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

Control of A High Performance Bipedal Robot using Viscoelastic Liquid Cooled Actuators

This paper describes the control, and evaluation of a new human-scaled biped robot with liquid cooled viscoelastic actuators (VLCA). Based on the lessons learned from previous work from our team on VLCA [1], we present a new system design embodying a Reaction Force Sensing Series Elastic Actuator (RFSEA) and a Force Sensing Series Elastic Actuator (FSEA). These designs are aimed at reducing the size and weight of the robot's actuation system while inheriting the advantages of our designs such as energy efficiency, torque density, impact resistance and position/force controllability. The system design takes into consideration human-inspired kinematics and range-of-motion (ROM), while relying on foot placement to balance. In terms of actuator control, we perform a stability analysis on a Disturbance Observer (DOB) designed for force control. We then evaluate various position control algorithms both in the time and frequency domains for our VLCA actuators. Having the low level baseline established, we first perform a controller evaluation on the legs using Operational Space Control (OSC) [2]. Finally, we move on to evaluating the full bipedal robot by accomplishing unsupported dynamic walking by means of the algorithms to appear in [3].Comment: 8 pages, 8 figure

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

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