Control of nonlinear flexible space structures

Abstract

CHAPTER 1. INTRODUCTION 1 1.1 Background 1 1.2 Thesis outline 10 CHAPTER 2. APPROXIMATE MATHEMATICAL MODELS OF FLEX IBLE SPACE STRUCTURES 11 2.1 Introduction 11 2.2 Linear model of flexible single body system 13 2.2.1 Linear rigid body motion equations 2.2.2 Elastic motion equations 2.3 Approximate nonlinear model of flexible single body system 2.3.1 Euler parameters 2.3.2 State equations for flexible single body systems 21 2.4 Approximate nonlinear model of flexible multibody system 2.4.1 Coordinate systems 2.4.2 Kinetic energy 2.4.3 Lagrange equation and a fundamental equation for a system of rigid bodies 2.4.4 State equations for flexible multibody systems 2.5 Remarks V CHAPTER 3. STABLE GENERALIZED PREDICTIVE CONTROL ... 27 3.1 Introduction 27 3.2 Input/output approach for Generalized Predictive Control (GPC) 28 3.3 State-space approach for Generalized Predictive Control (GPC) 29 3.3.1 Stable generalized predictive control law 29 3.3.2 GPC control law with end-point state weighting 3.3.3 Computation of desired state trajectories 35 3.4 Q-synthesis methods 37 3.4.1 Fake Algebraic Riccati Equations (FARE) based Q-synthesis 3.4.2 Constrained nonlinear optimization based Q-synthesis 3.5 Reconfigurable control 3.5.1 Definitions 3.5.2 Stability under reconfigurable control 3.6 Numerical example 3.7 Remarks CHAPTER 4. CONTROL DESIGN 4.1 Introduction 4.2 Modal analysis 4.3 Stable reconfigurable GPC design 4.4 Nonlinear control design for single body systems 4.4.1 Linear GPC design 63 4.4.2 Feedback linearization based GPC (FLGPC) design 65 4.4.3 Nonlinear dissipative control design 77 4.4.4 Nominal performance comparison 82 4.4.5 Robust performance comparison 82 4.5 Nonlinear dissipative control design for multibody systems 96 4.5.1 Dynamical model verification 98 4.5.2 Nonlinear dissipative control design 99 vi 4.6 Remarks CHAPTER 5. CONCLUSIONS 107 5.1 Main research contributions

Adaptive Coordinated Decentralized Control of State Delayed Systems With Actuator Failures

“…The damping of elastic motions in flexible structures with co-located sensors and actuators makes for a control prob-lem that satisfies the assumption see, e.g. [19].…”

Nonlinear fixed-order dynamic compensation for passive systems

“…# denotes the Euclidean vector norm, it follows that P satisfies (1) and (2). Finally, (3) follows from (14) by setting x"0.…”