Fractional Repetitive Control Research Articles

Youla Parameterization-Based Fractional Repetitive Control of Arbitrary Frequency Disturbance Rejections for Line-of-Sight Stabilization

Youla Parameterization-Based Fractional Repetitive Control of Arbitrary Frequency Disturbance Rejections for Line-of-Sight Stabilization

Fractional Repetitive Control of Nanopositioning Stages for High-Speed Scanning Using Low-Pass FIR Variable Fractional Delay Filter

The repetitive control (RC), capable of tracking periodic trajectories and rejecting periodic disturbances, is a promising technique to control the nanopositioning stages for high-speed raster scanning. In digital implementation of the RC scheme, the number of delay points has to be an integer, which implies that the sampling frequency should be an integer multiple of the desired tracking frequency. Clearly, this is a severe limitation on the range of the trajectory frequencies where the RC scheme can effectively be applied. To overcome this limitation, this article proposes a low-pass FIR variable fractional delay filter as an alternative to the conventional interpolating method employed in conventional fractional RC scheme. This filter combines the interpolating and the low-pass filtering that are employed in the fractional RC and its coefficients are analytically computed as a function of fractional delay; thereby, making it suitable for trajectories of all frequencies. The weighted-least-square method is employed to design the low-pass FIR variable fractional delay filter, where the weights are tuned to minimize the approximation errors within the bandwidth-of-interested. Experimental results are presented to demonstrate the advantages of the proposed method over the conventional RC scheme as well as the interpolating-based fractional RC scheme. These results show that the proposed RC scheme with low-pass FIR variable fractional delay filter improves the tracking performance of the nanopositioner significantly, especially for the trajectories with high-frequency.

Harmonic Current Suppression of Magnetically Suspended Rotor System via Odd-Harmonic Fractional RC

As an efficient actuator for microvibration applications, a magnetically suspended rotor (MSR) system is always stymied by rotor mass imbalance and sensor runout, which will result in a harmonic disturbance in control current and further lead to severe periodic vibrations. In this paper, an odd-harmonic fractional repetitive control strategy is investigated for MSR systems to suppress odd-harmonic current with pertinence at low rotation speed. In contrast with conventional repetitive control (RC), only half of the delay units are required in the proposed control scheme. Therefore, it can achieve less computational burden and a faster convergence rate. Additionally, suppression accuracy of RC is vastly improved by adopting fractional delay filters, especially in fractional scenarios. The inset mode of RC is also modified for a simple system structure. Experimental results on a magnetically suspended flywheel are provided to validate the effectiveness of the proposed method.

Fractional repetitive control of nanopositioning stages for tracking high-frequency periodic inputs with nonsynchronized sampling.

The repetitive control (RC) has been employed for high-speed tracking control of nanopositioning stages due to its abilities of precisely tracking periodic trajectories and rejecting periodic disturbances. However, in digital implementation, the sampling frequency should be integer multiple of the tracking frequency of the desired periodic trajectory. Otherwise, the rounding error would result in a significant degradation of the tracking performance, especially for the case of high input frequencies. To mitigate this rounding effect, the fractional repetitive control (FRC) technique is introduced to control the nanopositioning stage so as to precisely track high-frequency periodic inputs without imposing constraints on the sampling frequency of the digital control system. The complete procedure of controller design and implementation is presented. The techniques to deal with the problems of non-minimum phase system and fractional delay points number are described in detail. The proposed FRC is plugged into the proportional-integral control, and implemented on a custom-built piezo-actuated nanopositioning stage. Validation experiments are conducted, and the results show that the tracking errors caused by the rounding effect in the traditional RC approach are almost completely eliminated, when tracking sinusoidal waveforms with frequencies from 1000 Hz to 1587.3 Hz under the sampling frequency of 50 kHz, where the fractional parts being rounded vary from 0 to 0.5.

Hybrid Fractional Repetitive Control for Magnetically Suspended Rotor Systems

This paper investigates a hybrid fractional repetitive control (HFRC) scheme for magnetically suspended rotor systems to suppress harmonic current caused by mass imbalance and sensor runout. With parallel structure, HFRC consists of a frequency-adaptive dual-mode repetitive controller (DMRC) and a phase-shift notch filter. By introducing fractional delay filters, the proposed DMRC provides frequency adaptability to eliminate odd and even harmonics independently at fixed sampling rate. Its delay time is halved compared with the conventional repetitive control scheme, and the control gains can be weighted to ameliorate system dynamic response according to harmonics distribution. Moreover, as the domination of control current, fundamental frequency current is additionally rejected by the notch filter; thus, achieving smaller overshoot and faster suppression performance. An improved phase compensator is designed in HFRC to expedite current convergence rate while stabilizing the overall system. Experimental results on a magnetically suspended flywheel demonstrate the advantages of the proposed method.

High-Performance Grid Simulator Using Parallel Structure Fractional Repetitive Control

In this paper, a high-performance grid simulator based on a parallel structure fractional repetitive control scheme is employed to emulate various operation scenarios of power grids for testing power products. In this paper, a simple fractional repetitive control scheme is proposed for grid simulators to achieve high-accuracy tracking performance. Using parallel branches, the proposed repetitive controller can flexibly select the interested harmonics for compensation, and independently, tune the convergency rate at selective harmonic frequencies. Compared with the conventional repetitive control, the proposed control scheme achieves faster transient response. Moreover, the number of delay units required in the proposed repetitive controller is reduced to at least half of that in a conventional repetitive controller. Design process and stability criteria are presented in details. A set of experimental results is provided to verify the effectiveness of the proposed approach.

Parallel Structure Fractional Repetitive Control for PWM Inverters

In this paper, a parallel structure fractional repetitive control (RC) scheme is proposed to improve the performance of pulsewidth-modulation (PWM) inverters in fractional cases where the sampling rate of the digital control system is not an integral multiple of the fundamental frequency. By introducing a correction factor, the new control scheme increases the control gains for all harmonics and locates poles accurately at targeted harmonic frequencies. As a result, the proposed control scheme achieves better tracking and rejection performance than conventional RC. Moreover, the parallel structure fractional repetitive controller requires less data memory. Dynamic response is also improved. The stability and convergence of this method are proved. Experimental results on a single-phase PWM inverter illustrate the advantages of this control scheme.