Linear systems control : deterministic and stochastic methods /

Linear systems control : deterministic and stochastic methods /

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Bibliographic Details
Author / Creator:Hendricks, Elbert.
Imprint:Berlin : Springer, c2008.
Description:1 online resource (xx, 555 p.) : ill.
Language:English
Subject:
Linear control systems.
Linear systems -- Mathematical models.
Automatic control.
Stochastic models.
Automatic control.
Linear control systems.
Stochastic models.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8887414
Hidden Bibliographic Details
Other authors / contributors:Jannerup, O. E.
Sørensen, Paul H. (Paul Haase)
ISBN:9783540784852 (acid-free paper)
3540784853 (acid-free paper)
9783540784869 (e-ISBN)
3540784861 (e-ISBN)
Notes:Includes bibliographical references (p. 547-548) and index.
Description based on print version record.
Other form:Print version: Hendricks, Elbert. Linear systems control. Berlin : Springer, c2008 3540784853 9783540784852
Standard no.:CIP08N090720
Table of Contents:
  • 1. Introduction
  • 1.1. The Invisible Thread
  • 1.2. Classical Control Systems and their Background
  • 1.2.1. Primitive Period Developments
  • 1.2.2. Pre-Classical Period Developments
  • 1.2.3. Classical Control Period
  • 1.2.4. Modern Control Theory
  • 2. State Space Modelling of Physical Systems
  • 2.1. Modelling of Physical Systems
  • 2.2. Linear System Models
  • 2.3. State Space Models from Transfer Functions
  • 2.3.1. Companion Form 1
  • 2.3.2. Companion Form 2
  • 2.4. Linearization
  • 2.5. Discrete Time Models
  • 2.6. Summary
  • 2.7. Problems
  • 3. Analysis of State Space Models
  • 3.1. Solution of the Linear State Equation
  • 3.1.1. The Time Varying System
  • 3.1.2. The Time Invariant System
  • 3.2. Transfer Functions from State Space Models
  • 3.2.1. Natural Modes
  • 3.3. Discrete Time Models of Continuous Systems
  • 3.4. Solution of the Discrete Time State Equation
  • 3.4.1. The Time Invariant Discrete Time System
  • 3.5. Discrete Time Transfer Functions
  • 3.6. Similarity Transformations
  • 3.7. Stability
  • 3.7.1. Stability Criteria for Linear Systems
  • 3.7.2. Time Invariant Systems
  • 3.7.3. BIBO Stability
  • 3.7.4. Internal and External Stability
  • 3.7.5. Lyapunov's Method
  • 3.8. Controllability and Observability
  • 3.8.1. Controllability (Continuous Time Systems)
  • 3.8.2. Controllability and Similarity Transformations
  • 3.8.3. Reachability (Continuous Time Systems)
  • 3.8.4. Controllability (Discrete Time Systems)
  • 3.8.5. Reachability (Discrete Time Systems)
  • 3.8.6. Observability (Continuous Time Systems)
  • 3.8.7. Observability and Similarity Transformations
  • 3.8.8. Observability (Discrete Time Systems)
  • 3.8.9. Duality
  • 3.8.10. Modal Decomposition
  • 3.8.11. Controllable/Reachable Subspace Decomposition
  • 3.8.12. Observable Subspace Decomposition
  • 3.9. Canonical Forms
  • 3.9.1. Controller Canonical Form
  • 3.9.2. Observer Canonical Form
  • 3.9.3. Duality for Canonical Forms
  • 3.9.4. Pole-zero Cancellation in SISO Systems
  • 3.10. Realizability
  • 3.10.1. Minimality
  • 3.11. Summary
  • 3.12. Notes
  • 3.12.1. Linear Systems Theory
  • 3.13. Problems
  • 4. Linear Control System Design
  • 4.1. Control System Design
  • 4.1.1. Controller Operating Modes
  • 4.2. Full State Feedback for Linear Systems
  • 4.3. State Feedback for SISO Systems
  • 4.3.1. Controller Design Based on the Controller Canonical Form
  • 4.3.2. Ackermann's Formula
  • 4.3.3. Conditions for Eigenvalue Assignment
  • 4.4. State Feedback for MIMO Systems
  • 4.4.1. Eigenstructure Assignment for MIMO Systems
  • 4.4.2. Dead Beat Regulators
  • 4.5. Integral Controllers
  • 4.6. Deterministic Observers and State Estimation
  • 4.6.1. Continuous Time Full Order Observers
  • 4.6.2. Discrete Time Full Order Observers
  • 4.7. Observer Design for SISO Systems
  • 4.7.1. Observer Design Based on the Observer Canonical Form
  • 4.7.2. Ackermann's Formula for the Observer
  • 4.7.3. Conditions for Eigenvalue Assignment
  • 4.8. Observer Design for MIMO Systems
  • 4.8.1. Eigenstructure Assignment for MIMO Observers
  • 4.8.2. Dead Beat Observers
  • 4.9. Reduced Order Observers
  • 4.10. State Feedback with Observers
  • 4.10.1. Combining Observers and State Feedback
  • 4.10.2. State Feedback with Integral Controller and Observer
  • 4.10.3. State Feedback with Reduced Order Observer
  • 4.11. Summary
  • 4.12. Notes
  • 4.12.1. Background for Observers
  • 4.13. Problems
  • 5. Optimal Control
  • 5.1. Introduction to Optimal Control
  • 5.2. The General Optimal Control Problem
  • 5.3. The Basis of Optimal Control - Calculus of Variations
  • 5.4. The Linear Quadratic Regulator
  • 5.4.1. The Quadratic Cost Function
  • 5.4.2. Linear Quadratic Control
  • 5.5. Steady State Linear Quadratic Regulator
  • 5.5.1. Robustness of LQR Control
  • 5.5.2. LQR Design: Eigenstructure Assignment Approach
  • 5.6. Discrete Time Optimal Control
  • 5.6.1. Discretization of the Performance Index
  • 5.6.2. Discrete Time State Feedback
  • 5.6.3. Steady State Discrete Optimal Control
  • 5.7. Summary
  • 5.8. Notes
  • 5.8.1. The Calculus of Variations
  • 5.9. Problems
  • 6. Noise in Dynamic Systems
  • 6.1. Introduction
  • 6.1.1. Random Variables
  • 6.2. Expectation (Average) Values of a Random Variable
  • 6.2.1. Average Value of Discrete Random Variables
  • 6.2.2. Characteristic Functions
  • 6.2.3. Joint Probability Distribution and Density Functions
  • 6.3. Random Processes
  • 6.3.1. Random Processes
  • 6.3.2. Moments of a Stochastic Process
  • 6.3.3. Stationary Processes
  • 6.3.4. Ergodic Processes
  • 6.3.5. Independent Increment Stochastic Processes
  • 6.4. Noise Propagation: Frequency and Time Domains
  • 6.4.1. Continuous Random Processes: Time Domain
  • 6.4.2. Continuous Random Processes: Frequency Domain
  • 6.4.3. Continuous Random Processes: Time Domain
  • 6.4.4. Inserting Noise into Simulation Systems
  • 6.4.5. Discrete Time Stochastic Processes
  • 6.4.6. Translating Continuous Noise into Discrete Time Systems
  • 6.4.7. Discrete Random Processes: Frequency Domain
  • 6.4.8. Discrete Random Processes: Running in Time
  • 6.5. Summary
  • 6.6. Notes
  • 6.6.1. The Normal Distribution
  • 6.6.2. The Wiener Process
  • 6.6.3. Stochastic Differential Equations
  • 6.7. Problems
  • 7. Optimal Observers: Kalman Filters
  • 7.1. Introduction
  • 7.2. Continuous Kalman Filter
  • 7.2.1. Block Diagram of a CKF
  • 7.3. Innovation Process
  • 7.4. Discrete Kalman Filter
  • 7.4.1. A Real Time Discrete Kalman Filter (Open Form)
  • 7.4.2. Block Diagram of an Open Form DKF
  • 7.4.3. Closed Form of a DKF
  • 7.4.4. Discrete and Continuous Kalman Filter Equivalence
  • 7.5. Stochastic Integral Quadratic Forms
  • 7.6. Separation Theorem
  • 7.6.1. Evaluation of the Continuous LQG Index
  • 7.6.2. Evaluation of the Discrete LQG Index
  • 7.7. Summary
  • 7.8. Notes
  • 7.8.1. Background for Kalman Filtering
  • 7.9. Problems
  • Appendix A. Static Optimization
  • A.1. Optimization Basics
  • A.1.1. Constrained Static Optimization
  • A.2. Problems
  • Appendix B. Linear Algebra
  • B.1. Matrix Basics
  • B.2. Eigenvalues and Eigenvectors
  • B.3. Partitioned Matrices
  • B.4. Quadratic Forms
  • B.5. Matrix Calculus
  • Appendix C. Continuous Riccati Equation
  • C.1. Estimator Riccati Equation
  • C.1.1. Time Axis Reversal
  • C.1.2. Using the LQR Solution
  • Appendix D. Discrete Time SISO Systems
  • D.1. Introduction
  • D.2. The Sampling Process
  • D.3. The Z-Transform
  • D.4. Inverse Z-Transform
  • D.5. Discrete Transfer Functions
  • D.6. Discrete Systems and Difference Equations
  • D.7. Discrete Time Systems with Zero-Order-Hold
  • D.8. Transient Response, Poles and Stability
  • D.9. Frequency Response
  • D.10. Discrete Approximations to Continuous Transfer Functions
  • D.10.1. Tustin Approximation
  • D.10.2. Matched-Pole-Zero Approximation (MPZ)
  • D.11. Discrete Equivalents to Continuous Controllers
  • D.11.1. Choice of Sampling Period
  • References
  • Index

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