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This paper proposes fractional delay filter-based repetitive controllers (FDF-RCs) for grid-tied converters. Finite impulse response filters and infinite impulse response filters are used to estimate the fractional-order delay filter in a conventional repetitive controller. To do this, both the Lagrange filter-based repetitive controller (LF-RC) and Thiran filter-based repetitive controller (TF-RC) are utilized as FDF-RCs to compensate a fractional delay. The operating principle, the ladder structure, and the performance analysis of FDF-RCs are addressed. The simulation and the experimental results on a single-phase grid-tied converter verify the harmonic suppression ability and reference-tracking performance of the proposed FDF-RC under the grid frequency variation. Moreover, the advantages of the TF-RC over the LF-RC are discussed by comparing and analyzing the simulation and experimental results.

Compared to the proportional-integral strategy, the repetitive control strategy possesses high suppression ability for the alternating current (AC) harmonics of control signals. Thus, RC controllers are widely used in closed-loop control systems to suppress the periodic harmonics. In order to further improve the brushless DC (BLDC) motor operation performance, a frequency adaptive repetitive controller (FARC) is proposed, and then a novel current loop scheme that concatenation of proportional-integral controller (PIC) and FARC controller is established in this paper. Firstly, due to the real sampling number of the delay element in the BLDC, the motor control system may not be an integer, the designing process of the FARC parameters was studied, and an adaptive internal model controller and a novel decomposition rule for FARC were designed based on Lagrange interpolation theory. Secondly, the PIC parameters were analyzed through three-dimensional and two-dimensional images of the frequency characteristics. Furthermore, a composite controller that added a forward channel in the novel current loop was proposed, and the stability of the control system used the composite controller was analyzed through Lyapunov theory. It should be noted that the analysis of FARC mainly focused on the simplified structure and the parameter optimization, which is usually ignored in the previous studies. Finally, the BLDC motor control system model was established through Matlab/Simulink software, and the operation performances of the BLDC motor control system utilizing different current loop controllers were studied. The simulation results show that the proposed FARC can reduce current distortion and torque ripples, thus, the BLDC motor operation performances can be improved effectively.

The multi-rate repetitive controller (MRC) can achieve zero steady-state error in tracking the reference current signal of grid-connected inverters, save the settling time effectively, and improve the running speed. However, when the grid frequency fluctuates, the harmonic suppression performance of MRC will degrade. Aiming at the problem of harmonic suppression performance degradation, a fractional-order MRC (FOMRC) based on the farrow structure fractional delay (FD) filter is proposed. Firstly, the equivalent digital model of MRC is established, and a Farrow structure fractional delay (FD) filter based on Taylor series expansion is selected as the internal model filter of MRC. The stability analysis and harmonic suppression characteristics of the FOMRC are analyzed. Then, the parameter design of FOMRC applied to an LCL single-phase grid-connected inverter control system is given. Finally, the simulation results show that the proposed method has better transient and steady-state performance than the CRC when the grid frequency fluctuates.

Due to the traditional grid-connected current control method of single Proportional Integral (PI) and Repetitive Control (RC) strategies, the photovoltaic inverter output current will have a distortion problem, which can not only maintain the stability of the whole photovoltaic system, but also the current quality of the photovoltaic inverter grid-connected system is reduced in the case of high-order LCL photovoltaic inverter control system operation. So, a strategy of PI + repetitive control in two-phase stationary frame is proposed. The introduction of the weighting coefficient m of the PI controller branch can enhance the adjustment ability of the PI link and accelerate the responding speed to meet the dynamic characteristics of the entire operating system, while the other weighting coefficient n on the repetitive controller branch can increase the correction capability and eliminate the steady-state error to meet system steady-state requirements. The scheme not only simplifies the coordinate transformation and decoupling calculation process, but also improves the harmonics suppression ability of the photovoltaic inverter and reduces the total harmonic distortion rate of the grid-connected current. At the same time, with the load operation mode change, the system can also retain better stability and keep a fast dynamic response capability, and the grid current can be able to return to a stable state in one cycle. Finally, the effectiveness of theoretical analysis and the strategy is verified by simulation.

Vibrations often result in fatigue breakage in quadcopter flight operations. Reducing the vibration effect is the main important issue for quadcopter flight. Enhanced dynamic stiffness is required in the quadcopter control system for the vibration rejection ability. In this paper, the dynamic stiffness of the quadcopter control system is constructed and is used as an index for the performance of the quadcopter control system to resist an external oscillatory load. To rapidly reduce the vibration effect, a repetitive controller is introduced in the quadcopter control system, where the direct dynamic stiffness and the quadrature dynamic stiffness with variable frequencies are proposed. A theoretical model of the dynamic stiffness of the quadcopter control system is established by analyzing the definition of dynamic stiffness. Simulated and experimental results show that the magnitudes of the direct dynamic stiffness with the proposed repetitive controller are larger than those without the repetitive controller. The quadrature dynamic stiffness with the proposed repetitive controller is relatively smooth compared to that without the proposed repetitive controller, which can be used to verify the stability being improved by the designed repetitive controller. In addition, the magnitudes of the loss factor of the quadcopter control system with the repetitive controller are lower than those without the repetitive controller.

In many applications, add-on type repetitive controllers have been reported to have prominent capability of attenuating periodic disturbances and/or tracking periodic reference commands. However, the effective information such as performance weighting functions for the design of feedback controllers has not been considered sufficiently on the design of repetitive controllers. In this study, we deal with a problem of a robust repetitive controller design for an uncertain feedback control system using its explicit performance information. We first show that a robust stability condition of repetitive control systems has a similar form with the well-known robust performance condition of general feedback control systems. The repetitive controller is designed using the performance weighting function for the design of the robust feedback controller. It is also shown that a steady-state tracking error of the repetitive control system is described in a simple form without time-delay term. This result yields that the repetitive control system has a much larger loop gain in the steady state than the feedback control system. Moreover, this paper provides sufficient conditions ensuring that the power of the steady-state tracking error in the repetitive control system is less than or equal to that of the feedback control system. Based on the obtained results, we present repetitive controller design method using the design information of the feedback control system. Finally, application studies on the track-following control system of optical disk drives are performed to show the validity of the proposed method.

In this paper, the tracking of the zero moment point (ZMP) trajectory for humanoid locomotion is addressed. For that, a combination of a repetitive controller (RC) and a linear quadratic regulator (LQR) is proposed. The RC controller achieves a zero steady state tracking error for any periodic desired output with a fixed period. Here, the robot model is simplified as a cart table model. In the first stage, a walking pattern with constant gait is considered to allow the use of a repetitive controller. The results are then compared to a classical PD control. In the second part, the proposed controller is applied to track a desired ZMP profile generated using a central pattern generator (CPG). Here, the speed of the oscillator is adjusted via a proper selection of the parameters of the CPG and the RC design is simultaneously updated to assure the perfect tracking of the ZMP.

Conventional repetitive controller can hardly obtain a fast dynamic response. In order to achieve a faster dynamic performance, an improved repetitive controller is proposed in this study. The controller adds a proportional link in parallel with the original repetitive control loop. Based on the regeneration spectrum theory and the sensitivity function, the stability, steady-state error and convergence of the control system are analysed. A parameter design method is also developed. The feasibility of the controller is shown in simulations and verified by the experimental works. The simulation and experiment results confirm that the improved repetitive controller and the parameter design method are effective in the active power filter design.

Vibration disturbances with variable instantaneous frequencies can be found in many industrial applications. Therefore, rejecting vibration disturbances is a key point for accuracy machining. This paper presents a new method for synthesizing repetitive controllers capable of rejecting variable instantaneous frequencies disturbance. The instantaneous frequencies of the disturbance signal are always consisted of multiple-periods characteristics. Therefore, multiple-periodic repetitive control scheme is obtained and multiple-periods are estimated by Hilbert-Huang transform (HHT). HHT is a way to decompose a signal into so-called intrinsic mode functions, and obtain instantaneous frequency data. It is designed to work well for data that is non-stationary and non-linear. Control performance and stability of the proposed repetitive controller with a multi-periodic disturbance are analyzed and its control scheme can be obtained. The decay rate of the rejecting error due to the multiple-periodic disturbance inputs is related to the peak value of a defined regeneration spectrum function. The control performance of the present method is evaluated in an experimental disturbance rejecting control system. Both computer simulation and experimental results are presented to illustrate the effectiveness of the proposed repetitive controller design.

PV inverters and active filters are topologically consistent, and this structural commonality facilitates the integration of the two, thus helping to improve the overall efficiency of the PV grid-connected system. In terms of control strategy, the quasi-proportional resonance (PR) controller exhibits excellent dynamic response performance, but it has the inherent limitation of steady-state tracking error; while the repetitive controller, although it can achieve zero steady-state error tracking, suffers from the problem of delayed dynamic response due to phase lag. To solve this contradiction, a composite control system is formed by combining the quasi-PR control with the optimised repetitive control, which retains the fast dynamic response advantage of the quasi-PR control and integrates the static-free tracking capability of the improved repetitive control, thus achieving a synergistic optimisation of the dynamic characteristics and steady state accuracy.