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In this paper, a new robust adaptive Disturbance Rejective Repetitive _ Second Order Sliding Mode (DRRISOSM) control scheme using improved sliding mode control (ISOSM) technique combine with repetitive control (RC) to achieve the accurate speed control and strong anti-disturbance for enhancing Field Oriented Control (FOC) performance of SPIM drives, is proposed. First, the super twisting algorithm (STA) is combined with second order sliding mode (SOSM) to make increase the convergence speed and the reference tracking ability, enhance the robust and stably of drive systems, eliminates the chattering phenomenon. Then, to optimize the anti-disturbance performance, a plug-in RC is integrated into the ISOSM structure, combining of the benefits of improved SOSM with RC helps effectively improve the closed-loop control performances in terms of tracking and rejection of harmonic disturbance of the nonlinear SPIM drive systems. This control strategy also proposes a simple but efficient load disturbance estimator to help identify and proactively eliminate disturbances. Furthermore, the virtual control vectors are chosen based on Lyapunov theory, so that the system stability can be assured. The performance of the DRRISOSM control scheme is validated by Matlab-2023b, the obtained simulation results demonstrated the effectiveness and superior performance in terms of tracking reference and rejecting periodic torque disturbance, reducing speed oscillations by cancelling the effect of the torque disturbance of DRRISOSM control strategy against the conventional control strategy. [ABSTRACT FROM AUTHOR]

Based on additive state decomposition technique, this article presents an adaptive dynamic‐surface repetitive control method for a class of uncertain nonlinear systems with mismatched disturbances and input delay. First, the original uncertain nonlinear system is decomposed into a linear time invariant (LTI) primary system responsible for the periodic signal tracing and rejection task, and a nonlinear secondary system with input time delay responsible for the robust stabilization task. A modified repetitive controller with a small correction to the delay constant is then independently designed for the LTI primary system, while an adaptive dynamic surface controller is designed for the nonlinear secondary system. Stability analysis is performed for each subsystem and the design procedure of the whole system is presented in detail. Finally, comparative simulations with other repetitive control and dynamic surface control methods show that the presented method not only relaxes the constraints on the reference inputs and exogenous disturbances, but also ensures that the system has better disturbance rejection and periodic‐signal tracking performance in both transient and steady states. As a result, this method broadens the application of both repetitive control and dynamic surface control. [ABSTRACT FROM AUTHOR]

This paper proposes a Repetitive Dynamic Matrix Control (RDMC) for systems with periodic specifications. The new algorithm is able to track periodic references and reject repetitive disturbances with a known period based on a modified prediction error. A repetitive version of the Generalized DMC (GDMC) is also proposed such that it can be applied to control open-loop unstable systems. Only the step-response coefficients are required to describe the dynamical system such that the RDMC preserves the modeling simplicity of the Dynamic Matrix Control (DMC). The proposed solution can be interpreted as an extension of the DMC for repetitive control applications. A data-driven filter design is proposed in order to ensure null prediction steady-state error in the presence of periodic disturbances even for unstable open-loop systems. Two case studies are presented to show the usefulness of the proposed strategy for control systems with periodic specification and to illustrate the typical advantages and drawbacks of the proposed repetitive control extension of the DMC algorithm. • A Repetitive DMC has been proposed for stable and unstable systems. • A new data-driven filter design is presented for unstable systems. • Periodic set-point tracking and repetitive disturbance rejection are achieved. [ABSTRACT FROM AUTHOR]

To address the control performance and harmonic suppression issues in maritime vessel rudder permanent magnet servo systems, a fractional-order PID controller was introduced into the existing improved repetitive control strategy. We used the Oustaloup approximation algorithm and particle swarm optimization for tuning the fractional-order PID controller. The optimized parameters substantially improved the control performance. By integrating the fractional-order PID controller with the improved repetitive controller, a composite fractional-order PID repetitive control strategy was formed. Finally, MATLAB/Simulink simulations were conducted to compare and verify the disturbance rejection and harmonic suppression capabilities of the improved control strategy. The results demonstrate its superior control performance, thereby increasing the practicality of the control system in dealing with various situations. [ABSTRACT FROM AUTHOR]

The achievable performance of conventional repetitive control (CRC) is constrained by the error amplification at the non-harmonic frequencies, the intrinsic sensitivity to the signal period shift and the limited tracking frequency range under fixed sampling rate. To remedy these undesirable behaviors, a notch-filter-based repetitive control (NF-RC) is proposed based on the spectrum-selection filtering scheme in this paper with application to fast tool servos (FTSs). The loop-shaping property of this NF-RC can be flexibly designed by the cascade of a series of parameterized IIR notch filters without the aforementioned limitations of the CRC, so as to provide a unified formula for various RCs and even resonant control schemes. A general realization along with several simplified versions of the IIR notch filter is derived for the digital implementation of the NF-RC. Comparative trajectory tracking experiments on a self-developed FTS have validated the superiorities of the proposed NF-RC in terms of the performance improvement for periodic reference tracking, the robustness against the signal period variations and the trackable frequency range under fixed sampling rate. Taking advantage of an excellent comprehensive performances of the NF-RC scheme, the radial sinusoidal surface and the water-drop surface were successfully produced with high form precision and excellent surface quality after the FTS-based diamond turning. • A novel notch-filter-based repetitive control (RC) scheme is proposed. • This RC scheme can suppress the nonperiodic errors amplification. • This RC scheme can maintain the robustness against the signal frequency fluctuation. • This RC scheme can track any harmonic references under a fixed sampling rate. • This RC scheme provides a unified design framework for various existing RCs. • Two high-accuracy micro-structured surfaces are fabricated with this RC scheme. [ABSTRACT FROM AUTHOR]

The proposed generalized electric spring (G-ES) topology effectively reduces the redundancy caused by the parallel structure of multiple electric springs in a microgrid system. A modeling method for the G-ES is urgently needed to accurately determine the G-ES parameters and to evaluate its transient operation characteristics. The correspondence between Hamilton's principle in mechanics and electricity is introduced, and the feasibility of Hamilton's principle under the smart load topology is verified. The modeling method of the G-ES under Hamilton's principle is discussed, followed by the application of repetitive control strategies on the G-ES. The filter parameters are designed using the normalization method and a simplified parameter design using repetitive controllers was applied. This article introduces the impedance analysis method into the generalized electric spring to analyze its stability under weak network conditions. This work also derives the stability judgment criteria for generalized electric springs. Finally, the feasibility of modeling the G-ES based on the Hamilton's principle was verified using MATLAB and a DSP hardware system. In addition, the consistency between the G-ES and a single intelligent load was verified under the Hamilton's modeling principle. The G-ES stability and dynamic performance under this modeling method meet industry requirements. [ABSTRACT FROM AUTHOR]

In this paper, a new adaptive method is proposed for online frequency estimation of a periodic disturbance by the output measurement based on the fast Fourier transform algorithm. The performance of the proposed algorithm is evaluated in the face of time varying frequency, time varying amplitude, non-sinusoidal periodic disturbance, and different plants. Also, the convergence rate of the method is compared by other estimation methods. Then, the online estimation is used in the repetitive controller structure for eliminating periodic disturbances with unknown frequencies. A new analysis is performed on RC and the stability conditions are determined in a theorem. These are illustrated in simulation results. The effectiveness of this method is shown on the application of ϕ -shaped PZT active suspension and it is compared by existing results. [ABSTRACT FROM AUTHOR]

With the expansion of renewable energy sources, the stable and high-quality operation of microgrids composed of new energy sources has attracted widespread attention. Among them, the power conversion system (PCS), as an important part of microgrids, plays a crucial role in their operation and management. The PCS operation modes are classified into grid-connected and off-grid modes. However, in off-grid mode, due to the access of nonlinear and unbalanced loads, the output voltage quality of a PCS is worse, and the voltage waveform distortion is serious. To solve these problems, a fast repetitive control (FRC) strategy is proposed for a power conversion system with an Active Neutral Point Clamped (ANPC) architecture of three levels. The voltage loop control strategy can be applied to the voltage/frequency ( V / f ) mode and the grid-forming mode. The control strategy can effectively realize the suppression of the harmonics of the output voltage and has a 100% capability to carry unbalanced loads. Finally, a 1725 kVA PCS prototype is developed, and the proposed control strategy is verified using the MT3200 HIL semiphysical simulator of ModelingTech in the V / f mode as an example. This practically verifies the feasibility and validity of the proposed control strategy, which has a certain degree of engineering practicability and reference due to the simplicity of the design and the ease of realization. [ABSTRACT FROM AUTHOR]

This paper develops a discrete-time repetitive control (RC) system with a fractional-delay internal model. Unlike the conventional RC, the time delay for constructing the internal model is not necessarily an integer, implying that the time delay is allowed to be fractional. In this work, a fractional delay-based repetitive control system is presented. Firstly, the fractional time delay is calculated based on the information of the reference or disturbance along with the associated sampling period. Secondly, the fractional time delay is divided into two parts, i.e., the large integer and small fractional delays. Finally, the fractional part is realized by a stable and causal infinite impulse response (IIR) filter, whose coefficients are calculated using the Thiran formula. The controller structure and stability analysis are developed for three different RCs, namely a fractional-delay general RC (FD-GRC), a fractional delay-odd harmonics RC (FD-OHRC), and a fractional delay-(6 l ±1) RC (FD-(6 l ±1)RC). Experiments and comparison studies of the integer delay-based RCs are conducted to verify the effectiveness and improved tracking accuracy of the proposed method. • The fractional delay-based internal models are formulated for three different RCs. • The proposed delay-based RCs are referred as FD-GRC, FD-OHRC, and FD- (6 l ± 1) RC. • Controller architectures and stability analyses of the proposed RCs are developed. • The fractional delay part in the controller is implemented by an IIR filter. • The IIR filter coefficients are obtained by using Thiran formula. [ABSTRACT FROM AUTHOR]

This paper introduces a novel control scheme to achieve precise repetitive motion within a dual-input-single-output (DISO) system consisting of course-actuator and fine-actuator. Repetitive motion stands as a crucial operation in various applications, particularly in manufacturing processes. Designing a control system capable of accurately tracking reference signals during repetitive motion is imperative for DISO systems. The proposed method focuses on adaptive feed-forward cancellation (AFC) to effectively compensate for position error signals related to the reference signal. A typical control scheme implements AFC for the entire control loop. In the control system, the same characteristic of AFC works for both actuators in the DISO control system. The same AFC output is working to both actuators. On the other hand, the proposed control scheme implements AFC to each actuator. It can generate suitable AFC output for the course-actuator, fine-actuator, respectively. That is, the major contribution of proposed control scheme individually optimizes the AFC in the course-fine control system. This design approach significantly enhances the control performance of DISO systems, considering the distinctive characteristics and stroke limitations of the actuators. Experimental implementation of the proposed control system validated its efficacy, affirming the improvement of control performance in DISO systems.

In order to effectively suppress rotor periodic synchronous vibration caused by the rotor mass eccentricity and sensor detection error of bearingless induction motor (BIM), a rotor vibration suppression control strategy with improved repetitive control is proposed based on the analysis of the problems existing in the traditional repetitive control. On the basis of the vector control model of the BIM system, a simplified suspension control model is derived. The fractional delay filter is used to optimize the repetitive control internal model. Furthermore, for enhancing the stability of the BIM control system, the design method of the repetitive control compensators in high-, middle- and low-frequency region is given in detail. The simulation and experimental results show that the vibration suppression control strategy with the improved repetitive control can effectively suppress the vibration of the rotor in steady state and improve the suspension accuracy of the BIM.

Repetitive controller provides a very low third harmonic dimension in the quantities under control. It exhibits an inherent issue when operated to track variable frequency references. The article deals with the analysis of the operating conditions when the controller is executed at variable frequency without any resynchronization with respect to the pulsewidth modulation carrier, which is the most common mode of operation. The delays introduced are then evaluated analytically concerning the sampling and output frequency that must be tracked. The proposed analysis allows obtaining the maximum delay affecting the control chain, which was introduced by the repetitive control desynched operation. The knowledge of the delay introduced in the control loops is at the basis of any control tuning procedure and gains selection, even when adaptive control strategies are used.

Summary: Control systems are frequently subject to the negative effects of time delays and disturbances, which diminish the systems' tracking performance. In response to these challenges, this paper presents a novel approach, that is, the improved sliding mode observer based repetitive control (ISMO‐RC), to enhance the system's periodic signal tracking in the presence of the input and state time delays and the input disturbances. The design takes the advantages of RC and ISMO, in which RC effectively compensates periodic signals, while ISMO compensates both aperiodic disturbances and the time‐varying input and state delays. The stability of the whole system is guaranteed via the linear matrix inequality (LMI) and the Lyapunov–Krasovskii functional analysis. The proposed controller is evaluated through extensive simulations and experiments, which demonstrate its superiority over comparative control methods. [ABSTRACT FROM AUTHOR]

Functional electrical stimulation (FES) is a medical device that delivers electrical pulses to the muscle, allowing patients with spinal cord injuries to perform activities such as walking, cycling, and grasping. It is critical for the FES to generate stimuli with the appropriate controller so that the desired movements can be precisely tracked. By considering the repetitive nature of the movements, the learning-based control algorithms are utilized for regulating the FES. Iterative learning control (ILC) and repetitive control (RC) are two learning algorithms that can be used to accomplish accurate repetitive motions. This study investigates a variety of ILC and RC designs with distinct learning functions; this constitutes our contribution to the field. The FES model of ankle angle, which is in a class of discrete-time linear systems is considered in this study. Two learning functions, i.e., proportional, and zero-phase learning functions, are simulated for the second-order FES model running at a sampling time of 0.1 s. The results indicate the superior performance of the ILC and RC in terms of convergence rate using the zero-phase learning function. ILC and RC with a zero-phase learning function can reach a zero root-mean-square error in two iterations if the model of the plant is correct. This is faster than proportional-based ILC and RC, which takes about 40 iterations. This indicates that the zerophase learning function requires two iterations to ensure that the patient's ankle angle precisely tracks the intended trajectory. However, the tracking performance is degraded for both control methods, especially when the model is subject to uncertainties. This specific problem can lead to future research directions. [ABSTRACT FROM AUTHOR]

The permanent magnet synchronous motor (PMSM) driven by the two-level voltage inverters features some drawbacks, such as dead-zone time, nonlinearity and other factors, leading to high amount harmonics in the stator currents. Additionally, the current harmonics amplitude will be decayed with the increasing of the harmonic order, and the main current harmonic components can be illustrated as 6th control signal harmonics. To improve the current harmonics suppression efficiency and maintain the simplicity of the PMSM driven system, the relationships between traditional repetitive controller and bandpass filter are analysed firstly. And then, a proportional–integral​ discrete Fourier transform repetitive control (PI-DFT-RC) scheme is proposed through adopting independent band-pass filters of state frequencies, which can provide infinite gain in stated frequency. Secondly, the discrete periodic signals for RC controller are analysed, and the lead step for DFT-RC controller is also studied, which can increase the signal tracking accuracy of the driven system. Furthermore, the stability of the driven system used PI-DFT-RC controller is analysed through Lyapunov theory. Finally, the effectiveness of the proposed PI-DFT-RC controller is verified by simulation results.

To address the control performance and harmonic suppression issues in maritime vessel rudder permanent magnet servo systems, a fractional-order PID controller was introduced into the existing improved repetitive control strategy. We used the Oustaloup approximation algorithm and particle swarm optimization for tuning the fractional-order PID controller. The optimized parameters substantially improved the control performance. By integrating the fractional-order PID controller with the improved repetitive controller, a composite fractional-order PID repetitive control strategy was formed. Finally, MATLAB/Simulink simulations were conducted to compare and verify the disturbance rejection and harmonic suppression capabilities of the improved control strategy. The results demonstrate its superior control performance, thereby increasing the practicality of the control system in dealing with various situations.

The integer-order delay of proportional–integral multi-resonant-type repetitive control (PIMR-RC) cannot provide excellent control performance for grid-tied inverters when the grid frequency fluctuates. To address this issue and reduce control errors, a fractional delay PIMR-RC (FD-PIMR-RC) scheme is proposed. In addition, to reduce the computational load and memory consumption, a Farrow-structure fractional delay (FFD) filter is adopted. The digital filter with the Farrow structure is flexibly and efficiently used for fractional delay. For each new fractional delay, a large number of calculations and storage for the FFD filter coefficients are avoided, which significantly reduces the computational load and memory consumption. The parameter design of the FD-PIMR-RC scheme is provided in detail, including the implementation of fractional delay based on the Farrow structure. Then, a system stability analysis and parameter optimization are presented. Finally, simulations for the steady-state and dynamic responses are presented, and the validity of the proposed method is demonstrated. [ABSTRACT FROM AUTHOR]

Fast tool servo (FTS) is a promising technique for the high-speed diamond turning of micro-structured functional surfaces due to its fast response capacity. However, the inherent actuator non-linearity, the lightly damped vibration mode and the external disturbance of the FTS would degrade its tracking performance severely and thus restrict its machining ability. To overcome this limitation, a band-stop-filter-based repetitive control (BSF-RC) scheme is proposed in this article to improve the operating performance of the FTS. Firstly, the spectra of the FTS tool paths (FTS-TPs) for machining typical micro-structured functional surfaces with the cylindrical coordinate machining method are analyzed in detail. The results reveal that the frequency components concentrate on the tiny neighborhoods of the rotational frequency of the spindle and its harmonic frequencies. Afterwards, the comb-like band-stop filter used by the BSF-RC is elaborately designed via the cascade of three comb-like notch filters to generate a comb-like band-stop loop shape for covering main spectral components of the FTS-TPs. The analytical expression of the comb-like band-stop filter amplitude as well as the stability condition of the closed-loop control system are derived to provide effective criteria for the parameter selection of the BSF-RC. The experimental validation of the developed BSF-RC scheme is conducted on a five-axis ultra-precision lathe equipped with a self-developed FTS via the diamond turning of three typical micro-structured functional surfaces. The experimental results show that good surface qualities with the maximal form error of a few hundred nanometers and the surface roughness of a several nanometers are achieved for all the obtained micro-structured surfaces by using the BSF-RC scheme under a high spindle speed. • A novel repetitive controller is proposed for fast tool servos to fabricate the micro-structured surfaces. • The frequency components of fast tool servo tool paths for the micro-structured surfaces are analyzed. • The design methods and the stability analysis of the proposed repetitive controller are presented. • Three typical micro-structured surfaces are fabricated by fast tool servo diamond turning. • A submicron form error and a nanometric surface roughness are obtained for all the generated surfaces. [ABSTRACT FROM AUTHOR]

Electrical machines generate unwanted flux and current harmonics. Harmonics can be suppressed using various methods. In this paper, the harmonics are significantly reduced using Iterative Learning Control (ILC) and Neural Networks (NNs). The ILC can compensate for the harmonics well for operation at constant speed and current reference values. The NNs are trained with the data from the ILC and help to suppress the harmonics well even in transient operation. The simulation model is based on flux and torque maps, depending on d q -currents and the electrical angle. The maps are generated from FEM simulation of an interior permanent magnet synchronous machine (IPM) and are published with the paper. They are intended to serve other researchers for direct comparison with their own methods. Simulation results in this paper verify that by using ILC and NNs together, current harmonics in transient operation can be eliminated better than without NNs. [ABSTRACT FROM AUTHOR]

This article presents a complete design of non‐causal finite impulse response (FIR) and infinite impulse response (IIR) compensators for repetitive control. The concept of repetitive controllers involves imitating the inverse frequency response of the feedback control system by minimizing the amplitude of error propagation from one period to the next in the frequency domain. The FIR compensator design has already been presented in our previous work. However, it was not complete since some parameters, such as the number of causal gains and total number of gains were still left open for the designers to select. This work provides a reasonable suggestion on how to choose parameters based on the steepest descent method. In addition, an IIR compensator is further developed based on the designed FIR design. The gains of the IIR compensator are adjusted by aiming to minimize the cost function using the steepest descent. As can be observed from the results, the IIR compensator developed from the FIR compensator cannot overcome the original FIR compensator since its learning performance is relatively slow and the extra gains added to the denominator increase memory usage when executing. [ABSTRACT FROM AUTHOR]

In recent years, modular multilevel converters (MMCs) have been increasingly used in the field of electric vehicle charging and discharging due to their unique performance advantages. However, the unique cascade structure of MMCs raises the problem of the circulating current. Due to chemical processes, aging effects, etc., the capacitance parameters of the upper and lower bridge arms will be asymmetric, which will introduce odd harmonics into the circulating current, increasing system losses and threatening the system reliability. To address this phenomenon, this paper proposes a circulating current suppression strategy with additional virtual impedance (VI) based on a repetitive controller (RC). The corresponding simulation models were built for the comparative study of different circulating current suppression strategies. The results show that the VI-RC circulating current suppression strategy can significantly reduce the odd and even harmonics in the circulating current under asymmetric conditions, and the total harmonic distortion (THD) of the bridge arm current is only 0.98%, which verifies the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper proposes a high precision harmonic controller combined with repetitive and modulated model predictive controllers for standalone inverter applications. The proposed method is configured as a dual loop controller that includes an outer voltage controller with a plug-in repetitive controller (RC) and an inner current controller with a modulated model predictive controller (MMPC). The RC in the outer control loop effectively synthesizes the harmonic current reference when connecting a nonlinear load with a periodic harmonic current. Then, the MMPC-based current controller, with its ultra-wide bandwidth, regulates the harmonic current without additional harmonic current controllers. Thus, the abilities to precisely control the harmonic current and improve the output voltage quality are achieved. To combine the MMPC and the repetitive controller, an equivalent transfer function is derived from the ac sweep result of the MMPC. The stability of the RC is analyzed by applying the equivalent transfer function to the closed-loop voltage control model. To validate the performance of the proposed control method, a 3 kVA single phase 3-level T-type inverter prototype is built and tested. The harmonic compensation and dynamic performance of the proposed method are verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

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This paper concerns the design problem of optimal preview repetitive control (OPRC) for impulse-free continuous-time descriptor systems. First, by using a linear transformation, the descriptor system is transformed into a normal system with relatively low dimensionality and an algebraic system. Based on this, an augmented system which contains the error vector and the derivative of the normal system is constructed. Then, applying the lift technique and introducing a new performance index, the OPRC designing problem is converted into a regulation problem. Based on the optimal control theory, the regulator problem of the augmented system is solved. Furthermore, the explicit OPRC law for the original system is deduced. Different from the existing results, the preview feed-forward and error integral compensations are added into the OPRC system, which can significantly improve the tracking performance. Finally, a numerical example simulation result verifies the validity of the proposed method.

Due to the existence of high amount stator current harmonics caused by the inverter nonlinearity, the operation performance of Permanent Magnet Servo System (PMSS) used Proportional–Integral (PI) controller will be affected. To suppress the current harmonics in the PMSS, a hybrid controller utilizing proportional and repetitive control scheme for the current loop is proposed. Firstly, the phase-frequency characteristic and the magnitude–frequency characteristic for the hybrid controller bode diagrams are analysed. To improve the open-loop gain in the frequency band of high-proportion harmonics and compensate the phase lag, the hybrid controller parameter setting method is also studied. Furthermore, the stability and the anti-interference ability of the PMSS used hybrid controller are analysed through Lyapunov theory. Finally, the PMSS model is established through Matlab/Simulink software, and the operation performances of the PMSS utilizing different current loop controllers are studied. The simulation results show that the proposed hybrid controller can suppress the current harmonics and the output torque ripple effectively.

Magnetic levitation rotating machinery has been widely used in industrial applications. Odd harmonic currents in the active magnetic bearing coils, which are caused by rotor mass unbalance and sensor runout, increase the power consumption and the base vibration. Repetitive control has recently been used to suppress harmonic currents in magnetic bearing systems. However, repetitive control needs the rotor rotational speed information and has some limitations without a speed sensor. In this paper, an adaptive odd repetitive control which does not need the speed sensors is proposed to suppress the active magnetic bearing odd harmonic currents. Compared to the conventional repetitive control, the second-order generalized integral frequency-locked loop is applied in adaptive odd repetitive control to estimate the rotor speed in real time without additional speed sensors. The magnetically suspended rotor with harmonic disturbances is modeled. The work principle, structure, and design of the adaptive odd repetitive control are addressed. The simulation and experiments are carried out on a rotor active magnetic bearing test rig to validate the effectiveness of the proposed adaptive odd repetitive control, and the results show that the active magnetic bearing odd harmonic currents are well suppressed. [ABSTRACT FROM AUTHOR]

Repetitive control (RC), which can track any periodic signal with a known integer period with zero steady-state error, is widely used for current control of grid-tied inverters in microgrids. However, the inherent one fundamental period time delay, leads to poor dynamic performance. Furthermore, the performance of conventional RC (CRC) will degrade when operating at a high variation grid frequency. Therefore, this paper proposes a frequency adaptive improved RC (FA-IRC) for grid-tied inverters. The improved RC (IRC) consists of a repetitive controller with a modified internal model filter, plus a proportional controller. In comparison to the CRC, the IRC has a good dynamic response, because it provides a higher gain and a wider bandwidth at the resonant frequency. Moreover, to achieve the frequency adaptability of the IRC, a fractional delay, based on a finite impulse response (FIR) filter, is built into the IRC system, to ensure that the resonant frequency of the IRC is approximately equal to the actual grid frequency and harmonic frequency. Stability analysis and characteristic analysis of the FA-IRC system are reported in this paper. Simulations are conducted, to demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Summary This paper presents the results of an advanced control strategy that employs active trailing edge flaps to reduce the fatigue loads of an experimental wind turbine. The strategy, called repetitive model predictive control, is a multiple‐input multiple‐output controller that aims at the alleviation of out‐of‐plane blade root bending moments. The strategy incorporates the control commands, output errors, and state deviation from the previous rotation. This way, the time lag in the strain sensor input due to the blade inertia is compensated. Additionally, a strategy to limit the computational costs is presented. The load alleviation performance is evaluated at different yaw cases and compared with different individual flap control strategies. The repetitive model predictive control is able to reduce the fatigue loads by up to 23% compared with the better performing individual flap control strategy. This improvement in load reduction is accompanied by an increase in flap travel of up to 7% compared with the individual flap control strategies.

In this paper, a composite control method combining repetitive control (RC) and deadbeat predictive control (DPC) is proposed to reduce the harmonic content of output voltage and improve the quality of voltage waveform, in order to solve the problem of voltage distortion caused by linear and nonlinear loads at the common grid-connected point of microgrid. First, the mathematical model of three-phase Z-source inverters is established, and the model is transformed into a state space expression. Then, Lyapunov's theory is used to find the design conditions of the state feedback control law based on linear matrix inequality. Finally, the parameters of the controller are solved by linear matrix inequality (LMI), and the parameter design of the improved repetitive controller is optimized. Furthermore, the system response speed is improved, and the system stability and robustness are guaranteed by combining the deadbeat predictive control technology. The simulation and experimental results verify the accuracy and superiority of the proposed deadbeat predictive repetitive control (DPRC) based on parameter optimization. [ABSTRACT FROM AUTHOR]

This paper presents a preview repetitive control for linear continuous-time systems when a periodic reference signal is previewed. First, an augmented two-dimensional (2D) system is constructed by state augmentation technique and a 2D model approach. Then, the preview repetitive control laws are proposed for the augmented 2D system, which transforms the preview repetitive control problem into a stabilization problem. Using Lyapunov functions, sufficient conditions for asymptotic stability of the 2D continuous-discrete system are derived in the form of linear matrix inequalities (LMIs). The design of a preview repetitive controller is proposed through the LMI approach. Finally, the developed design techniques are applied to two examples. The simulation results demonstrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

The paper presents a design of repetitive control (RC) in the current control system of a three-phase grid-tied converter. The goal of the control system is to provide sinusoidal input filter currents under the conditions of distorted and asymmetrical grid voltage. A novel design of the RC is presented, in which the repetitive part is not excited by sharp and non-periodic changes of the reference signal, but it enables high-quality performance under periodic disturbance conditions. In the proposed system. RC cooperates with a discrete state feedback controller. An innovative approach to tuning is proposed in which parameters of the repetitive, as well as the state feedback controller, are selected as a result of the optimization process with the use of a particle swarm algorithm. The proposed control system is verified experimentally on a laboratory test bench. The achieved results confirm the high-quality system performance. [ABSTRACT FROM AUTHOR]

This article presents a novel tracking control strategy for unknown linear systems perturbed by odd-harmonic periodic disturbances that combine adaptive and repetitive control methods. The proposed control strategy results in a robust adaptive odd-harmonic repetitive controller (RA-OHRC). Direct adaptive control with a robust adaptation law is utilized to accurately track the desired trajectory, ensuring the boundedness and convergence of the tracking error. An internal-model-based repetitive controller is added to compensate for periodic disturbances with odd-harmonic components. The boundedness and the convergence of the tracking error are verified through the Lyapunov-based stability analysis. The effectiveness of the proposed RA-OHRC scheme can be demonstrated using the simulation studies involving a servomotor model, which achieves accurate reference tracking, excellent disturbance rejection capability, and robustness against uncertainties. [ABSTRACT FROM AUTHOR]

This paper focuses on voltage source inverters used in new energy user power supply and energy storage power supply systems. If it is equipped with linear load, the power quality of output voltage can be easily guaranteed. If it is equipped with a nonlinear load, the system is affected by output impedance, and the output voltage is easy to be distorted. In this paper, the mechanism of output voltage distortion of inverter with a nonlinear load is studied. It is concluded that the distortion is caused by the voltage drop of nonlinear load current in the output impedance of the inverter. We proposed an embedded repetitive control compensator to improve the output voltage quality. In addition, we give out the Bode diagram parameters select method. The simulation results show that the proposed control strategy is feasible and effective.

Repetitive control (RC), which can track the periodic input or suppress the periodic disturbance with a zero steady-state error, is a promising control strategy for shunt active power filters (SAPF). However, the conventional RC (CRC) scheme will suffer a severe performance degradation caused by the grid frequency variations. In this article, a frequency-adaptive odd-harmonic repetitive control scheme with a single and fixed sampling rate is proposed for SAPF to deal with grid frequency variations and provide fast transient response for RC system. The frequency-adaptability of proposed repetitive control scheme can be implemented by updating the coefficients of the approximate expression for the delay unit in repetitive controller. The FIR filter based on Lagrange linear interpolation is used to transform the multirate repetitive control system into single-rate repetitive control system to address the problems caused by the multirate repetitive control system. Moreover, a fractional-order linear compensator with a simple structure is designed to compensate the magnitude and phase of the system accurately. Compared with other classical repetitive control strategies, the proposed repetitive control scheme can provide a better adaptation to the steady-state deviation and dynamic variation of grid frequency and ensure the control performance of SAPF system. Simulation and experimental results verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The proposed paper deals with the complete analysis which is the basis of the common tuning procedure of variable sampling Repetitive Controllers for adjustable output frequency applications. The described approach can be applied without limitations to grid-tied inverters (narrow frequency variations), as well as to AC waveform generators (wide frequency variations). The operation of the proposed approach is to keep the Repetitive Control main delay line at a constant size, resulting in a very suitable implementation on FPGA-based control platforms. The effects of the desynchronization between the PWM modulator and the Control Loop will be accurately described, and the inherent delays will be expressed in closed form. Additional effects, like beating frequencies, are illustrated as well and described by closed-form expressions. Experimental verification is carried out to prove the effectiveness of the presented analysis.

This article presents a predictive extended state observer-based repetitive controller (PESO-RC) to simultaneously track and reject periodic signals on systems with long input delay and parameter uncertainties. First, a novel extended state observer (ESO) is proposed to tackle periodic signals on processes with input delay. Then a simple low pass filter is incorporated and tuned to improve robustness against modelling errors. Moreover, the modified repetitive controller (MRC) is integrated to enhance the performance when compensating periodic signals without affecting the overall system’s stability. Stability criteria and robust stability analysis under modelling errors are studied to develop tuning guidelines. Furthermore, validation of the proposed controller and comparison studies are simulated in MATLAB and tested on a brushless DC servo motor which highlight the superior performance of PESO-RC.

Power electronic systems present a non-linear behavior mainly due to their switching nature. This is often combined with their interaction with non-linear systems, such as other switching converters, diode rectifiers, motor drives, etc. and with possible non linearities of the power grid in the case of grid connected systems. The major effect of these non-linear interactions is the generation of harmonic distortion on voltages and currents (both in DC and AC), which needs to be compensated to achieve high power quality systems. The use of passive filters is often the simplest and most immediate solution; however, this decreases converter efficiency and increases its weight and volume. Thus, the use of a control strategy capable of tracking periodic signals, rejecting periodic disturbance and largely improving steady state behavior and harmonic distortion with a limited bandwidth is a very desirable feature. Repetitive Control (RC) represents an extremely practical and efficient solution for the aforementioned issues, and it is widely employed in many different applications. This paper focuses on state of the art of RC used in power electronics and drives. RC basic concepts, different control structures, design methods, fixed and variable frequency operating conditions, etc. are investigated. Furthermore, many example applications and existing control approaches developed in recent years for power electronics and drive systems based on RC, have also been discussed in detail.

A repetitive predictive control for grid-connected inverter current control scheme is presented in this paper under voltage harmonic distortion in the stationary reference frame. Predictive control is an approach that uses a receding horizon to achieve the optimal track for the reference. In this approach, the repetitive controller behavior is added to the predictive control to increase its performance under distorted voltage conditions. In addition, to apply the controller in the generation system, controller is designed from the perspectives of the power system. The controller is designed considering the state-space model in the stationary reference frame. The controller performance was verified using a laboratory experimental setup under distorted grid voltage condition. Experimental results confirm that the proposed controller can effectively suppress harmonics under both normal operation and distorted grid voltage conditions, and also satisfy the requirements stipulated in IEEE Std. 1547.2-2008.

We developed a digital electro-optical phase-locked-loop (EO-PLL) utilizing a repetitive control, allowing the use of very nonlinear tunable lasers for frequency-modulated continuous-wave (FMCW) light detection and ranging (LIDAR) applications. This approach allows reducing the phase error of continuously repeated frequency chirps to virtually zero by using information of previous chirps and additionally guaranties sub-second settling times. With this method, much higher nonlinearities in the laser frequency modulation slope γ are tolerable than with common real-time analog PLLs. Furthermore, we applied a Goertzel algorithm generalized to non-integer multiples of the fundamental frequency to achieve a mean measurement precision of 5.41 µm and 16.35 µm at a distance from the interferometer baseline of 3 m and 10.3 m, respectively.

This paper presents a novel design of discrete-time dual internal model-based repetitive control systems. The design strategy is accomplished by combining general and high-order modified repetitive control schemes for simultaneous tracking repetitive tasks and rejection of uncertain periodic disturbances. The proposed controller is constructed from two different discrete-time internal models, rendering a dual internal model-based repetitive controller (DIMRC). The first internal model is intended to track repetitive commands with a fixed fundamental frequency. Meanwhile, the second internal model is coupled to compensate for an exogenous periodic disturbance with an uncertain frequency. The controller structure, stability conditions, and convergence analysis are discussed in this paper. The performance of the proposed controller is validated through simulation studies showing accurate tracking and excellent disturbance rejection simultaneously. [ABSTRACT FROM AUTHOR]

The active magnetic bearing system exhibits mass imbalance and sensor runout which cause the system to generate harmonic vibration force and moment. Repetitive control is an effective method to eliminate such harmonic vibration. Traditional repetitive control will eliminate all of the harmonic frequency components. However, in a practical system, the odd harmonic components usually dominate. Meanwhile, the existing method only suppresses the vibration force in the magnetic bearing system, and there is little research on the suppression of moment. Aiming at these problems, the harmonic vibration moment of the active magnetic bearing system is taken as the control object. This study investigates a hybrid control method that combines a second-order odd harmonic repetitive control with finite-dimensional repetitive control. And the virtual variable sampling is applied to construct any virtual sampling period in the proposed method, which effectively solves the problem of non-integer delay of digital repetitive control. The stability of the active magnetic bearing system is analyzed. The experimental results show that this method has faster response speed and better robustness when the frequency fluctuates. [ABSTRACT FROM AUTHOR]

In the presence of system coupling and dynamic uncertainties, extensive research has been conducted on the precise motion control of industrial manipulators with general reference trajectories. Since repetitive operations are common tasks in industrial applications, it is an essential and practical problem to further improve the control accuracy by taking advantage of the periodicity of the reference trajectory. In this paper, a desired compensation adaptive robust repetitive control is proposed for multi-DoFs industrial manipulators to perform repetitive tasks. Specifically, the link dynamics identified offline is compensated directly to decouple the system and capture the main characteristics of the link effect. Then, the uncertain friction is dealt with through an online adaptation scheme, in which the desired compensation is utilized to avoid measurement noise and chattering at low speed. And periodic disturbances are approximated by Fourier series expansion with unknown Fourier coefficients, which will be learned online. Finally, the robust feedback is designed to guarantee transient control accuracy and robustness against dynamic uncertainties. Comparative experiments on an industrial manipulator show that the proposed controller possesses better transient and steady-state control accuracy and error convergence rate. [ABSTRACT FROM AUTHOR]