Linear Multivariable Control Engineering Using GNU Octave

• Autore: Borutzky Wolfgang
• Pubblicazione: Cham : , : Springer, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (363 pages)
• Disciplina: 629.895
• Nota di contenuto: Intro -- Preface -- Contents -- Abbreviations -- List of Figures -- Listings -- 1 Introduction -- 1.1 Objectives of a Control System -- 1.2 Multivariable System Control -- 1.2.1 Multi-loop Control -- 1.2.2 Centralised Control -- 1.3 Linear Time Invariant Models -- 1.4 Organisation of the Book -- 1.5 Notation -- References -- 2 Multiple Input Multiple Output Systems -- 2.1 Input-Output Decoupling -- 2.1.1 Decoupling of Linear MIMO Systems -- 2.1.2 Relative Gain Array (RGA) -- 2.1.3 Singular Value Decomposition (SVD) -- 2.1.4 Stability of Decentralised Control Systems -- 2.2 Directions in MIMO Systems -- 2.3 Multivariable Systems Zeros -- 2.4 Multivariable Systems Poles -- 2.5 Summary -- 2.6 Problems -- References -- 3 State Observability -- 3.1 Observability Matrix -- 3.2 Observability Gramian -- 3.3 Hautus' Observability Criterion -- 3.4 Observability of State-Space Models in Canonical Form -- 3.4.1 Observability of a System in Observer Canonical Form -- 3.4.2 Transformation of an Observable System to Observer Canonical Form -- 3.5 Summary -- 3.6 Problems -- References -- 4 State Controllability -- 4.1 Controllability Gramian -- 4.2 Controllability Matrix -- 4.3 Duality of State Controllability and State Observability -- 4.4 Controllability Under a Similarity Transformation -- 4.5 Prescaling a State-Space Model -- 4.6 Controllability of State-Space Models in a Canonical Form -- 4.6.1 Transformation to a State-Space Representation in Jordan Canonical Form -- 4.6.2 Controllability of a System in Controller Canonical Form -- 4.6.3 Transformation of a Controllable System to Controller Canonical Form -- 4.7 Non-controllable System Modes -- 4.8 Summary -- 4.9 Problems -- References -- 5 Structural System Properties -- 5.1 Decomposition into a Controllable and a Non-controllable Subspace. ; 5.2 Decomposition into an Observable and an Unobservable Subspace -- 5.3 Kalman Decomposition of State-Space Model -- 5.4 Subspaces -- 5.5 Structural Controllability and Structural Observability -- 5.6 Summary -- 5.7 Problems -- References -- 6 Minimal State-Space Realisation of a Transfer Function Matrix -- 6.1 Constructing a Realisation of a Transfer Function Matrix -- 6.1.1 Converting a SISO Transfer Function to a State-Space Model in Controller Canonical Form -- 6.1.2 Representing an MIMO System as the Superposition of SIMO Systems -- 6.2 Finding a Minimal Realisation of a Transfer Function Matrix -- 6.3 Gilbert's Minimal Realisation -- 6.4 Summary -- 6.5 Problems -- References -- 7 Stability of Multivariable Systems -- 7.1 Internal Stability -- 7.2 Input-Output Stability -- 7.3 Summary -- 7.4 Problems -- Reference -- 8 Closed-Loop Systems -- 8.1 Controllability and Observability of Closed-Loop Systems -- 8.2 Sensitivity Function and Complementary Sensitivity Function -- 8.3 Control Loop Stability -- 8.3.1 Internal Stability of an MIMO Feedback Loop -- 8.3.2 Multivariable Nyquist Stability Criterion -- 8.3.3 Eigenvalue Loci -- 8.4 Robust Stability -- 8.5 Stability of Closed-Loop Systems with a Decentralised Controller -- 8.6 Summary -- 8.7 Problems -- References -- 9 State Feedback -- 9.1 Introduction -- 9.2 Properties Invariant Under State Feedback -- 9.2.1 Multivariable Plant Zeros -- 9.2.2 Complete State Controllability -- 9.2.3 Complete State Observability -- 9.3 SISO Systems in Controller Canonical Form -- 9.3.1 Finding a Feedback Gain Matrix for Desired Closed-Loop System Poles -- 9.3.2 Ackermann's Formula -- 9.3.3 Transformation of Behaviour Requirements into Closed-Loop Pole Locations -- 9.3.4 Adding Integral Control to a State-Feedback Loop for Reference Tracking -- 9.4 Non-uniqueness of the State-Feedback Matrix for MIMO Systems. ; 9.4.1 Parametric State Feedback -- 9.4.2 Cyclic Design -- 9.5 MIMO Systems in Controllable Form -- 9.6 State Observer-Based State Feedback -- 9.6.1 Full-Order Observer Design -- 9.6.2 Separation Principle -- 9.6.3 Design Procedure -- 9.6.4 Reduced Order Observer -- 9.6.5 Observer Behaviour in the Presence of Disturbances on the Plant -- 9.6.6 Unknown Input Observers (UIOs) -- 9.7 Summary -- 9.8 Problems -- References -- 10 Optimal Control -- 10.1 Introduction -- 10.2 Optimal Linear Quadratic State Feedback -- 10.2.1 The Linear Quadratic Regulation Problem (LQR) -- 10.2.2 Derivation of the Optimal State-Feedback Control Law -- 10.2.3 Solution of the Algebraic Riccati Equation -- 10.2.4 Stability of a Closed State-Feedback Loop with an Optimal Controller -- 10.3 Optimal Linear Quadratic State Estimation (LQE): The Kalman Filter -- 10.4 H2-Optimal Control -- 10.4.1 The H2-Norm -- 10.4.2 H2-Static State-Feedback Control -- 10.4.3 The Optimal H2-Observer -- 10.4.4 The Output Feedback H2-Control Problem -- 10.5 H∞-Optimal Control -- 10.5.1 The H∞-Norm -- 10.5.2 The H∞-Suboptimal Control Problem -- 10.6 Summary -- 10.7 Problems -- References -- 11 Robust Control -- 11.1 Introduction -- 11.2 Modelling Uncertainty -- 11.3 Robust Stability of Feedback Loops with Unstructured Uncertainty -- 11.4 Parametric Uncertainties -- 11.5 Robust Stability of Feedback Loops with Structured Uncertainty -- 11.6 Structured Singular Value -- 11.7 Synthesis of a Robust Controller: D-K Iteration -- 11.8 Robust Performance -- 11.8.1 Mixed Sensitivity H∞-Controller Design -- 11.8.2 Model Order Reduction -- 11.8.2.1 System Model Order Reduction by Balanced Truncation -- 11.8.2.2 Singular Perturbation Approximation of a Balanced System Fernando:1982 -- 11.8.2.3 Modal Truncation -- 11.8.3 Controller Order Reduction. ; 11.8.4 Capturing Performance Specifications by a Fictitious Uncertainty Block -- 11.8.5 Performance Bounds for SISO Systems in Terms of Weighting Functions -- 11.9 Summary -- 11.10 Problems -- References -- 12 Linear Matrix Inequalities in Control -- 12.1 Optimisation -- 12.2 Convex Sets and Convex Functions -- 12.3 Recap of Some Properties of Symmetric and of Hermitian Matrices -- 12.4 Linear Matrix Inequalities -- 12.5 Some LMI Properties -- 12.6 Control Problems in an LMI Setting -- 12.6.1 Matrix Scaling as an LMI Problem -- 12.6.2 Asymptotic Stability -- 12.6.3 State-Feedback Stabilisation -- 12.6.4 LMI-Based Observer Design -- 12.6.5 LMI Formulation of the LQR Problem -- 12.6.6 Computing the H2-Norm by Solving an LMI Optimisation Problem -- 12.6.7 LMI Formulation of the H2-State-Feedback Control Problem -- 12.6.8 Computing the H∞-Norm by Solving an LMI Optimisation Problem -- 12.6.9 H∞-State-Feedback Control -- 12.6.10 Quadratic Stability of Uncertain Systems -- 12.7 Basic Idea Underlying the Numerical Solution of Convex LMI Optimisation Problems -- 12.8 Summary -- 12.9 Problems -- References -- A Some Useful Mathematical Basics -- A.1 Matrices -- A.1.1 Definitions -- A.1.2 Matrix Identities -- A.1.3 Determinants -- A.1.4 Eigenvalues and Eigenvectors -- A.1.5 Singular Value Decomposition -- A.1.6 Relative Gain Array -- A.2 Matrix Norms and Induced Matrix Norms -- A.2.1 Vector Norms -- A.2.2 Matrix Norms -- A.3 Signal Norms -- A.4 System Norms -- A.5 Generalised Inequalities -- References -- B Further Reading -- References -- Index.
• Titolo autorizzato: Linear Multivariable Control Engineering Using GNU Octave
• ISBN: 3-031-44508-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910855372503321
• Lo trovi qui: Univ. Federico II