Analog, hybrid, and digital simulation

Analog, hybrid, and digital computerized simulation technique

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

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Measurements, Models, Systems and Design

531 s.

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control

Higher order sinusoidal input describing functions : extending linear techniques towards non-linear systems analysis

In modern positioning systems, accuracy and speed requirements have increased significantly. These accuracies can only be realized if account is given to nonlinear system behavior in both the mechanical and the control design. This requires additional tools for frequency based identification of nonlinear system behavior since existing tools either are either too limited to successfully describe nonlinear behavior or the results are very difficult to interpret and as such do not relate to the background of the intended user. In this thesis an alternative concept for frequency based nonlinear system analysis is presented, the required measurement techniques are described and some application examples are shown. The method is applicable for the class of causal, stable, time-invariant non-linear systems which have a harmonic response to a sinusoidal excitation. This new concept is the generalization of the Sinusoidal Input Describing Function to Higher Order Sinusoidal Input Describing Functions (HOSIDF) as it yields the magnitude and phase relations between the individual higher harmonics in the response signal and the sinusoidal excitation signal, both as function of magnitude and frequency of the excitation signal. An essential element in the HOSIDF theory is the concept of the Virtual Harmonics Expander (VHE). This nonlinear function describes the transformation of a single sinusoid into an infinite amount of harmonics, each with equal amplitude as the input signal and with a phase equal to the phase of the input signal times the harmonic number. Nonlinear systems belonging to the class can be modeled as a parallel connection of an (infinite) amount of HOSIDF describing quasi-linear subsystems in series with the VHE. Two measurement methods for nonparametric identification of HOSIDF are presented. The Fast Fourier Transform based method on fast fourier transforms shows ideal characteristics due to its perfect selectivity. The IQ (In phase-Quadrature phase) demodulation method has limited performance due to non perfect selectivity. The bias in the HOSIDF estimates caused by harmonic components in the input signal is analyzed and a compensation algorithm is presented to reduce this bias. Accept- ing harmonic distortion in the excitation signal allows the application of non-constant amplitude-time profiles for testing. It is demonstrated that a ramped amplitude-time signal reduces the required settling time of the digital filters used in the IQ methode. The capabilities of the HOSIDF technique are demonstrated in a real measurement in which the stick to gross sliding transition of a mechanical system with dry friction is captured as function of frequency. The odd HOSIDF clearly reveal this transition which is not possible with the Frequency Response Function technique. From the HOSIDF the pre-sliding displacement and the friction-induced stiffness are determined and the friction force which must be present in the stick-phase is calculated. Validation with force measurements shows excellent agreement. Special attention is paid to the determination of the HOSIDF of a nonlinear plant operating in feedback. In a controlled systemthe harmonics generated by the non-linear system will be fed back to the input, changing the sinusoidal excitation into an harmonic excitation. Two different solutions are presented to deal with this problem. The first method applies a numerical compensatie techniques to compensate the bias caused by the harmonic components in the excitation signal. The secondmethod uses amodified repetitive control scheme to suppress the harmonic components in the excitation signal. The effectiveness of both methods is tested in simulation experiments of a mass operating in feedback subjected to Coulomb friction, Stribeck-effect and hysteresis in the pre-sliding regime. The friction forces are modeled with the modified Leuven friction model. The results are compared with the HOSIDF measured under open loop condition and both methods yield correct results. It is shown that by rearranging the repetitive control loop, the output signal of a class of stable, time-invariant nonlinear systems becomes sinusoidal as response to an harmonic excitation. For this class of signals Higher Order Sinusoidal Output Describing Functions (HOSODF) can be defined as the dual of the HOSIDF. The HOSODF describe magnitude and phase relations between the individual higher harmonics in the input signal and the sinusoidal output signal, both as function of magnitude and frequency of the output signal. The required dual of the Virtual Harmonics Expander is defined as the Virtual Harmonics Compressor. This nonlinear function describes the transformation of an infinite amount of harmonics into a single sinusoid. Finally, an application example shows the extreme sensitivity of the HOSIDF technique for changes in friction characteristics, indicating interesting opportunities for application in the field of machine condition monitoring. De eisen die gesteld worden aan de snelheid en positioneringsnauwkeurigheid van moderne positioneringssystemen zijn significant toegenomen. Deze nauwkeurigheden kunnen alleen maar gerealiseerd worden als met niet-lineair systeemgedrag rekening wordt gehouden in zowel het mechanische als het regeltechnische ontwerp. In tegenstelling tot de tijddomein gebaseerde systeemidentificatie is de moderne regeltechniek op frequentiedomein technieken gebaseerd. Maar de transformatie van niet-lineaire tijddomeinmodellen naar het frequentiedomein is nietmogelijkmet alleen lineaire technieken. Dit vereist extra gereedschappen ten behoeve van de frequentiedomein gebaseerde identificatie van niet-linear systeemgedrag omdat de bestaande gereedschappen ofwel te beperkt zijn om met succes niet-linear gedrag te beschrijven ofwel resultaten leveren in een formaat dat moeilijk te interpreteren is en niet aansluit bij de achtergrond van de gebruiker. In dit proefschrift wordt een alternatief concept gepresenteerd voor een op frequentiedomeintechnieken gebaseerde niet-lineaire systeemanalyse. Eveneens worden de vereiste meetmethodes beschreven en enkele toepassingsvoorbeelden getoond. De methode is van toepassing op de klasse I gedefinieerd als de klasse van causale, stabiele, tijdsinvariante, niet-lineaire systemen welke een harmonische responsie hebben ten gevolge van een sinusvormige excitatie. Dit nieuwe concept is de generalisatie van de Sinusoidal Input Describing Function tot de Higher Order Sinusoidal Input Describing Functions (HOSIDF). De HOSIDF beschrijven de magnitude- en faserelaties die bestaan tussen de afzonderlijke hogere harmonische componenten in het responsiesignaal en de sinusvormige excitatie, allen als functie van amplitude en frequentie van dat excitatiesignaal. In de HOSIDF theorie wordt een essentiële plaats ingenomen door het begrip Virtual Harmonics Expander (VHE). Deze niet-lineaire functie beschrijft de transformatie van een zuiver sinusvormig signaal in een oneindige reeks harmonischen, elk met identieke amplitude gelijk aan de amplitude van het ingangssignaal en een fase gelijk aan de fase van het ingangssignaal maal het rangnummer van de harmonische component. Systemen die behoren tot de klasse I kunnen gemodelleerd worden als een parallel schakeling van een (oneindig) aantal HOSIDF in serie met de VHE. Twee meetmethodes voor de niet-parametrische identificatie van HOSIDF worden gepresenteerd. De op Fast Fourie

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Hybrid analog-digital techniques and random-process studies, 1964-1965

Hybrid computer techniques for evaluating statistics from quantized dat

Synthesis and Analysis of Design Methods in Linear Repetitive, Iterative Learning and Model Predictive Control

Repetitive Control (RC) seeks to converge to zero tracking error of a feedback control system performing periodic command as time progresses, or to cancel the influence of a periodic disturbance as time progresses, by observing the error in the previous period. Iterative Learning Control (ILC) is similar, it aims to converge to zero tracking error of system repeatedly performing the same task, and also adjusting the command to the feedback controller each repetition based on the error in the previous repetition. Compared to the conventional feedback control design methods, RC and ILC improve the performance over repetitions, and both aiming at zero tracking error in the real world instead of in a mathematical model. Linear Model Predictive Control (LMPC) normally does not aim for zero tracking error following a desired trajectory, but aims to minimize a quadratic cost function to the prediction horizon, and then apply the first control action. Then repeat the process each time step. The usual quadratic cost is a trade-off function between tracking accuracy and control effort and hence is not asking for zero error. It is also not specialized to periodic command or periodic disturbance as RC is, but does require that one knows the future desired command up to the prediction horizon. The objective of this dissertation is to present various design schemes of improving the tracking performance in a control system based on ILC, RC and LMPC. The dissertation contains four major chapters. The first chapter studies the optimization of the design parameters, in particular as related to measurement noise, and the need of a cutoff filter when dealing with actuator limitations, robustness to model error. The results aim to guide the user in tuning the design parameters available when creating a repetitive control system. In the second chapter, we investigate how ILC laws can be converted for use in RC to improve performance. And robustification by adding control penalty in cost function is compared to use a frequency cutoff filter. The third chapter develops a method to create desired trajectories with a zero tracking interval without involving an unstable inverse solution. An easily implementable feedback version is created to optimize the same cost every time step from the current measured position. An ILC algorithm is also created to iteratively learn to give local zero error in the real world while using an imperfect model. This approach also gives a method to apply ILC to endpoint problem without specifying an arbitrary trajectory to follow to reach the endpoint. This creates a method for ILC to apply to such problems without asking for accurate tracking of a somewhat arbitrary trajectory to accomplish learning to reach the desired endpoint. The last chapter outlines a set of uses for a stable inverse in control applications, including Linear Model Predictive Control (LMPC), and LMPC applied to Repetitive Control (RC-LMPC), and a generalized form of a one-step ahead control. An important characteristic is that this approach has the property of converging to zero tracking error in a small number of time steps, which is finite time convergence instead of asymptotic convergence as time tends to infinity