Yet Another Tutorial of Disturbance Observer: Robust Stabilization and Recovery of Nominal Performance

This paper presents a tutorial-style review on the recent results about the disturbance observer (DOB) in view of robust stabilization and recovery of the nominal performance. The analysis is based on the case when the bandwidth of Q-filter is large, and it is explained in a pedagogical manner that, even in the presence of plant uncertainties and disturbances, the behavior of real uncertain plant can be made almost similar to that of disturbance-free nominal system both in the transient and in the steady-state. The conventional DOB is interpreted in a new perspective, and its restrictions and extensions are discussed

미지의 정현파 외부 입력을 갖는 선형시스템을 위한 적응 출력 제어

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2016. 2. 심형보.This dissertation investigates the output regulation problem (which is equivalent to the problem of asymptotic tracking and disturbance rejection when the reference inputs and the disturbances are generated by an autonomous differential equation, the so-called exosystem) for linear systems driven by unknown sinusoidal exosystems. Unlike previous researches, our ultimate goal is to achieve asymptotic regulation of the plant output to the origin for the sinusoidal exogenous signals (representing the reference inputs and disturbances) generated by the exosystems whose magnitudes, phases, bias, frequencies, and even the number of frequencies are all unknown. Here, the plant is linear time-invariant (LTI) single-input-single-output (SISO) systems (including non-minimum phase systems) without uncertainty. Before achieving the final control goal, we first start by considering an output regulation problem under the assumption that the number of frequencies contained in the exogenous inputs is known but magnitudes, phases, bias, and frequencies are unknown. To solve this problem, an add-on type output regulator with an adaptive observer is presented. The adaptive observer, based on the persistently exciting (PE) property, is used to estimate the frequencies of sinusoidal exogenous inputs as well as the states of plant and exosystem. Also, by add-on controller we mean an additional controller which runs harmonically with a preinstalled controller that has been in operation for the plant. When the desired performance of the preinstalled controller is not satisfactory, the add-on controller can be used. Some advantages of the proposed add-on controller include that it can be designed without much information about the preinstalled controller and it can be plugged in the feedback loop any time in operation without causing unnecessary transient response. Both simulation and experimental results of the track-following control for commercial optical disc drive (ODD) systems confirm the effectiveness of the proposed method. As the next step, we deal with the case where, as well as magnitudes, phases, bias, and frequencies, the number of frequencies contained in the exogenous inputs is unknown. To this end, a closed-form solution is given under the assumptions that the plant has hyperbolic zero dynamics (i.e., there is no zero on the imaginary axis of the complex plane), and that the number of unknown frequencies has known upper bound. In particular, the PE property is not necessary for the estimation of the unknown frequencies. For this, an adaptive observer is proposed to estimate the frequencies and the number of frequencies, simultaneously. This is important contribution, because, sufficient persistency of excitation is usually required since the unknown parameters are estimated by the adaptive control. Moreover, we propose a suitable dead-zone function with a computable dead-band only using the plant parameters to avoid the singularity problem in the transient-state and, at the same time, to achieve output regulation in the steady-state.Chapter 1 Introduction 1 1.1 Research Background 1 1.2 Contributions and Outline of the Dissertation 5 Chapter 2 Reviews of Related Prior Studies 9 2.1 Control Methods for Rejecting of Sinusoidal Disturbance 9 2.1.1 Adaptive Feedforward Cancellation (AFC) 9 2.1.2 Repetitive Control 12 2.1.3 Disturbance Observer (DOB) with Internal Model 15 2.2 Frequency Estimation Algorithms for Indirect Approach 19 2.2.1 Adaptive Notch Filtering 19 2.2.2 Phase-Locked Loops 20 2.2.3 Extended Kalman Filtering 21 2.2.4 Marinos Frequency Estimator 23 Chapter 3 Highlights of Output Regulation for Linear Systems 27 3.1 Problem Formulation 27 3.2 Output Regulation via Full Information 29 3.3 Output Regulation via Error Feedback 31 Chapter 4 Adaptive Add-on Output Regulator for Unknown Sinusoidal Exogenous Inputs 37 4.1 Add-on Output Regulator 39 4.1.1 Problem Formulation 39 4.1.2 Controller Design and Stability Analysis 41 4.2 Adaptive Add-on Output Regulator 44 4.2.1 Problem Formulation 44 4.2.2 Controller Design and Analysis 46 4.3 Industrial Application: Optical Disc Drive (ODD) Systems 54 4.3.1 Introduction of ODD Systems 54 4.3.2 Simulation Results 58 4.3.3 Experimental Results 63 Chapter 5 Adaptive Output Regulator for Unknown Number of Unknown Sinusoidal Exogenous Inputs 69 5.1 Problem Formulation 71 5.2 Adaptive Output Regulator 72 5.3 Constructive Proof of Theorem 5.2.1 75 5.4 Numerical Examples 88 Chapter 6 Conclusions and Further Issues 93 6.1 Conclusions 93 6.2 Further Issues 94 APPENDIX 97 A.1 Stabilizability and Detectability of the Plant in Chapter 4 97 A.2 Nonsingularity of the Matrix T(θ) in Chapter 4 99 A.3 Pseudo Code Implemented on the DSP Board in Chapter 4 99 A.4 Observability Property of the Pair (S, γ) in Chapter 5 101 A.5 Structure of the Matrix Tc(θ) in Chapter 5 102 A.6 Convergence Property of det2(i(t)) in Lemma 5.3.2 104 BIBLIOGRAPHY 109 국문초록 121Docto

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

On relationship between time-domain and frequency-domain disturbance observers and its applications

This paper provides a generic analysis of the relationship between time/frequency-domain DOB design methodology. It is discovered that the traditional frequency-domain DOBs using a low pass filter with unity gain can only handle disturbances satisfying matching condition, while the traditional time-domain DOBs always generate an observer with a high order. A Functional Disturbance OBserver (FDOB) is proposed to improve the existing results together with its design guideline, frequency analysis and existence condition. Compared with the existing frequency-domain DOBs, the proposed FDOB can handle more classes of disturbances, while compared with the existing time-domain DOBs the proposed FDOB can generate an observer with a lower order. Numerical examples are presented to illustrate the main findings of this paper including a rotary mechanical system of nonminimum phase

Relaxing Fundamental Assumptions in Iterative Learning Control

Iterative learning control (ILC) is perhaps best decribed as an open loop feedforward control technique where the feedforward signal is learned through repetition of a single task. As the name suggests, given a dynamic system operating on a finite time horizon with the same desired trajectory, ILC aims to iteratively construct the inverse image (or its approximation) of the desired trajectory to improve transient tracking. In the literature, ILC is often interpreted as feedback control in the iteration domain due to the fact that learning controllers use information from past trials to drive the tracking error towards zero. However, despite the significant body of literature and powerful features, ILC is yet to reach widespread adoption by the control community, due to several assumptions that restrict its generality when compared to feedback control. In this dissertation, we relax some of these assumptions, mainly the fundamental invariance assumption, and move from the idea of learning through repetition to two dimensional systems, specifically repetitive processes, that appear in the modeling of engineering applications such as additive manufacturing, and sketch out future research directions for increased practicality: We develop an L1 adaptive feedback control based ILC architecture for increased robustness, fast convergence, and high performance under time varying uncertainties and disturbances. Simulation studies of the behavior of this combined L1-ILC scheme under iteration varying uncertainties lead us to the robust stability analysis of iteration varying systems, where we show that these systems are guaranteed to be stable when the ILC update laws are designed to be robust, which can be done using existing methods from the literature. As a next step to the signal space approach adopted in the analysis of iteration varying systems, we shift the focus of our work to repetitive processes, and show that the exponential stability of a nonlinear repetitive system is equivalent to that of its linearization, and consequently uniform stability of the corresponding state space matrix.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133232/1/altin_1.pd

외란 관측기의 이론적 해석 : 안정성 및 성능

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2014. 8. 심형보.This dissertation provides the stability and performance analysis of the disturbance observer and proposes several design methods for guaranteeing the robust stability and for enhancing the disturbance rejection performance. Compared to many success stories in industry, theoretic analysis on the disturbance observer itself has attracted relatively little attention. In order to enlarge the horizon of its applications, we provide some rigorous analysis both in the frequency and time domain. In the frequency domain, we focus on two main issues: disturbance rejection performance and robust stability. In spite of its powerful ability for disturbance rejection, the conventional disturbance observer rejects the disturbance approximately rather than asymptotically. To enhance the disturbance rejection performance, based on the well-known internal model principle, we propose a design method to embed an internal model into the disturbance observer structure for achieving the asymptotic disturbance rejection and derive a condition for robust stability. Thus, the proposed disturbance observer can reject not only approximately the unmodeled disturbances but also asymptotically the disturbances of sinusoidal or polynomial-in-time type. In addition, a constructive design procedure to satisfy the proposed stability condition is presented. The other issue is to design of the disturbance observer based control system for guaranteeing robust stability under plant uncertainties. We study the robust stability for the case that the relative degree of the plant is not exactly known and so it happens to be different from that of nominal model. Based on the above results, we propose a universal design method for the disturbance observer when the relative degree of the plant is less than or equal to 4. Moreover, from the observation about the role of each block, we generalize the design of disturbance observer and propose a reduced order type-k disturbance observer to improve the disturbance rejection performance and to reduce the design complexity simultaneously. As a counterpart of the frequency domain analysis, we analyze the disturbance observer in the state space for the purpose of extending the horizon of the disturbance observer applications and obtaining the deeper understanding of the role of each block. Based on the singular perturbation theory, it reveals not only well-known properties but also interesting facts such as the peaking in the transient response. Moreover, we investigate robust stability of the disturbance observer based control systems with and without unmodeled dynamics and derive an explicit relation between the nominal performance recovery and the time constant of Q-filter. Since the classical linear disturbance observer does not ensure the recovery of transient response, a nonlinear disturbance observer, in which all the benefits of the classical one are still preserved, is presented for guaranteeing the recovery of transient as well as steady-state response.Abstract List of Figures Symbols and Acronyms 1. Introduction 1.1 Motivation 1.2 Contributions and Outline of the Dissertation 2. Robust Stability for Closed-loop System with Disturbance Observer 2.1 Structure of Disturbance Observer 2.2 Robust Stability Condition for Closed-loop System with Disturbance Observer 2.3 Illustrative Example 3. Embedding Internal Model in Disturbance Observer with Robust Stability 3.1 Design Method for Embedding Internal Model of Disturbance 3.2 Design of Q-filter for Guranteeing Robust Stability 3.2.1 Robust Stability Condition of Closed-loop System 3.2.2 Selecting a_i's for Robust Stability 3.3 Illustrative Example 3.4 Discussions on Robustness 3.4.1 Pros and Cons of Proposed Design Procedure 3.4.2 Bode Diagram Approach 4. Disturbance Observer with Unknown Relative Degree of the Plant 4.1 Robust Stability 4.2 A Guideline for Selecting Q and P_n 4.2.1 A Universal Robust Controller 4.3 Technical Proofs 4.4 Illustrative Examples 5. Reduced Order Type-k Disturbance Observer under Generalized Q-filter 5.1 Concept of Disturbance Observer with Generalized Q-filter Structure 5.2 Robust Stability 5.3 Reduced Order Type-k Disturbance Observer 5.4 Illustrative Examples 6. State Space Analysis of Disturbance Observer 6.1 State Space Realization of Disturbance Observer 6.2 Analysis of Disturbance Observer based on Singular Perturbation Theory 6.3 Discussion on Disturbance Observer Approach 6.3.1 Relation of Robust Stability Condition between State Space and Frequency Domain Approach 6.3.2 Effect of Zero Dynamics 6.3.3 Stability of Nominal Closed-loop System 6.3.4 Infinite Gain Property with p-dynamics 6.3.5 Peaking in Fast Transient 6.4 Nominal Performance Recovery with respect to Time Constant of Q-filter 7. Nominal Performance Recovery and Stability Analysis of Disturbance Observer under Unmodeled Dynamics 7.1 Problem Formulation 7.2 Stability and Performance Analysis based on Singular Perturbation Theory 7.2.1 Nominal Performance Recovery 7.2.2 Multi-time-scale Singular Perturbation Analysis 7.3 Nominal Performance Recovery by Disturbance Observer under Unmodeled Dynamics 8. Extensions of Disturbance Observer for Guaranteeing Robust Transient Performance 8.1 Extensions to MIMO Nonlinear Systems 8.1.1 SISO Nonlinear Disturbance Observer with Nonlinear Nominal Model 8.1.2 MIMO Nonlinear Disturbance Observer with Linear Nominal Model 9. Conclusions Appendix Bibliography 국문초록Docto

Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

Advances in Control of Power Electronic Converters

This book proposes a list of contributions in the field of control of power electronics converters for different topologies: DC-DC, DC-AC and AC-DC. It particularly focuses on the use of different advanced control techniques with the aim of improving the performances, flexibility and efficiency in the context of several operation conditions. Sliding mode control, fuzzy logic based control, dead time compensation and optimal linear control are among the techniques developed in the special issue. Simulation and experimental results are provided by the authors to validate the proposed control strategies

High performance disturbance observer based control system design for permanent magnet synchronous AC machine applications

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonAn electrical machine is one of the main workforces in different industries and serves them in various applications. Machine drive control design involves many technical issues for efficient and robust exploitation. Over several decades, Permanent Magnet Synchronous Motor (PMSM) is getting preferred for industrial applications over its counterpart Squirrel Cage Induction Motor (SCIM) drive, because of their higher efficiency, power density, and higher torque to inertia ratio. In the prospective that PMSM drives are considered the drives of the future, there are still technical challenges and issues related to PMSM control. Many studies have been devoted to PMSM control in the past, but there are still some open research areas that bring worldwide researchers’ interests back to PMSM drive control. One of the approaches that may facilitate better performance, higher efficiency, and robust and reliable work of the control system is the disturbance observer-based control (DOBC) with linear and nonlinear output feedback control for PM synchronous machine applications. DOBC is adopted due to its ability to reject external and internal disturbances with improving tracking performance in the variable speed wind energy conversion system (WECS) to maximize power extraction. The high order disturbance observer (HODO) is utilized to estimate the aerodynamic torque-based wind speed without the use of a traditional anemometer, which reduces the overall cost and improves the reliability of the whole system. Also, this method has been designed to improve the angular shaft speed tracking of the PMSM system under load torque disturbance and speed variations. The model-based linear and nonlinear feedback control are used in the proposed control systems. The sliding mode control (SMC) with switching output feedback control law and integral SMC with linear feedback and state-dependent Riccati equation (SDRE) based approaches have been designed for the systems. The SDRE control accounts for the nonlinear multivariable structure of the WECS and is approximated with Taylor series expansion terms. The chattering inherited from SMC is eliminated by the continuous approximation technique. The sliding mode is guaranteed by eliminating the reaching mode in the proposed integral SMC. The model-free cascaded linear feedback control system based on the proportional-integral (PI) controllers use a back-calculation algorithm anti-windup scheme. The proposed speed controllers are synthesized with HODO to compensate for the external disturbance, model uncertainty, noise, and modelling errors. Moreover, servomechanism-based SDRE control, a near-optimal control system is designed to suppress the model uncertainty and noise without the use of disturbance observers. The proposed control systems for PMSM speed regulation have demonstrated a significant improvement in the angular shaft speed-tracking performance at the transients. Their performances have been tested under speed, load torque variations, and model uncertainty. For example, HODO-based SMC with switching output feedback control law (SOFCL) has demonstrated improvement by more than 78% than the PI-PI control system of the PMSM. The performance of the HODOs-based Integral SMC with SDRE nonlinear feedback is improved by 80.5% under external disturbance, model uncertainty, and noise than Integral SMC with linear feedback in the WECS. The HODO-based SDRE control with servomechanism has shown an 80.2% improvement of mean absolute percentage error under disturbances than Integral SMC with linear feedback in the WECS. The PMSM speed tracking performance of the proposed HODO-based discrete-time PI-PI control system with back-calculation algorithm anti-windup scheme is improved by 87.29% and 90.2% in the speed commands and load torque disturbance variations scenarios respectively. The simulations for testing the proposed control system of the PMSM system and WECS have been implemented in Matlab/Simulink environment. The PMSM speed control experimental results have been obtained with Lucas-Nuelle DSP-based rapid control prototyping kit.Center for International Program “Bolashak” of the Ministry of Education and Science Republic of Kazakhsta