399 research outputs found
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
Disturbance Observer
Disturbance observer is an inner-loop output-feedback controller whose role
is to reject external disturbances and to make the outer-loop baseline
controller robust against plant's uncertainties. Therefore, the closed-loop
system with the DOB approximates the nominal closed-loop by the baseline
controller and the nominal plant model with no disturbances. This article
presents how the disturbance observer works under what conditions, and how one
can design a disturbance observer to guarantee robust stability and to recover
the nominal performance not only in the steady-state but also for the transient
response under large uncertainty and disturbance
Robust Distributed Control Protocols for Large Vehicular Platoons with Prescribed Transient and Steady State Performance
In this paper, we study the longitudinal control problem for a platoon of
vehicles with unknown nonlinear dynamics under both the predecessor-following
and the bidirectional control architectures. The proposed control protocols are
fully distributed in the sense that each vehicle utilizes feedback from its
relative position with respect to its preceding and following vehicles as well
as its own velocity, which can all be easily obtained by onboard sensors.
Moreover, no previous knowledge of model nonlinearities/disturbances is
incorporated in the control design, enhancing in that way the robustness of the
overall closed loop system against model imperfections. Additionally, certain
designer-specified performance functions determine the transient and
steady-state response, thus preventing connectivity breaks due to sensor
limitations as well as inter-vehicular collisions. Finally, extensive
simulation studies and a real-time experiment conducted with mobile robots
clarify the proposed control protocols and verify their effectiveness.Comment: IEEE Transactions on Control Systems Technology, accepte
Optimal tracking control for uncertain nonlinear systems with prescribed performance via critic-only ADP
This paper addresses the tracking control problem for a class of nonlinear systems described by Euler-Lagrange equations with uncertain system parameters. The proposed control scheme is capable of guaranteeing prescribed performance from two aspects: 1) A special parameter estimator with prescribed performance properties is embedded in the control scheme. The estimator not only ensures the exponential convergence of the estimation errors under relaxed excitation conditions but also can restrict all estimates to pre-determined bounds during the whole estimation process; 2) The proposed controller can strictly guarantee the user-defined performance specifications on tracking errors, including convergence rate, maximum overshoot, and residual set. More importantly, it has the optimizing ability for the trade-off between performance and control cost. A state transformation method is employed to transform the constrained optimal tracking control problem to an unconstrained stationary optimal problem. Then a critic-only adaptive dynamic programming algorithm is designed to approximate the solution of the Hamilton-Jacobi-Bellman equation and the corresponding optimal control policy. Uniformly ultimately bounded stability is guaranteed via Lyapunov-based stability analysis. Finally, numerical simulation results demonstrate the effectiveness of the proposed control scheme
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 disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition
For a multi-input multi-output (MIMO) nonlinear system, the existing disturbance observer-based control (DOBC) only provides solutions to those whose disturbance relative degree (DRD) is higher than or equal to its input relative degree. By designing a novel disturbance compensation gain matrix, a generalised nonlinear DOBC method is proposed in this article to solve the disturbance attenuation problem of the MIMO nonlinear system with arbitrary DRD. It is shown that the disturbances are able to be removed from the output channels by the proposed method with appropriately chosen control parameters. The property of nominal performance recovery, which is the major merit of the DOBCs, is retained with the proposed method. The feasibility and effectiveness of the proposed method are demonstrated by simulation studies of both the numerical and application examples
Lyapunov based optimal control of a class of nonlinear systems
Optimal control of nonlinear systems is in fact difficult since it requires the solution to the Hamilton-Jacobi-Bellman (HJB) equation which has no closed-form solution. In contrast to offline and/or online iterative schemes for optimal control, this dissertation in the form of five papers focuses on the design of iteration free, online optimal adaptive controllers for nonlinear discrete and continuous-time systems whose dynamics are completely or partially unknown even when the states not measurable. Thus, in Paper I, motivated by homogeneous charge compression ignition (HCCI) engine dynamics, a neural network-based infinite horizon robust optimal controller is introduced for uncertain nonaffine nonlinear discrete-time systems. First, the nonaffine system is transformed into an affine-like representation while the resulting higher order terms are mitigated by using a robust term. The optimal adaptive controller for the affinelike system solves HJB equation and identifies the system dynamics provided a target set point is given. Since it is difficult to define the set point a priori in Paper II, an extremum seeking control loop is designed while maximizing an uncertain output function. On the other hand, Paper III focuses on the infinite horizon online optimal tracking control of known nonlinear continuous-time systems in strict feedback form by using state and output feedback by relaxing the initial admissible controller requirement. Paper IV applies the optimal controller from Paper III to an underactuated helicopter attitude and position tracking problem. In Paper V, the optimal control of nonlinear continuous-time systems in strict feedback form from Paper III is revisited by using state and output feedback when the internal dynamics are unknown. Closed-loop stability is demonstrated for all the controller designs developed in this dissertation by using Lyapunov analysis --Abstract, page iv
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