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
