitive controller design approach when both frequency and time domain criteria are considered. These criteria include limited control force, convergence rate, and robustness. In particular, the design formulation is based on MISO (multiple-input-single-output) plants which aim at solving nodal point problems encountered in flexible dynamic systems. Nodal points represent physical constraints for feedback control, especially when their frequencies are within the control bandwidth. If multiple control paths with distinct nodal frequencies are available, the proposed method is able to design controllers to compensate the effect and reach certain design objectives. The ellipsoid algorithm is used to calculate controllers’ parameters. Experiments were conducted to demonstrate the proposed method.

This paper presents the theoretical work about active noise cancellation in ducts. The proposed control system is designed based on the assumption of a one-dimensional sound field. The controller consists of a feedforward block which serves as a noise observer. The feedback portion of the control algorithm is to minimize residual disturbances. Closed-loop stability of the MIMO (multiple-input-multiple-output) system is analyzed and the result shows that the dynamic influenced by the space-feedforward and feedback controllers can be decoupled. Both semi-infinite and finite-length ducts are considered in this study and simulation examples are given to illustrate the effectiveness of the proposed controllers.

In this paper, the problem of active sound cancellation in finite-length ducts is investigated. The closed-form solution of a one-dimensional wave equation is obtained as the plant model. The controllability, observability, and transmission zeros are discussed based on the transfer function model. For ducts with totally reflective boundaries, stabilization can be achieved by using a speaker (actuator) and a microphone (sensor). Cases of collocated and noncollocated sensors and actuators are presented. A repetitive control algorithm was developed to drive the actuator so that harmonic noises in a duct are attenuated. For a duct with partially reflective boundaries, the application of repetitive control prevents sound from leaking out of the duct at a chosen end. A simulation study demonstrating the effects of this feedback control scheme is also presented.

This paper presents the structure and analysis of the segmented discrete-time repetitive controller. The repetitive controller is designed to reject periodic disturbance and/or track periodic reference signal with known period. Resulted from the Internal Model Principle, the repetitive control law is applied to the entire control path. However, when crucial segments within a control path are of concern, the segmented repetitive control law, which applies control actions only to those segments, can be utilized to save the memory space. It is shown that such a segmented repetitive control system is stable if the original nonsegmented one is stable.

In this paper, an adaptive digital algorithm for rejecting periodic disturbances is proposed. Modified from the adaptive tracking controller [4], the controller is constructed in a “plug-in” manner, i.e., it can be added to an existed feedback control system without altering the original closed-loop configuration. It is shown that the controller can reject disturbances at selected frequencies independently. Furthermore, since the controller only deals with phase and gain of the error signal, no structural information about the plant is required. The controller is implemented on a disk drive system for track following. The result shows that by rejecting the disturbance up to four times of its fundamental frequency, the tracking error is reduced substantially.