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This article summarizes developments in linear repetitive control (RC) that represent an effective overall design approach, allowing the user to optimize performance. This involves the design of a compensator, a zero-phase low-pass filter, and an interpolator. Mathematical background is developed that justifies and interprets the compensator frequency domain optimization criterion. The compensator designs can be very effective with a small number of gains, with fast well-behaved learning. Robustness to model parameter uncertainties is accomplished by optimizing the cost summed over models, by adjusting the learning rate as a function of frequency, and by relaxing the zero error requirement as a function of frequency. The mathematical background needed is developed for mult-input multi-output (MIMO) systems, and the generalized MIMO optimization criterion and solution are presented. One can also design a set of single-input single-output designs to handle MIMO systems. Regarding the zero-phase filter used to robustify to unmodeled high-frequency dynamics, specially tailored finite impulse response filter designs cut off or cut down the learning at high frequencies. Interpolation is used to improve performance when the period of interest is not an integer number of time steps, and it is shown how to use the designs when there are multiple unrelated disturbance periods. RC designed to eliminate periodic measurement error is also presented, with results from computer disk drives. [PUBLICATION ABSTRACT]

This paper designs a decentralized sliding mode preview repetitive control (SMPRC) for interconnected nonlinear systems. First, an augmented error system, which is composed of the derivative equation of the available future reference dynamics, the output of the modified repetitive controller and the tracking error dynamics, is constructed. Next, an integral switching surface is designed to verify the robust asymptotic stability of the considered system subject to nonlinearity. Then, the preview repetitive-control (PRC) law design problem is transformed into the stability problem of the augmented system considering the nominal conditions. Thereafter, a sliding mode control (SMC) law cooperates with the PRC law with the purpose to ensure the robustness of the interconnected systems in the presence of nonlinearity. Further, the required stability conditions are derived on the basis of a Lyapunov analysis, linear matrix inequalities (LMI) and the singular-value-decomposition (SVD) technique. Finally, the numerical simulation results demonstrate the effectiveness of the proposed method.

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.

Individual pitch control (IPC) is an effective and widely used strategy to mitigate blade loads in wind turbines. However, conventional IPC fails to cope with blade and actuator faults, and this situation may lead to an emergency shutdown and increased maintenance costs. In this paper, a fault‐tolerant individual pitch control (FTIPC) scheme is developed to accommodate these faults in floating offshore wind turbines (FOWTs), based on a Subspace Predictive Repetitive Control (SPRC) approach. To fulfill this goal, an online subspace identification paradigm is implemented to derive a linear approximation of the FOWT system dynamics. Then, a repetitive control law is formulated to attain load mitigation under operating conditions, both in healthy and faulty conditions. Since the excitation noise used for the online subspace identification may interfere with the nominal power generation of the wind turbine, a novel excitation technique is developed to restrict excitation at specific frequencies. Results show that significant load reductions are achieved by FTIPC, while effectively accommodating blade and actuator faults and while restricting the energy of the persistently exciting control action.

For grid-connected inverters, switching harmonics can be effectively attenuated through an LCL-type filter. In order to suppress resonance and guarantee good performance, many strategies (e.g. active damping (AD), harmonic resonant control, repetitive control and grid feedforward) have been proposed. However, the wide variation of grid impedance value challenges system stability in practical applications. The aforementioned methods need to be investigated. This study evaluates the applicability of each part of the overall control in a weak grid case with the use of a stability criterion. It has been demonstrated that the feedback-based AD control can work well in a wide range of grid conditions. However, the resonant and repetitive control methods meet constraints. The grid feedforward method brings in an extra positive feedback path, and consequently results in high harmonics or even instability. Finally, a recommendation for system design has been presented. Simulations and experiments have been provided to verify the analysis.

This paper investigates the disturbance rejection for a modified repetitive control system (MRCS) that is described by a class of linear singular systems in the presence of external disturbances and time-varying delay. In particular, an equivalent-input-disturbance (EID)-based estimator is included in the MRCS to compensate both periodic and aperiodic disturbances which yields an EID-based MRCS. More precisely, the incorporation of the EID-based estimator into the control input enables rejection of all types of disturbances in MRCS and tracking of a periodic reference input is archived via a repetitive controller. Attention is focused on the state-feedback repetitive controller design which not only guarantees the regular, impulse free, and asymptotic stability of the closed-loop singular MRCS, but also provides an optimized upper bound of the time-varying delay. Based on Lyapunov stability theory and utilizing some advanced mathematical techniques, a new set of delay-dependent sufficient conditions is presented in terms of linear matrix inequalities for obtaining the required result. Then, an explicit expression for the desired state-feedback repetitive control law is developed. Further, the obtained results are validated through two numerical examples in the simulation section.

A novel fractional-order repetitive control based on phase angle information interpolation is proposed for single-phase LCL-type inverters in this paper. Conventional fractional-order repetitive control typically relies on inaccurate grid frequency information detected by a phase-locked loop or the frequency-locked loop, which may result in a potential degradation in harmonics suppression capability. To address this issue, phase information is investigated to implement the fractional order of the repetitive controller through the linear interpolation method. A major advantage of the proposed scheme lies in that it avoids explicit frequency calculation and reduces sensitivity to frequency estimation fluctuations compared with conventional fractional-order repetitive control, enhancing its frequency adaptability. The stability analysis and the design process for the proposed scheme based on a plug-in-type repetitive control are given. Experimental results support the efficacy and advantages of the proposed control strategy.

As power electronic converters increase in scale, impedance measurement has become critical for assessing system stability, detecting islanding, and performing other critical analyses. This paper derives the impedance from the voltage and current responses measured after controlled perturbations, employing d-q frame impedance matrices. A static var generator (SVG) with redundant capacity is employed as the perturbation source, and a fractional-order repetitive control (FORC) strategy is introduced to inject the multi-frequency signal efficiently, eliminating the need for additional hardware. By optimizing the perturbation design and suppressing the dynamic error of the phase-locked loop, the method achieves both convergence and accuracy. Comprehensive simulations and experiments validate the approach.

When a three-phase four-wire grid-connected energy storage inverter is connected to unbalanced or single-phase loads, a large grid-connected harmonic current is generated due to the existence of a zero-sequence channel. A controller design approach for grid-connected harmonic current suppression is proposed based on proportion–integral–repetitive (PI–repetitive) control for a three-level neutral point clamped (3L-NPC) three-phase four-wire inverter. By designing the variable parameters n (gain coefficient of the PI controller) and Q s (gain of the repetitive controller), the effect of the PI–repetitive controller gain on current harmonic suppression is analyzed using a three-dimensional amplitude gain curve. A simplified impedance model in the d 0-frame for a three-phase four-wire inverter is proposed. Based on the impedance model in the d 0-frame, the system stability is analyzed under different PI–repetitive control gains by the generalized Nyquist criterion. Finally, the optimal controller design is obtained by a gain characteristic and system stability analysis. The controller obtained by this harmonic suppression analysis method can simultaneously ensure the best grid-connected current quality of the three-phase four-wire inverter and the dynamic stability of the system. Simulation and experimental results verify the effectiveness and correctness of the proposed controller design approach for grid-connected harmonic current suppression.

Due to attractive features, including high efficiency, low device stress, and ability to boost voltage, a Vienna rectifier is commonly employed as a battery charger in an electric vehicle (EV). However, the 6k ± 1 harmonics in the acside current of the Vienna rectifier deteriorate the THD of the ac current, thus lowering the power factor. Therefore, the current closed-loop for suppressing 6k ± 1 harmonics is essential to meet the desired total harmonic distortion (THD). Fast repetitive control (FRC) is generally adopted; however, the deviation of power grid frequency causes delay link in the six frequency fast repetitive control to become non-integer and the tracking performance to deteriorate. This paper presents the detailed parameter design and calculation of fractional order fast repetitive controller (FOFRC) for the non-integer delay link. The finite polynomial approximates the non-integer delay link through the Lagrange interpolation method. By comparing the frequency characteristics of traditional repetitive control, the effectiveness of the FOFRC strategy is verified. Finally, simulation and experiment validate the steadystate performance and harmonics suppression ability of FOFRC.