Repetitive Control Technique Research Articles

Repetitive control design for switched neutral systems with input time‐delay

SummaryThe design of tracking control problem and compensation of disturbance for switched neutral systems with multiple time‐delays and external disturbances are addressed in this paper. In this regard, a modified repetitive control technique based on the Matausek‐Micic modified Smith predictor approach is being implemented, which assures the exact tracking performance and disturbance attenuation with high precision in the considered system. To be specific, the integration of transfer function with modified Smith predictor block not only provides the accurate compensation of input time‐delays but also ensures the exact estimation and attenuation of external disturbances effectually. Furthermore, according to Lyapunov stability approach combined with average‐dwell‐time technique, a group of adequate conditions is derived in the form of matrix inequalities. Simultaneously, by solving the established matrix inequalities using available software the controller gain matrices are calculated. Ultimately, the simulation results of three numerical examples are presented to validate the efficiency and dominance of the suggested control procedure.

A Predictive Repetitive Current Control in Stationary Reference Frame for DFIG Systems Under Distorted Voltage Operation

This article presents a stationary reference frame implementation of the predictive repetitive controller under ideal and nonideal stator voltage conditions. Thanks to the combination of the model predictive control (MPC) and the repetitive control techniques, the predictive repetitive control uses the capabilities of both techniques to achieve the control objectives without the need of using a PLL for the stator flux in ideal conditions as the approach is developed in the stationary reference frame <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha \beta $ </tex-math></inline-formula> . For the operation of the technique, it is also not necessary to know the harmonic content of the nonideal stator voltage beforehand, but, for this case, and given the nature of the distortions, the use of the PLL is necessary to estimate the phase angle and the magnitude of the voltage’s fundamental component. This means a great advantage over previous techniques due to the fact that special considerations are not needed over the mathematical model of the doubly fed induction generator (DFIG). Experimental results of the proposed technique are presented in ideal and nonideal grid conditions, and under variable rotor speed. Moreover, a comparison with the classic MPC technique is presented.

Repetitive control design for vehicle lateral dynamics with state‐delay

In this work, the authors precisely concentrate on the subject of enhanced vehicle handling performance of the bicycle model with two-degrees-of-freedom via improved-equivalent-input-disturbance and repetitive control technique. To be specific, improved-equivalent-input-disturbance estimator is inserted into the controller design for attenuating the effect of the crosswind in the considered vehicle system with state-delay. A modified two-dimensional repetitive control design is implemented for improving the accurate tracking performance of the considered model. In particular, by combining an improved-equivalent-input-disturbance approach together with two-dimensional modified repetitive control design, steering angles of front and rear wheels of the considered vehicle have been controlled in order to achieve the accurate tracking performance of the vehicle states. The criteria for the robust asymptotic stability on the basis of Lyapunov stability theory is developed by means of the sufficient conditions which are obtained in the form of linear-matrix-inequalities. Simultaneously, through these inequality conditions, the parameters of proposed improved-equivalent-input-disturbance based repetitive control strategy are designed for improving the accurate tracking performance against the crosswind effect. Finally, simulation results are presented to show that the proposed control design is more effective when aperiodic disturbances occur.

Comparative study of two repetitive process control techniques for a grid-tie converter under distorted grid voltage conditions

The paper describes two main approaches of periodic control under variable frequency conditions: frequency adaptive multioscillatory control (FAMOSC) and fractional delay repetitive control (FDRC). The methods are applied in the control system of a grid-tie converter to increase the quality of phase currents in case of distorted grid voltages. The paper compares structures, performance and implementation of FAMOSC, FDRC and the conventional approach of repetitive and multioscillatory control. Performances of the control systems are illustrated with experiments on a laboratory test bench. The article describes tuning process of FDRC and FAMOSC with the usage of Particle Swarm Optimization algorithm. A detailed analyse and research of the techniques in terms of computational complexity is presented. Practical hints for implementation and resource optimization of both techniques on DSP are included. For FAMOSC a fast implementation of prewarping is proposed.

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.

Robust Repetitive Control Design for a Three-Phase Four Wire Shunt Active Power Filter

This paper presents a discrete repetitive control technique for three-phase four wire (3P4W) shunt active power filter (SAPF). Generally, the control design for power electronics devices involves two control loops: slow acting outer voltage loop and fast acting inner current control loop. The reference for inner current loop is periodic in nature and cannot be easily tracked by a proportional-integral regulator. The repetitive controllers (RCs) are well known for their tracking ability of periodic signals and offer high gain at all the frequencies. The high gain in higher frequency range may lead to instability. Therefore, in the proposed work, the regular RC is modified by squaring its sensitivity function. This approach results in low amplitude of sensitivity function while offering deep notches at low to mid frequencies range and smaller notches at higher frequencies. This control approach has been simulated and implemented on 3P4W SAPF.

Multi-objective fuzzy-decision-making-based FS-MPC with improved performance for grid-connected converters

In this paper, a multi-objective fuzzy-decision-making-based (MO-FDM) finite-state model predictive control (FS-MPC) method is proposed for improving both steady-state and transient-state operations of the grid-connected converters (GCCs). The main objectives of the proposed method are to achieve the excellent steady-state tracking performance and high dynamics without any weighting factors in the designed controller. Firstly, a repetitive control technique is embedded in the predictive controller, and an integral error term is introduced into the standard cost function used in the GCCs. Secondly, a simple and systematic procedure, which relies on MO-FDM technique, is employed to avoid the selection of weighting factors. As such, this scheme has a good potential to avoid the complicated tuning work while the control performance is not affected. Furthermore, in order to enhance the dynamic response and improve the computational efficiency, a dynamic reference design with a simplified cascade-free FS-MPC strategy is embedded into the predictive controller. Finally, simulation results are presented for demonstrating the effectiveness of the proposed control strategy.

Odd-harmonic repetitive control for high-speed raster scanning of piezo-actuated nanopositioning stages with hysteresis nonlinearity

In raster scanning applications of atomic force microscopies, precisely tracking periodic triangular trajectories is the major objective of nanopositioning stages. Considering the fact of periodic operations, the repetitive control technique becomes promising and has been recently developed to reduce tracking errors. In our new experiments, it is found that, with triangular reference input, the hysteresis nonlinearity mainly affects the system at the odd harmonics of the input signal. In this sense, an odd-harmonic repetitive control (ORC) strategy is proposed to handle the hysteresis nonlinearity, with the hysteresis treated as the odd-harmonic periodic disturbance. Therefore, it avoids the modeling and inverting of the complex hysteresis nonlinearity. Another benefit of the developed ORC strategy is that it can also account for the tracking errors caused by the linear dynamics effect. To verify the effectiveness of the ORC strategy, real-time experiments are performed on a custom-built piezo-actuated nanopositioning stage. Experimental results show that the developed ORC strategy achieves precise tracking of 1562.5-Hz triangular trajectory with the hysteresis nonlinearity mitigated to a negligible level, which demonstrates the feasibility and effectiveness of the developed ORC strategy on hysteresis compensation during high-speed raster scanning.

High-Precision Control of Ball-Screw-Driven Stage Based on Repetitive Control Using $n$-Times Learning Filter

This paper presents a novel learning control method for ball-screw-driven stages. In recent years, many types of friction models that are based on complicated equations have been studied. However, it is difficult to treat friction models with equations because the level of precision that is associated with real friction characteristics and parameter tuning are difficult to achieve. In contrast, repetitive perfect tracking control (RPTC) is a repetitive control technique that achieves high-precision positioning. In this paper, we propose the use of RPTC with n-times learning filter. The n-times learning filter has a sharper rolloff property than conventional learning filters. With the use of the n-times learning filter, the proposed RPTC can converge tracking errors n times faster than the RPTC with the conventional learning filter. Simulations and experiments with a ball-screw-driven stage show the fast convergence of the proposed RPTC. Finally, the proposed learning control scheme is combined with data-based friction compensation, and the effectiveness of this combination is verified for the x-y stage of a numerically controlled machine tool.

Model Predictive Control of MEMS Vibratory Gyroscope

This paper presents a MPC (Model Predictive Control) algorithm for MEMS vibratory gyroscopes based on force-balancing control strategy. In the proposed MPC method, using a set of orthonormal basis functions named Laguerre functions, a new prediction and optimization technique is designed. To enhance the capability of proposed MPC method for tracking time-varying reference trajectories, first a repetitive control technique is developed. Second, following representing the governing dynamical equations of the vibratory gyroscope, discrete-time Laguerre network based MPC has been developed. The effective tracking performance of the proposed control methods has been shown through computer simulations.

Control System Design of Shunt Active Power Filter Based on Active Disturbance Rejection and Repetitive Control Techniques

To rely on joint active disturbance rejection control (ADRC) and repetitive control (RC), in this paper, a compound control law for active power filter (APF) current control system is proposed. According to the theory of ADRC, the uncertainties in the model and from the circumstance outside are considered as the unknown disturbance to the system. The extended state observer can evaluate the unknown disturbance. Next, RC is introduced into current loop to improve the steady characteristics. The ADRC is used to get a good dynamic performance, and RC is used to get a good static performance. A good simulation result is got through choosing and changing the parameters, and the feasibility, adaptability, and robustness of the control are testified by this result.

Mitigation of distorted and unbalanced stator voltage of stand‐alone doubly fed induction generators using repetitive control technique

Unbalanced or non-linear loads result in distorted stator currents and electromagnetic torque pulsations in stand-alone doubly fed induction generators (DFIGs). This study proposes the use of a proportional-integral repetitive control (PIRC) scheme so as to mitigate the levels of harmonic and unbalance at the stator terminals of the DFIG. The PIRC is structurally simpler and requires much less computation than existing methods. Analysis of the PIRC operation and the methodology to determine the control parameters is included. Simulation study as well as laboratory test measurements demonstrate clearly the effectiveness of the proposed PIRC control scheme.

Research on fast transient and 6 n ±1 harmonics suppressing repetitive control scheme for three‐phase grid‐connected inverters

The repetitive control technique is widely adopted in ac systems, because of its excellent steady-state tracking performance and low total harmonic distortion. The repetitive control method with one-sixth of the system fundamental period T0 as the delay time has been proposed to achieve fast transient response. In this study, an improved control scheme based on the T0/6 repetitive control is proposed for three-phase grid-connected inverters. The proposed scheme adopts T0/6 as the delay time in the positive-rotating and negative-rotating synchronous reference frames to suppress the 6n ± 1 harmonics. Meanwhile, the proportional-integral regulator and the plug-in repetitive controller are combined to reinforce the system performance. A new auxiliary function based on the linear interpolation is proposed to maintain the ideal repetitive control performance when one-sixth of the ratio of the sampling frequency to the grid fundamental frequency is non-integer. The effectiveness of the proposed scheme on improving the T0/6 repetitive control is confirmed by simulation and experimental results finally.

An Improved Repetitive Control Scheme for Grid-Connected Inverter With Frequency-Adaptive Capability

The power quality of grid-connected inverters has drawn a lot of attention with the increased application of distributed power generation systems. The repetitive control technique is widely adopted in these systems, due to its excellent tracking performance and low output total harmonic distortion (THD). However, in an actual system, the ratio of the sampling frequency to the grid frequency cannot always maintain an integer, and then, the resonant frequencies of the repetitive control technique will deviate from the real grid fundamental and harmonic frequencies. This will degrade the performance of the system, particularly when the grid frequency varies. Even if the ratio is a fixed integer, the auxiliary function for stabilization in the conventional repetitive control technique will also increase the steady-state tracking error and THD of the system. In this paper, an improved repetitive control scheme with a special designed finite impulse response (FIR) filter is proposed. The FIR filter cascaded with a traditional delay function can approximate the ideal repetitive control function of any ratio. The proposed scheme varies the FIR filter according to varied grid frequency and maintains its resonant frequencies matching the grid fundamental and harmonic ones. Finally, the simulation and experimental results show that the improved repetitive control scheme can effectively reduce the tracking error and compensate harmonics of the inverter systems.

Low-THD, Fast-Transient, and Cost-Effective Synchronous-Frame Repetitive Controller for Three-Phase UPS Inverters

This paper presents a novel synchronous-frame repetitive controller for three-phase UPS inverters. Distinguished from conventional repetitive control techniques, the proposed synchronous-frame approach minimizes the repetitive control time delay to one-sixth of the fundamental period such that the dynamic response is significantly improved. In order to overcome the harmonic distortions under severe load conditions (e.g., unbalanced and nonlinear), in this paper, three synchronous rotating frames are deliberately selected, in each of which the repetitive controller is incorporated. Resultantly, the (6n ±1)th harmonics as well as the triplen harmonics are compensated. Moreover, a high-performance fourth-order linear phase infinite-impulse-response filter is applied to further enhance the accuracy of steady-state tracking. The proposed controller is programmed on the 16-bit fixed-point digital signal processor (TI TMS320LF2407) and eliminates high-resolution current sensors for cost effectiveness. Simulations and experimental tests have been carried out based on an 18-kW three-phase UPS system. Low total harmonic distortion (<;0025;) has been achieved under heavily distorted nonlinear load and unbalanced load. Fast dynamic response has been demonstrated during step load transients.

Research on the Repetitive Control Technique in Gird-Side Converter of the Double-Fed Wind Power System

With the unit capacity of the wind turbine is increasing, analyzing, suppressing of gird harmonic and reducing the grid harmonic pollution by the wind turbine have become one of the issues of common concern. For the characteristic of the grid voltage harmonic components which is the interference source with the fixed period, the repetitive control theory was adopted to design the gird-side converter, and the traditional control strategy of the voltage current double closed-loop was compared with the repetitive control. Harmonic suppression characteristics were studied in the paper. Finally, Matlab-Simulink simulation software established a repetitive controller simulation model of the gird-side converter controller, simulation results showed the correctness and feasibility of suppression for the periodic harmonic by the repetitive control strategy.

Learning Control for Systems with Saturated Output

Sensor saturation is a common physical constraint in control systems.Two learning control algorithms are proposed in this research for a class of linear systems with saturated output.Specifically,an open-loop P-type iterative learning controller is first designed for repetitive operating systems to ensure entire tracking in limited interval,and the convergence condition is derived by employing λ norm analysis.Furthermore,for controlled systems with periodic desired trajectory,the asymptotic tracking condition of closed-loop P-type repetitive learning control technique is deduced as well.Finally,the simulation results show the effectiveness of the proposed algorithms.

A Current-Control Strategy for Voltage-Source Inverters in Microgrids Based on $H^{\infty }$ and Repetitive Control

In this paper, a current-control strategy is proposed for voltage-source inverters in microgrids. The main objective of the proposed controller is to inject a clean sinusoidal current to the grid, even in the presence of nonlinear/unbalanced loads and/or grid-voltage distortions. The repetitive control technique is adopted because it can deal with a very large number of harmonics simultaneously. The proposed current controller consists of an internal model and a stabilizing compensator, which is designed by using the H∞ control theory. It turns out that the stabilizing compensator may be simply an inductor. This leads to a very low total harmonic distortion (THD) and improved tracking performance. In order to demonstrate the improvement of performance, the proposed controller is compared with the traditional proportional-resonant, proportional-integral, and predictive deadbeat controllers. The control strategies are evaluated in the grid-connected mode with experiments under different scenarios: steady-state and transient responses without local loads, and steady-state responses with unbalanced resistive and nonlinear local loads. The proposed controller significantly outperforms the other control schemes in terms of the THD level, with the price of slightly slower dynamic responses.

H ∞ repetitive voltage control of grid-connected inverters with a frequency adaptive mechanism

A voltage controller is proposed and implemented for grid-connected inverters based on H∞ and repetitive control techniques. A frequency adaptive mechanism is introduced to improve system performance and to cope with grid frequency variations. The repetitive control, based on the internal model principle, offers excellent performance for voltage tracking, as it can deal with a very large number of harmonics simultaneously. This leads to a very low total harmonic distortion and improved tracking performance. It turns out that the controller can be reduced to a proportional gain cascaded with the internal model (in a re-arranged form), which can be easily implemented in real applications. The proposed controller is experimentally tested to validate its performance, focusing on reducing tracking error and total harmonic distortion, under different scenarios (e.g. in the stand-alone mode or in the grid-connected mode, with or without the frequency adaptive mechanism, with linear or non-linear loads etc).

Achievement method of high‐speed response of error prediction tracking control for optical disk system

AbstractThis paper proposes the new design method of error‐prediction control systems combining the ZPET control and the robust feedback control. The error‐prediction control system based on ZPET control can reduce the tracking error caused by periodic disturbances more efficiently than the conventional repetitive control technique. However, the proposed tracking servo system does not reduce the residual tracking error caused by the low‐pass filter of the feedforward compensation and by the long sampling time. In order to overcome this problem, this paper proposes the new structure of the feedforward tracking control system. The modified ZPET control tracking servo system for optical disk recording system does not include the low‐pass filter and its sampling time becomes faster. On the other hand, the sudden disturbance observer reduces the influence of nonperiodic disturbances. The experimental results point out that the proposed tracking servo system has a precise tracking response against both the periodic disturbances and the nonperiodic disturbances. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 170(4): 51–59, 2010; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/eej.20800