Digital Repetitive Control Research Articles

Advanced digital repetitive control of shunt active power filter

Advanced digital repetitive control of shunt active power filter

Constant Delay-Line Frequency Adaptive Repetitive-Resonant Control for Grid-Tied and Intentional Islanding Operations

Repetitive Control (RC) enables inverters to inject, at fundamental frequency, high quality sinusoidal current into the grid or to provide low THD voltages in off-grid applications. However, digital RC, which can obtain a zero steady-state error for each periodic signal with a known period, gets its performance significantly degraded in the case of periodic signals with variable frequency. In other words, RC algorithms require an integer number of samples per period, while in some industrial applications the number of samples per period could be a non-integer time-varying value. Therefore, RC would lead to a significant quality degradation of the provided tracking capabilities when the grid frequency or the off-grid desired frequency changes. According to that, a newly RC structure with adaptive decoupled sampling is proposed to work with a RC implemented with constant delay line, regardless of the desired output frequency in both grid-tied and stand-alone operation. After the FPGA implementation, the experimental campaign highlights the effectiveness of the proposed control architecture.

Harmonic vibration moment suppression using hybrid repetitive control for active magnetic bearing system

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.

Low THD Grid Connected Converter Under Variable Frequency Environment

This paper is aimed at achieving unity power factor and low total harmonic distortion (THD) at the input side of a grid connected three-phase rectifier in a variable grid frequency environment. Variable grid frequency results in performance degradation of the digital controllers. Advanced repetitive control (ARC) scheme is an internal model principal-based digital control scheme, capable of tracking a variable frequency signal with nearly constant and very low (nearly zero) steady-state error. The ARC is a Taylor series expansion-based digital repetitive controller whose parameters can be tuned online with reasonably fast transient response to track the signal with an updated frequency. In this paper, the ARC has been applied to a three-phase grid connected rectifier where the reference frequency is variable. Controller coefficients are calculated and updated online. The experimental results demonstrate that the ARC tracks a variable frequency signal very effectively and results in very low THD of input current under steady state.

Taylor series expansion based repetitive controllers for power converters, subject to fractional delays

Digital repetitive controllers are widely employed to track/reject the periodic signals with zero steady-state error. Their implementation involves the use of single or multiple digital delay elements. Practically, the delay element is implemented by the use of memory locations, where samples are held and released after a specific number of sampling periods, equivalent to the desired time delay. A problem arises when the desired time delay becomes a non-integer multiple of the sampling time. Such time delays can be accurately realized by employing a fractional delay filterThis paper presents a Taylor Series expansion based digital repetitive controller designed to implement any (integer, non-integer) delay in the control of power converters, occurring due to uncontrollable variations in the reference frequency. The T3644aylor Series expansion transforms the fractional delay filter design problem to a differentiator/sub-filter design. Finite impulse response (FIR) and infinite impulse response (IIR) fractional delay (FD) filter concepts can be applied to realize the required fractional delay. This structure provides efficient on-line tuning capabilities i.e. FD can easily generate any required fractional delay without redesigning the filter when the delay parameter varies. An example is demonstrated to show the effectiveness of this approach, for a single-phase power inverter feeding a passive load.

Analysis and Application of Repetitive Control Scheme for Three-Phase Active Power Filter with Frequency Adaptive Capability

Active power filter (APF) has been proved as a flexible solution for compensating the harmonic distortion caused by nonlinear loads in power distribution power systems. Digital repetitive control can achieve zero steady-state error tracking of any periodic signal while the sampling points within one repetitive cycle must be a known integer. However, the compensation performance of the APF would be degradation when the grid frequency varies. In this paper, an improved repetitive control scheme with frequency adaptive capability is presented to track any periodic signal with variable grid frequency, where the variable delay items caused by time-varying grid frequency are approximated with Pade approximants. Additionally, the stability criterion of proposed repetitive control scheme is given. A three-phase shunt APF experimental platform with proposed repetitive control scheme is built in our laboratory. Simulation and experimental results demonstrate the effectiveness of the proposed repetitive control scheme.

Digital repetitive controller design via sampled-data delayed signal reconstruction

In this paper, we propose a design method of digital repetitive controllers to track continuous-time periodic references based on sampled-data H∞ delayed signal reconstruction. It is well known that perfect tracking is not possible for arbitrary periodic signals with a fixed period if the plant to be controlled is strictly proper.For this reason, we adopt the internal model control (IMC), with which the repetitive control is cast into the framework of sampled-data H∞ delayed signal reconstruction problem. We also extend this formulation to multi-rate and robust control. Design examples show the effectiveness of our method.

High-Performance Voltage Controller Design Based on Capacitor Current Control Model for Stand-alone Inverters

This study proposes high-performance voltage controller design that employs a capacitor current control model for single-phase stand-alone inverters. The single-phase stand-alone inverter is analyzed via modeling, which is then used to design the controller. A design methodology is proposed to maximize the bandwidth of the feedback controller. Subsequently, to compensate for the problems caused by the bandwidth limitations of the controller, an error transfer function that includes the feedback controller is derived, and the stability of the repetitive control scheme is evaluated using the error transfer function. The digital repetitive controller is then implemented. The simulation and experimental results show that the performance of the proposed controller is high in a 1.5 kW singlephase stand-alone inverter prototype.

Fractional‐order repetitive control of programmable AC power sources

Programmable AC power sources that provide variable-frequency and variable-amplitude output voltages are widely used in automatic testing equipment and bench top applications. Under various load conditions, a high-performance programmable AC power source not only can generate very clean sinusoidal output voltages, but also to accurately synthesise specified harmonic distorted wave-shapes. Digital repetitive control (RC) can achieve zero steady-state error tracking of any periodic signal with known integer period, but usually fails to provide precise tracking of variable-frequency periodical waveform with fractional period. In this study, a frequency adaptive fractional-order RC (FORC) strategy at fixed sampling rate is proposed to track or eliminate any periodic signals with variable frequency, where a Lagrange interpolation-based fractional delay filter is used to approximate the factional delay items in RC. The proposed FORC that offers fast on-line tuning of the fractional delay and the fast update of the coefficients, provide a simple but high-performance real-time control approach to dealing with variable-frequency variable-magnitude periodic signals. A case study of FORC-based programmable AC power source is conducted. Experimental results are provided to show the effectiveness of the proposed FORC strategy. It can be widely used in extensive applications.

Digital Plug-In Repetitive Controller for Single-Phase Bridgeless PFC Converters

This paper investigates a plug-in repetitive control scheme for bridgeless power factor correction (PFC) converters to mitigate input current distortions under continuous conduction mode and discontinuous conduction mode operating conditions. From the PFC converter model and the fact that a type-II compensator is used, a design methodology to maximize the bandwidth of the feedback controller is suggested. After that, the error transfer function including the feedback controller is derived, and the stability of the repetitive control scheme is evaluated using the error transfer function. The implementation of the digital repetitive controller is also discussed. The simulation and experimental results show that the input current THD is significantly improved by using the proposed control scheme for a 1-kW single-phase bridgeless PFC converter prototype.

General parallel structure digital repetitive control

This article presents a parallel structure digital repetitive control (PSDRC) scheme, where the internal models of all harmonics are decomposed into multiple parallel connected groups. Compared with conventional repetitive controller, the proposed parallel structure enables repetitive controller to regulate the error convergence rate at each group of harmonic frequencies independently and offers faster total error convergence rate. Moreover, PSDRC can achieve zero-error tracking or perfect disturbance rejection for all harmonics without occupying more data memory. A stability criterion with rigorous proof for PSDRC system is addressed, which is compatible with those existing stability criteria for existing RC schemes. An application example of three-phase pulse-width modulation inverter is provided to demonstrate the effectiveness of the proposed PSDRC scheme.

Control repetitivo digital de sistemas con frecuencia incierta o variante en el tiempo

Digital repetitive control is an internal model principle-based control technique that aims at tracking/rejecting periodic signals. A key assumption in traditional repetitive control designs is that the frequency of such signals is constant and known, its main drawback being the dramatic loss of performance that occurs when this frequency is uncertain or time-varying. This article reviews the most relevant proposals introduced so far to overcome this problem.

Design and analysis strategies for digital repetitive control systems with time-varying reference/disturbance period

This article analyses stability and performance features of different design schemes for digital repetitive control systems subject to references/disturbances that exhibit non-uniform frequency. Aiming at maintaining a constant value for the ratio T p /T s , T p being the period of the reference/disturbance signal and T s being the sampling period, two approaches are proposed. The first one deals with the real-time adaptation of T s to the actual changes of T p ; stability is studied by means of an LMI gridding method and also using robust control techniques. The second one propounds the introduction of an additional compensator that annihilates the effect of the time-varying sampling in the closed-loop system and forces its behaviour to coincide with that of an a priori selected nominal sampling period; the internal stability of the compensator-plant subsystem is checked by means of LMI gridding. The theoretical results are experimentally tested and compared through a mechatronic plant model.

A survey of repetitive control in varying frequency conditions

Digital repetitive control is a strategy that allows tracking/ rejecting periodic signals. Repetitive controllers are designed assuming that the exogenous signal period is constant and known, its main drawback being the dramatic loss of performance when signal frequency varies. This paper reviews the most relevant proposals advanced for overcoming this problem.

Digital Repetitive Control under Nonuniform Sampling: An LMI Stability Analysis

Digital repetitive control is a technique which allows tracking periodic references and/or rejecting periodic disturbances. Repetitive controllers are usually designed assuming a fixed fundamental frequency for the signals to be tracked/rejected and its main drawback being a dramatic performance decay when this frequency varies. A usual approach to overcome the problem consists of an adaptive change of the sampling period according to the reference/disturbance period variation. This paper presents a stability analysis of a digital repetitive controller working under time‐varying sampling period by means of an LMI gridding approach. Theoretical developments are illustrated with experimental results, which are preceded by a detailed description of fundamental issues related to the implementation procedure.

Stability analysis of digital repetitive control systems under time-varying sampling period

Repetitive control is an internal model principle-based technique for tracking periodic references and/or rejecting periodic disturbances. Digital repetitive controllers are usually designed assuming a fixed frequency for signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. Such a structural change may indeed compromise closed-loop stability. Nevertheless, no formal stability proofs are reported in the literature. This study addresses the stability analysis of a digital repetitive control system operating under time-varying sampling period. The procedure adapts the robust control approach introduced by Fujioka and Suh, which treats the time-varying parts of the system description as norm-bounded uncertainties, to the special features of digital repetitive control systems. This results in a conservatism reduction leading to an improvement in the obtained stability intervals. The proposed technique is also applicable to a more general class of systems incorporating a discrete-time dynamic controller. The article is completed with the application of the method to two standard examples in the repetitive control literature. Experimental results confirm the theoretical predictions.

Design of a Plug-In Repetitive Control Scheme for Eliminating Supply-Side Current Harmonics of Three-Phase PWM Boost Rectifiers Under Generalized Supply Voltage Conditions

This paper presents a digital repetitive control (RC) scheme to minimize the even-order harmonics at the dc link voltage and odd-order harmonics in the line-side currents under distorted and unbalanced supply voltage conditions. The proposed current control scheme consists of a conventional PI and a plug-in repetitive controller. On the basis of the mathematical model of the three-phase pulsewidth-modulated (PWM) boost rectifier under the generalized supply voltage conditions, the control task is divided into: 1) dc-link voltage harmonics control and 2) line-side current harmonics control . In the voltage harmonics control scheme, a reference current calculation algorithm has been derived accordingly to ensure that the dc link voltage is maintained constant at the demanded value and the supply-side power factor is kept close to unity. In the line-side current harmonics control scheme, a plug-in repetitive controller is designed to achieve low total harmonic distortion (THD) line-side currents of the three-phase PWM boost rectifier. The experimental test results obtained from a 1.6-kVA laboratory-based PWM rectifier confirm that the proposed control scheme can reduce the line-side current THD from 16.63% to 4.70%, and improve the dc-link voltage tracking accuracy substantially over the conventional PI-based controller.

Adaptive compensation strategy for the tracking/rejection of signals with time-varying frequency in digital repetitive control systems

Digital repetitive control is a technique which allows to track periodic references and/or reject periodic disturbances. Repetitive controllers are usually designed assuming a fixed frequency for the signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to reference/disturbance period variations. However, the sampling period adaptation implies structural changes that may degrade the closed-loop time response. This article presents a design strategy which allows to compensate for the effect of non-uniform sampling and forces the closed-loop behavior to coincide with that of the system operating under an a priori selected nominal sampling period. The stability of the overall closed-loop system is also analyzed. Experimental results obtained from a mechatronic plant model validate the proposal.

Digital Repetitive Control of a Three-Phase Four-Wire Shunt Active Filter

Shunt active power filters have been proved as useful elements to correct distorted currents caused by nonlinear loads in power distribution systems. This paper presents an all-digital approach based on a particular repetitive control technique for their control. Specifically, a digital repetitive plug-in controller for odd-harmonic discrete-time periodic references and disturbances is used for the current control loops of the active filter. This approach does not introduce a high gain at those frequencies for which it is not needed and, thus, improves robustness of the controlled system. The active power balance of the whole system is assured by an outer control loop, which is designed from an energy-balancing perspective. The design is performed for a three-phase four-wire shunt active filter with a full-bridge boost topology. Several experimental results are also presented to show the good behavior of the closed-loop system

Dual-mode structure digital repetitive control

A flexible repetitive control (RC) scheme named “dual-mode structure repetitive control” (DMRC) is presented in this article. A robust stability criterion for DMRC systems is derived in terms of two parameters: odd-harmonic RC gain and even-harmonic RC gain. Several useful corollaries for the stability are addressed to reveal the compatibility of DMRC. The general framework of DMRC offers the flexibility in the development of various RC controllers. Without additional complexity and loss of tracking accuracy, DMRC can achieve faster error convergence rate than conventional RCs. DMRC requires the same data memory size as that of conventional RC one. An application example of DMRC controlled PWM inverter illustrates the validity of our proposed DMRC scheme. Comparisons of DMRC, conventional RC and odd-harmonic RC highlight the advantages of the presented DMRC approach.