Digital repetitive control under varying frequency conditions

Premi extraordinari doctorat curs 2011-2012, àmbit d’Enginyeria IndustrialThe tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.Award-winningPostprint (published version

Universal fractional-order design of linear phase lead compensation multirate repetitive control for PWM inverters

Repetitive control (RC) with linear phase lead compensation provides a simple but very effective control solution for any periodic signal with a known period. Multirate repetitive control (MRC) with a downsampling rate can reduce the need of memory size and computational cost, and then leads to a more feasible design of the plug-in repetitive control systems in practical applications. However, with fixed sampling rate, both MRC and its linear phase lead compensator are sensitive to the ratio of the sampling frequency to the frequency of interested periodic signals: (1) MRC might fails to exactly compensate the periodic signal in the case of a fractional ratio; (2) linear phase lead compensation might fail to enable MRC to achieve satisfactory performance in the case of a low ratio. In this paper, a universal fractional-order design of linear phase lead compensation MRC is proposed to tackle periodic signals with high accuracy, fast dynamic response, good robustness, and cost-effective implementation regardless of the frequency ratio, which offers a unified framework for housing various RC schemes in extensive engineering application. An application example of programmable AC power supply is explored to comprehensively testify the effectiveness of the proposed control scheme

Learning for Advanced Motion Control

Iterative Learning Control (ILC) can achieve perfect tracking performance for mechatronic systems. The aim of this paper is to present an ILC design tutorial for industrial mechatronic systems. First, a preliminary analysis reveals the potential performance improvement of ILC prior to its actual implementation. Second, a frequency domain approach is presented, where fast learning is achieved through noncausal model inversion, and safe and robust learning is achieved by employing a contraction mapping theorem in conjunction with nonparametric frequency response functions. The approach is demonstrated on a desktop printer. Finally, a detailed analysis of industrial motion systems leads to several shortcomings that obstruct the widespread implementation of ILC algorithms. An overview of recently developed algorithms, including extensions using machine learning algorithms, is outlined that are aimed to facilitate broad industrial deployment.Comment: 8 pages, 15 figures, IEEE 16th International Workshop on Advanced Motion Control, 202

Non-uniform sampling in digital repetitive control systems: An LMI stability analysis

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 usual approach to overcome the problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. This report 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

Design and Analysis Strategies for Digital Repetitive Control Systems with Time-Varying Reference/Disturbance Period

This article introduces and analyzes the performance features of different design schemes for digital repetitive control systems subject to references/disturbances that exhibit non-uniform frequency. Aiming for the maintenance of a constant value for the ratio Tp/Ts, where Tp is the period of the reference/disturbance signal and Ts is the sampling period, two approaches are proposed. The first one deals with the realtime adaptation of Ts to the actual changes of Tp; the stability issue 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 behavior to coincide with the one corresponding to an a priori selected nominal sampling period; the procedure needs the internal stability of the compensator-plant subsystem, which is checked by means of LMI gridding. The theoretical results are experimentally tested and compared through a mechatronic plant model.Postprint (published version

Virtual variable sampling discrete fourier transform based selective odd-order harmonic repetitive control of DC/AC converters

This paper proposes a frequency adaptive discrete Fourier transform (DFT) based repetitive control (RC) scheme for DC/AC converters. By generating infinite magnitude on the interested harmonics, the DFT-based RC offers a selective harmonic scheme to eliminate waveform distortion. The traditional DFT-based selective harmonic RC, however, is sensitive to frequency fluctuation since even very small frequency fluctuation leads to a severe magnitude decrease. To address the problem, virtual variable sampling method, which creates an adjustable virtual delay unit to closely approximate a variable sampling delay, is proposed to enable the DFT-based selective harmonic RC to be frequency adaptive. Moreover, a selective odd-order harmonic DFT filter is developed to deal with the dominant odd order harmonic. Because it halves the number of sampling delays in the DFT filter, the system transient response gets nearly 50% improvement. A comprehensive series of experiments of the proposed VVS DFT-based selective odd-order harmonic RC controlled programmable AC power source under frequency variations are presented to verify the effectiveness of the proposed method

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Frequency adaptive repetitive control of grid-connected inverters

Grid-connected inverters (GCI) are widely used to feed power from renewable energy distributed generators into smarter grids. Repetitive control (RC) enables such inverters to inject high quality fundamental-frequency sinusoidal currents into the grid. However, digital RC which can get approximately zero tracking error of any periodic signal with known integer period in steady-state, cannot exactly track or reject periodic signal of frequency variations. Thus digital RC would lead to a significant power quality degradation of GCIs when grid frequency varies and causes periodic signal with non-integer periods. In this research paper a frequency adaptive repetitive control scheme (FARC) at a predefined sampling rate is proposed to deal with all types of periodic signal of variable frequency. A fractional delay filter which is based on Lagrange interpolation is used to estimate the fractional period terms in RC. This proposed FARC controller offers the fast, during process modification of fractional delay and fast revise of filter parameters, and then provides GCIs with a simple but very accurate real-time frequency adaptive control solution to the injection of high quality sinusoidal current under grid frequency variations. A case study a three-phase GCI is conducted to testify the validity of the proposed strategy

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 al- lows to track periodic references and/or reject peri- odic disturbances. Repetitive controllers are usually de- signed assuming a fixed frequency for the signals to be tracked/rejected, its main drawback being a dramatic per- formance decay when this frequency varies. A usual ap- proach to overcome the problem consists of an adap- tive change of the sampling time according to the refer- ence/disturbance period variation. However, this sam- pling period adaptation implies parametric changes af- fecting the closed-loop system behavior, that may compro- mise the system stability. This article presents a design strategy which allows to compensate for the parametric changes caused by sampling period adjustment. Stabil- ity of the digital repetitive controller working under time- varying sampling period is analyzed. Theoretical devel- opments are illustrated with experimental results.Peer ReviewedPostprint (published version