Introduction to Dynamics and Control of Flexible Structures.

Cover -- Title -- Copyright -- Foreword -- Preface -- Table of Contents -- 1 Introduction -- 1.1 Some Biased Historical Notes -- 1.2 Scope and Organization -- 2 Mathematical Background: Matrix Analysis and Computation -- 2.1 Introduction and Basic Notions -- Simultaneous Linear Algebraic Equations -- Numerical Methods to Solve the Least Square Problem -- Partitioned Matrix Inversion Formulas and the Matrix Inversion Lemma -- 2.2 Matrix Decompositions -- Spectral Decomposition -- Singular Value Decomposition -- Cholesky Decomposition -- Schur Decomposition -- 2.3 Sensitivity and Conditioning Issues -- Eigenvalue/Eigenvector Sensitivities -- Conditioning of Eigenvalue Problem -- Stability Robustness Criteria: Conditioning of the Eigenstructure -- Partial Derivatives of the Singular Values -- 2.4 Case Study: Parameterization of Orthogonal Matrices -- Some Geometrical and Kinematical Insignts from R[sup(3×3)] -- Parameterizations of Orthogonal Matrices in R[sup(n×n)] -- Applications of the Cayley Transform -- 3 Stability in the Sense of Lyapunov: Theory and Applications -- 3.1 Basic Definitions -- 3.2 Lyapunov's Stability Theorem (Direct Method) -- 3.3 Stability of Linear Systems -- Lyapunov Theorem for Linear Systems -- Linear Dynamic Systems Subject to Arbitrary Disturbances -- Stability Analysis for Mechanical Second Order Systems -- 3.4 Nonlinear, Time Varying, and Distributed Parameter Systems -- Local Stability of Linearized Systems -- What to do When U is Only Negative Semi-Definite -- Lyapunov Control Law Design Method -- Work Energy Rate Principle and Laypunov Stable Control Laws -- Globally Stable Tracking Controller: Lyapunov Approach -- 3.5 Case Study: Application for Near-Minimum-Time Large Angle Maneuvers of Distributed Parameter Systems -- Simulated Results for the Large Angle Maneuvers -- Experimental Results.

4 Mathematical Models of Flexible Structures -- 4.1 Lagrangian Approach to Equation of Motion Formulation -- 4.2 Infinite-Dimensional Models of Distributed Parameter Systems -- Classical Application of Hamilton's Principle -- Explicit Generalization of Lagrange's Equations -- The Differential Eigenvalue Problem -- 4.3 Approximate Methods for Finite Dimensional Models -- Assumed Modes Method -- Finite Element Method -- Comparison Between Two Spatial Discretization Models -- 4.4 Case Study: Consequences of Neglecting Coupling between Rigid Motion and Elastic Motion -- 5 Design of Linear State Feedback Control Systems -- 5.1 Linear Optimal Control -- Necessary Conditions for Optimality -- Linear Regulator Problem -- Numerical Algorithms for Solving the Riccati Equations -- Generalized Linear Quadratic Regulator Formulations -- 5.2 Robust Eigenstructure Assignment -- Sylvester's Equation -- Projection Method for Eigenstructure Assignment -- Specialization for Mechanical Second Order Systems -- Eigenstructure Assignment by IMSC Method -- Sequential Robust Eigenstructure Assignment -- Sequential Eigenvalue Assignment -- 5.3 Case Study: Robust Eigenstructure Assignment -- 6 Controllability and Observability of Finite-Dimensional Dynamical Systems -- 6.1 Definitions of Controllability and Observability -- 6.2 Measures of Controllability -- Degree of Controllability -- Balanced Realization -- Measure of Modal Controllability -- 6.3 Cost Analysis -- Component Cost Analysis -- Modal Cost Analysis for Mechanical Second Order Systems -- 6.4 Case study: Measures of Controllability for Actuator Placement -- Control Design 1: Symmetric Output Feedback Design -- Control Design 2: Linear Quadratic Regulator Design -- Selection of Optimal Actuator Locations -- 7 Design of Linear Output Feedback Control Systems -- 7.1 Literature Survey.

7.2 Theoretical Background of the Symmetric Output Feedback -- Stability and Robustness Analysis -- Relation to LQR -- 7.3 Optimization Problem Formulation using Pole Placement -- 7.4 Two-Stage Homotopic Nonlinear Programming -- 7.5 Case Studies: Numerical Applications -- Simple Example (3 Degree of Freedom Problem) -- Draper/RPL Model -- Vibration Suppression for a Flexible Grid Structure -- Appendices -- A. Description of MATLAB Codes -- B. Proof of Theorem 2.7 (Patel and Toda) -- C. Derivation of Singular Value Sensitivities -- D. Work Energy Rate Principle -- E. Analytical Solution of the Lyapunov Equation for Modal Second Order Systems -- F. Partial Derivatives of Symmetic Gain Matrices -- G. Derivatives of Damping Factors and Damped Frequencies -- H. Minimum Norm Differential Correction Algorithm -- I. TAMU/AFSOR Maneuver Experiment Hardware Description -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.