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

Robust Nonlinear Output Regulation by Identification Tools

The present thesis focuses on the problem of robust output regulation for minimum phase nonlinear systems by means of identification techniques. Given a controlled plant and an exosystem (an autonomous system that generates eventual references or disturbances), the control goal is to design a proper regulator able to process the only measure available, i.e the error/output variable, in order to make it asymptotically vanishing. In this context, such a regulator can be designed following the well known “internal model principle” that states how it is possible to achieve the regulation objective by embedding a replica of the exosystem model in the controller structure. The main problem shows up when the exosystem model is affected by parametric or structural uncertainties, in this case, it is not possible to reproduce the exact behavior of the exogenous system in the regulator and then, it is not possible to achieve the control goal. In this work, the idea is to find a solution to the problem trying to develop a general framework in which coexist both a standard regulator and an estimator able to guarantee (when possible) the best estimate of all uncertainties present in the exosystem in order to give “robustness” to the overall control loop

Robust nonlinear regulation: Continuous-time internal models and hybrid identifiers

The paper deals with the problem of robust output regulation for minimum-phase nonlinear systems in a semiglobal setting. We present a different perspective to the problem of adaptive regulation in which prediction error identification methods, which are routinely used in other control contexts, can be adopted to design robust nonlinear regulators. The proposed control structure combines continuous-time dynamics and "hybrid identifiers", the latter specifically designed to estimate the actual steady state control law. Besides presenting the main idea and a general framework, the paper addresses the specific case in which a linear regression law is used as model structure for the steady state control law and a least square optimization criterion is adopted as estimation method. The proposed framework encompasses existing frameworks proposed so far in the nonlinear continuous-time literature

DISCRETE-TIME ADAPTIVE CONTROL ALGORITHMS FOR REJECTION OF SINUSOIDAL DISTURBANCES

We present new adaptive control algorithms that address the problem of rejecting sinusoids with known frequencies that act on an unknown asymptotically stable linear time-invariant system. To achieve asymptotic disturbance rejection, adaptive control algorithms of this dissertation rely on limited or no system model information. These algorithms are developed in discrete time, meaning that the control computations use sampled-data measurements. We demonstrate the effectiveness of algorithms via analysis, numerical simulations, and experimental testings. We also present extensions to these algorithms that address systems with decentralized control architecture and systems subject to disturbances with unknown frequencies

An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required