This paper proposes the design of robust repetitive control with time-varying sampling periods. First, it develops a new frequency domain method to design a low-order, stable, robust, and causal IIR repetitive compensator using an optimization method to achieve fast convergence and high tracking accuracy. As such, a new stable and causal repetitive controller can be implemented independently to reduce the design complexity. The comprehensive analysis and comparison study are presented. Then, this paper extends the method to design a robust repetitive controller, which compensates time-varying periodic signals in a known range. A complete series of experiments is successfully carried out to demonstrate the effectiveness of the proposed algorithms.

The repetitive control is well known for rejecting the periodic disturbances. However, most of the existing repetitive control algorithms assume that either the plant is known or the disturbance period is fixed. This study proposes the digital design of adaptive repetitive control for a class of linear systems subject to time‐varying periodic disturbances, whose periods are assumed to be identifiable. The proposed control is based on the direct adaptive control scheme and the internal model principle. A comparative study is conducted and the effectiveness of the approach is verified in simulations and experiments on a servo motor system.

Time of Flight (ToF) Lidar range finder is widely used in various applications such as automotive driving, marine environment surveying, atmospheric observing, and physical distancing monitoring. The ToF Lidar offers a high-resolution range, which can be achieved by increasing the modulation frequency. However, when the modulation frequency is increased, the maximum unambiguous range tends to decrease. To overcome such a problem, we develop a novel ToF Lidar range finder based on dual-modulation frequencies switching, capable of providing an extended range while maintaining the high-resolution. In the design, the modulation frequency is alternately changed between 2 MHz and 10 MHz to modulate the intensity of the laser diode as a transmitter. We operate an avalanche photodetector as a receiver to obtain a reflection of modulated light from a target. By switching between dual-modulation frequencies, the photodetector detects two-phase shifts, which are calculated by our phase-shift algorithm. It is shown that the proposed algorithm can solve the ambiguous range problem. As proof of the concept, we experimentally demonstrate a range measurement of a target up to 55 m distance, where the ambiguous range is experienced four times if only a single modulation frequency of 10 MHz is used. Interestingly, the range ambiguity no longer appears after applying the proposed design and algorithm.

Tracking and rejecting periodic signals are common tasks in many control applications. A well-known use of Repetitive Control (RC) is to both track a periodic reference signal and reject periodic disturbance. This paper reviews various designs of RC that are classified into basic RC design and robust RC design. The recent applications of RC are also presented in this paper.

Repetitive Control (RC) has been widely used to track/reject periodic signal. However, RC alone fails to track any non-periodic reference signal. Another control scheme such as Model Reference Control (MRC) or Model Reference Adaptive Control (MRAC) is required to do such task. MRC is employed when the plant parameters are known, while MRAC is used when the plant parameters are unknown. Therefore, MRC/MRAC needs to be combined with RC in order to simultaneously track any reference signal (not necessarily periodic) and reject the periodic disturbance. The design of RC mostly assumes the constant frequency of disturbance which leads to the selection of a fixed sampling period. In practical, disturbance is possibly time-varying in frequency. The sampling period has to be carefully adjusted in order to keep the number of samples per period remains constant. This sampling period adjustments change the plant parameters. This paper proposes the design of MRAC combined with RC for system subject to periodic disturbance with time-varying frequency. As a preliminary, the design of MRC combined with RC is also discussed here.

Repetitive controller is usually designed by assuming constant period of reference/disturbance signal, which leads to the selection of fixed sampling period. However, in practical, reference signal and disturbance are varying in period. Therefore, sampling period is carefully adjusted to overcome period variation, which makes characteristic of the plant is also changing. Robust design is employed to obtain pre-compensator which stabilizes closed loop repetitive system for all values of sampling period in the known interval. The design consists of two steps; constructing a nominal pre-compensator and designing robust pre-compensator which works well for large range of sampling period variation. In the design, time-varying plant parameters due to sampling period variation are treated as parametric uncertainties. The new form of pre-compensator which works with this robust design is also proposed.