High-order Repetitive Control Research Articles

General High-Order Selective Harmonic Repetitive Control for PWM Converters

In this article, a general high-order selective harmonic repetitive control (HO-SHRC) scheme is proposed, which is composed of a standard high-order repetitive controller structure and a new order-expandable SHRC. Different from conventional SHRC, the proposed new SHRC is capable of being applied into the standard high-order repetitive control (HORC) structure for generating any high-order SHRC. The proposed HO-SHRC can be used to improve the steady-state tracking accuracy of the pulsewidth modulation (PWM) converter systems and is robust to system frequency variations without changing the controller parameters online. The order expansion of the controller will lead to the increase of the implementation complexity, but it will bring the overall improvement of the controller performance, such as the improvement of frequency adaptability, steady-state tracking accuracy, and dynamic performance. Therefore, HO-SHRC can achieve a good compromise between the controller performance and the implementation complexity. Moreover, the proposed HO-SHRC provides a general structure for various repetitive controls (RCs), such as conventional RC (CRC), odd-harmonic RC (OHRC), high-order CRC (HO-CRC), and HO-odd-harmonic RC (HO-OHRC). Application examples of second-order (SO)- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6k~\pm $ </tex-math></inline-formula> 1 RC-controlled three-phase PWM inverter show the effectiveness and advantages of the proposed control scheme.

High-order repetitive model reference control for linear systems with uncertain periodic references and disturbances

This paper presents a systematic method to design a high-order repetitive model reference controller (HO-RMRC) for a discrete-time linear system that is subject to uncertain periodic references and disturbances. The controller design method we propose is established by combining two controller design schemes: high-order repetitive control (HORC) and model reference control (MRC). Here, the HORC is used to suppress uncertain periodic disturbances significantly and the MRC is used to track time-varying references without introducing new transient responses. The stability analysis of the resulting closed-loop system is provided and describes how admissible learning gains are determined to achieve stability and a desirable convergence rate. The efficacy of the proposed control method is demonstrated via numerical simulations where the performance of the resulting HO-RMRC is compared with those of the HORC and the MRC as standalone controllers. It is evident that the HO-RMRC outperforms the HORC and the MRC in simultaneously achieving perfect reference tracking and disturbance cancellation/attenuation.

On the synthesis of a stable and causal compensator for discrete-time high-order repetitive control systems

This paper presents a novel methodology to design a discrete-time compensator for a high-order repetitive control system. An optimization-based approach is applied to design the compensator, which is required to be stable and causal. This methodology is applicable to both minimum and non-minimum phase systems, for which stability and tracking error convergence are ensured. The compensator is yielded in the form of a proper transfer function and can be implemented separately without being merged with a high-order internal model. The high-order internal model is used to provide robustness against period variations of the reference signal. Simulation and experimental results are provided to show the effectiveness of the compensator design methodology.

First-Order and High-Order Repetitive Control for Single-Phase Grid-Connected Inverter

With the increasing demand of users for power sources and quality, how to provide high-quality renewable clean energy has become a key issue of power electronics. The main idea of this paper is to develop a composite control including a PI control and repetitive control for a single-phase grid-connected inverter to eliminate the effects of harmonics, which can obtain better steady-state and dynamic responses of the single-phase inverter system and reduce the net current harmonics. The modelling of a single-phase inverter is first introduced; then a first-order repetitive control is developed for the proposed grid-connected inverter. Moreover, a high-order repetitive controller is adopted to further improve the robustness against the uncertainties in the period of signals. The stability and performance analysis are given for the first-order repetitive control and high-order repetitive control. Finally, comparative simulations are conducted in a circuit-level inverter model, which show the effectiveness of the proposed method.

A Design Method of High Order Repetitive Controllers

It turns out that higher-order RC is useful for improving the robustness of the entire control system, and its importance is only increasing. In this paper, we propose a new high-order RC design method. The proposed high-order RC design method includes more design parameters than the same order conventional high-order RC, which increases design flexibility. Further improvement of robustness can be expected. It will also prove useful for improving time response. Further, it is possible to suppress a disturbance having a frequency different from the frequency of the target periodic signal. This is not possible with conventional high-order RC.

Second‐order RC: analysis, augmentation, and anti‐frequency‐variation for single‐phase grid‐tied inverter

High-order repetitive control can deal with period variation. An augmented second-order repetitive control (RC) scheme is presented to improve system performance under grid frequency variation. Firstly, the relationship between proportional-integral/inertial, multiple-resonant, multi-quasi-resonant control, and second-order RC is analysed. The weight range of second-order RC is discussed. Then, a second-order RC approach augmented by proportional control is proposed for a single-phase grid-tied inverter. Experiments are provided to verify the superiority of second-order RC compared with single-order RC under frequency variation.

Robust design of high order repetitive controllers under control saturation

Abstract This paper presents a methodology to simultaneously design a high order repetitive controller (HORC) and an anti-windup compensator for systems subject to control saturation and parametric uncertainties. With the proposed structure it is possible to ensure a certain level of steady-state tracking and/or rejection performance when dealing with uncertain periodic signals. Based on a modified state-feedback formulation of the HORC and an static anti-windup structure, linear matrix inequality (LMI) conditions are proposed to guarantee closed-loop stability provided that the state trajectory and the reference/disturbance signals are inside admissible sets. A systematic procedure to determine upper bounds for the system initial conditions and maximum reference/disturbance values is also proposed. A numerical example illustrates the method.

Phase compensation second-order repetitive control for CVCF PWM inverters

ABSTRACTPhase compensation for high-order repetitive control (HORC) can improve system transient and steady-state performances. The phase compensator is often designed as the inverse transfer function of a closed-loop system. No other phase compensation methods for HORC have been reported up to now. Hence, in this paper, a simple approximate phase cancellation second-order repetitive control (RC) is proposed. The compensator is a linear combination of two different linear phase lead compensators, which can better fit the inverse of a plant model phase curve compared with the conventional linear phase compensator. Optimisation is introduced to design the parameters of the approximate phase cancellation second-order RC. Analysis and design of the second-order repetitive controlled pulse width modulation inverter system are presented. Simulations and experiments are provided to demonstrate the effectiveness of the optimisation method and verify the advantage of the approximate phase cancellation compensator.

High-order repetitive control for discrete-time linear switched systems

ABSTRACTThis paper is concerned with the design of a high-order repetitive control (RC) law for a class of discrete-time linear switched systems with repetition-varying reference trajectories. First, a high-order RC law, which embeds the characteristic of known variation of the reference trajectories, is proposed to the system, and a two-dimensional (2D) model is presented to describe the control and learning actions of the repetitive control system by using the lifting technique. By choosing appropriate multiple Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the proposed results.

High performance control of a three-phase PWM rectifier using odd harmonic high order repetitive control

El objetivo de control en rectificadores de potencia trifásicos se basa en generar corrientes de entrada sinusoidales y regular el voltaje de salida DC. Aunque el Control Repetitivo y Resonante son enfoques de control que han presentado excelentes resultados, su principal desventaja se basa en la pérdida considerable de desempeño cuando la frecuencia de la red se desvía de su valor nominal. En este artículo, se presenta el uso de un Controlador Repetitivo Impar de Alto Orden para controlar los lazos de corrientes de un rectificador trifásico con un desempeño considerablemente superior a otras alternativas tradicionalmente implementadas en este campo. Este controlador permite el rechazo de los armónicos impares introducidos en el sistema, lo que mantiene una complejidad computacional similar a la obtenida con los controladores repetitivos convencionales con la ventaja de incrementar la robustez cuando la frecuencia de la señal varíe. Las simulaciones y los resultados experimentales muestran un alto desempeño aún cuando se presenten desviaciones de la frecuencia de la red respecto a su valor nominal.

High performance control of a three-phase PWM rectifier using odd harmonic high order repetitive control

El objetivo de control en rectificadores de potencia trifásicos se basa en generar corrientes de entrada sinusoidales y regular el voltaje de salida DC. Aunque el Control Repetitivo y Resonante son enfoques de control que han presentado excelentes resultados, su principal desventaja se basa en la pérdida considerable de desempeño cuando la frecuencia de la red se desvía de su valor nominal. En este artículo, se presenta el uso de un Controlador Repetitivo Impar de Alto Orden para controlar los lazos de corrientes de un rectificador trifásico con un desempeño considerablemente superior a otras alternativas tradicionalmente implementadas en este campo. Este controlador permite el rechazo de los armónicos impares introducidos en el sistema, lo que mantiene una complejidad computacional similar a la obtenida con los controladores repetitivos convencionales con la ventaja de incrementar la robustez cuando la frecuencia de la señal varíe. Las simulaciones y los resultados experimentales muestran un alto desempeño aún cuando se presenten desviaciones de la frecuencia de la red respecto a su valor nominal.

Robust State Feedback Formulation for High Order Repetitive Controllers

AbstractThis paper presents a robust state feedback formulation for high order repetitive controllers (HORC) able to track references and/or reject disturbances with uncertain period. We propose a modified structure of the HORC with low‐pass filter in series with the delay element, allowing us to work in the state‐space framework. The filter cut‐off frequency effects and the controller sensitiveness to harmonic and intermediary components are analyzed. A methodology based on the solution of an optimization problem subject to linear matrix inequality constraints is presented for robust synthesis of feedback gains. The advantages regarding the proposed control scheme are discussed with a simulated example of a DC motor driving an eccentric mass.

Optimal anti-windup synthesis for repetitive controllers

Repetitive controllers use internal models that provide very high gain at a selected fundamental frequency and its harmonics, additionally, some of the internal models may result unstable, as in the high order repetitive control approach. These characteristics make the repetitive control system susceptible to exhibit wind-up when actuator saturation occurs. This paper proposes an anti-windup scheme for repetitive control based on the model recovery anti-windup strategy. The proposed scheme provides low order, low computational burden and also isolation of the controller from the saturation effects. The anti-windup compensator is constructed from the plant model and provides an additional linear feedback path aimed at enhancing system performance. This feedback path is designed to obtain a deadbeat behaviour, which makes the system recovery faster. Finally, internal stability and deadbeat features are designed in a compact procedure based on linear matrix inequalities and an optimal linear quadratic design. Experimental validation of the proposed anti-windup compensator is provided using a mechatronic plant.

Power factor correction and harmonic compensation using second-order odd-harmonic repetitive control

Repetitive control has proven to be an efficient control technique in power factor correction by active filtering. Unfortunately, this technique shows a dramatic performance decay when the network frequency is not exactly known or it varies with time. In order to overcome the varying/uncertain frequency problem, a robust high-order repetitive control strategy can be used; however, most internal models obtained by these approaches are unstable. Although this fact does not compromise the closed-loop stability, practical problems can arise during the implementation. This study proposes and studies a stable second-order odd-harmonic repetitive control system, presents a stability analysis of high-order internal models and describes the performance degradation of the standard repetitive control in terms of the active filter (AF) application. In this way, an experimental validation has been carried out implementing the proposed internal model in a shunt AF current controller. As a result, this high-order controller allows dealing with the grid frequency variations without using adaptive schemes.

Robust high-order repetitive control: Optimal performance trade-offs

High-order repetitive control has previously been introduced to either improve the robustness for period-time uncertainty or reduce the sensitivity for non-periodic inputs of standard repetitive control schemes. This paper presents a systematic, semidefinite programming based approach to compute high-order repetitive controllers that yield an optimal trade-off between these two performance criteria. The methodology is numerically illustrated through trade-off curves for various controller orders and levels of period-time uncertainty. Moreover, existing high-order repetitive control approaches are shown to correspond to specific points on these curves.

Design of noise and period-time robust high-order repetitive control, with application to optical storage

Repetitive control is useful if periodic disturbances or setpoints act on a control system. Perfect (asymptotic) disturbance rejection is achieved if the period time is exactly known. The improved disturbance rejection at the periodic frequency and its harmonics is achieved at the expense of a degraded system sensitivity at intermediate frequencies. A convex optimization problem is defined for the design of high-order repetitive controllers, where a trade-off can be made between robustness for changes in the period time and for reduction of the error spectrum in-between the harmonic frequencies. The high-order repetitive control algorithms are successfully applied in experiments with the tracking control of a CD-player system.