The Digital Control of Systems: Applications to Vehicles and Robots

The Digital Control of Systems: Applications to Vehicles and Robots

by C. Fargeon

Paperback(Softcover reprint of the original 1st ed. 1989)

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Product Details

ISBN-13: 9781461568551
Publisher: Springer US
Publication date: 05/18/2012
Edition description: Softcover reprint of the original 1st ed. 1989
Pages: 450
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

One.- to Automatic Control.- 1. The Representation of Signals and Systems.- 1.1 Introduction.- 1.2 The Representation of Deterministic Signals.- 1.2.1 Notes on Continuous Signals.- 1.2.2 Notes on Discrete Signals.- 1.3 Representation of Deterministic Linear Systems.- 1.3.1 Representation of Systems in Continuous Form.- 1.3.2 Representation of Discrete Systems.- 1.4 Introduction of Aleatory Signals into Linear Systems.- 1.4.1 Continuous Random Signals.- 1.4.2 Discrete Random Signals.- 1.4.3 Approximation of a Continuous Random Signal by a Discrete Signal.- 1.5 Conclusion.- References.- 2. From Continuous to Discrete Control.- 2.1 Synthesis of Continuous Laws.- 2.1.1 Modal Methods.- 2.1.2 Linear Quadratic Optimal Methods.- 2.1.3 Control of Systems with Time Delays.- 2.2 Digitisation of Continuous Laws.- 2.2.1 Discrete Equivalent of a Continuous Controller.- 2.2.2 The Techniques of Digitisation.- 2.2.3 Analysis of the Closed Loop System.- 2.3 Conclusion.- References.- 3. Digital Controllers of Deterministic Systems The Polynomial Approach.- 3.1 Introduction.- 3.2 Controllers for a Minimum Time Criterion.- 3.2.1 Stabilising Controllers.- 3.2.2 Synthesis of Discrete Controllers Minimising the Response Time.- 3.2.3 Synthesis of Discrete Controllers Minimising a Quadratic Criterion.- 3.2.4 Synthesis of Controllers for Multivariable Systems.- 3.3 Pole Placement Controllers.- 3.3.1 Disturbance-free Servo Problem.- 3.3.2 Special Case in which the Controller Cancels all the Process Zeros (Minimum Phase System).- 3.4 Control Laws Based on the Minimisation of a One Step Quadratic Criterion.- 3.4.1 Optimal k-step-ahead Predictor.- 3.4.2 Minimum Variance Regulator.- 3.4.3 Generalised Minimum Variance Controller.- 3.4.4 Numerical Example.- 3.5 Conclusion.- References.- 4. Principles of Internal Model Control.- 4.1 Introduction and Definitions.- 4.2 Transferring from Conventional Regulation to Internal Model Control (C.M.I.).- 4.2.1 Principle.- 4.2.2 Properties.- 4.2.3 Choice of the Control Law: Calculation of D(z).- 4.2.4 Consequences.- 4.3 Principles of Internal Model Control.- 4.3.1 Internal Model.- 4.3.2 Reference Trajectory.- 4.3.3 Control Algorithm.- 4.3.4 Stability and Robustness.- 4.4 Example of Application in the Case of a System Described by its State Equations.- 4.4.1 Definition of the Control Problem.- 4.4.2 Control Strategy.- 4.4.3 Transfer Matrix of the Control System.- 4.4.4 Study of Convergence.- 4.4.5 Study of the Dynamic Performances.- 4.5 Conclusion.- References.- 5. Discrete Optimal Control of Linear Stochastic Systems.- 5.1 Introduction.- 5.2 Optimal Control by the Techniques of Polynomial Algebra.- 5.2.1 Single-input, Single-output Case.- 5.2.2 The Multivariable Case.- 5.2.3 Conclusion.- 5.3 The State Vector Modelling Approach.- 5.3.1 Notes on the Principal Results Obtained in Discrete Optimal Stochastic Control.- 5.3.2 Special Formulations.- 5.3.3 Example.- 5.4 Comparison of the Two Approaches.- 5.4.1 Rational Matrices.- 5.4.2 Polynomial Matrices.- 5.5 Conclusion.- References.- 6. Adaptive Control of Stochastic Systems.- 6.1 Introduction.- 6.2 Classification of Self-adaptive Control Systems.- 6.2.1 Self-adaptive Stochastic Optimal Control.- 6.2.2 Definition of the Concepts.- 6.2.3 Example.- 6.2.4 Classification of Controllers.- 6.3 Introduction to Self-tuning Controllers.- 6.4 Weighted Least Squares Estimation Algorithm.- 6.4.1 Ordinary Least Squares Estimation Algorithm.- 6.4.2 Recursive Weighted Least Squares Estimation Algorithm.- 6.5 Description of Self-tuning Controllers.- 6.5.1 Minimum Output Variance Control Strategy.- 6.5.2 Minimum Generalised Output Variance Control Strategy.- 6.5.3 Numerical Example.- 6.6 Conclusion.- References.- 7. Brief Description of Algebraic and Geometrical Methods for Non-linear Control.- 7.1 Introduction.- 7.2 State Space in Continuous Time.- 7.2.1 On the Concept of Vector Fields.- 7.2.2 Lie Brackets.- 7.2.3 Controllability.- 7.3 Generating Series.- 7.3.1 Bilinear Systems in Discrete Time.- 7.3.2 Bilinear Systems in Continuous Time.- 7.3.3 Implementation.- 7.4 Further Information.- 7.5 Brief References.- Two: Applications of Digital Control to Vehicles and Robots.- 8. Digital Control of Systems at the Limit of Stability: Application to the Stabilisation of Satellite.- 8.1 Introduction.- 8.2 Stabilisation of Satellites in Rotation.- 8.2.1 Outline of the Problem.- 8.2.2 Short-term Control.- 8.2.3 Long-term Control.- 8.3 Three-Axis Stabilisation of a Satellite with Flexible Appendages.- 8.3.1 Outline of the Problem.- 8.3.2 Dynamic Model of the Satellite.- 8.3.3 Roll and Yaw Axes.- 8.3.4 Pitch Axis.- References.- 9. Digital Control System of a Launch Vehicle.- 9.1 Introduction.- 9.2 Modelling the System.- 9.2.1 Notation.- 9.2.2 Hypotheses.- 9.2.3 Equations.- 9.2.4 State Representation.- 9.3 Choice of the Criterion and of the Covariance Matrices.- 9.3.1 Optimisation Criterion.- 9.3.2 Covariance Matrix.- 9.3.3 Choice of Parameters.- 9.4 Determination of the Controller — Application.- 9.4.1 Control Gains.- 9.4.2 Kaiman Gains.- 9.4.3 Application.- 9.5 Comments.- 9.6 Conclusion.- References.- 10. Reduction of Disturbances: Application to Passenger Comfort on Aircraft.- 10.1 Introduction.- 10.2 Principle of Turbulence Absorption for the Improvement of Passenger Comfort.- 10.3 Model of a Rigid Aircraft in a Turbulent Atmosphere.- 10.4. Determination of the Control Laws.- 10.5 Control Structures.- 10.6 Digital Implementation of the Controller.- 10.7 Example of Application — Conclusion.- References.- 11. Application of Internal Model Control to the Automatic Steering of a Ship.- 11.1 Introduction.- 11.2 General Description.- 11.3 Description of the Pact System.- 11.3.1 Functional Characteristics of Pact.- 11.3.2 Performance.- 11.3.3 Developments and Prospects.- References.- 12. Control by Reference Model: Application to Decoupling and Manoeuvrability in a Helicopter.- 12.1 Introduction.- 12.2 General Description of the Helicopter.- 12.3 Principle of Determination of the Control Law.- 12.3.1 General Theory.- 12.3.2 Parameter Optimisation.- 12.4 Choice of the Reference Model.- 12.4.1 Manoeuvrability Standard.- 12.4.2 Design of the Reference Model.- 12.5 Adjustment of the Control Law.- 12.5.1 Blocks Ku, T, F, S.- 12.5.2 Block Km.- 12.5.3 Block K.- 12.5.4 Block C.- 12.5.5 Block Ku.- 12.6 Results.- 12.6.1 Frequency Results.- 12.6.2 Time Results.- 12.7 Conclusion.- References.- 13. Adaptive Control Applied to the Reduction of Vibrations in Helicopters.- 13.1 Introduction.- 13.2 Helicopter Model.- 13.3 Optimal Controller Synthesis.- 13.4 Estimation of the Parameters of the Matrix S.- 13.4.1 First Case: With Constant Parameters.- 13.4.2 Second Case: With Variable Parameters.- 13.5 Experimental Results.- 13.5.1 Constant Speed Configuration.- 13.5.2 Variable Speed Configuration.- 13.6 Conclusion.- References.- 14. Minimisation of the Operating Cost of an Aircraft Flight by Optimisation of the Trajectory.- 14.1 Introduction.- 14.2 Criterion and Mathematical Model.- 14.2.1 Criterion.- 14.2.2 Dynamic Model.- 14.2.3 Constraints.- 14.3 Choice of the Optimisation Method.- 14.3.1 Sequential Procedure.- 14.3.2 Parallel Procedure.- 14.4 Method of Forced Singular Perturbations.- 14.5 Application to the Present Problem.- 14.5.1 Reduced Solution (Cruising Phase).- 14.5.2 Solution for the First Initial Layer.- 14.5.3 Solution in the Second Layer.- 14.5.4 Synthesis of the Overall Trajectory.- 14.6 Conclusion.- References.- 15. Interception in Minimum Time with Specified Final Conditions.- 15.1 Description of the Problem.- 15.2 Optimality Equations.- 15.3 Determination of the Optimal Control.- 15.4 Determination of the End Point.- 15.5 Conclusion.- 16. Robot Control Techniques.- 16.1 General.- 16.1.1 General Notes.- 16.1.2 Principal Functions to be Performed.- 16.2 Use of Kinematic and Geometrical Models.- 16.2.1 Generation of Movements in the Configuration Space.- 16.2.2 Generation of Movements in the Operation Space.- 16.3 Use of Models of the Dynamics.- 16.3.1 Theoretical Controllers.- 16.3.2 Dynamic Control Approaches in the Operation Space.- 16.3.3 Conclusion on Dynamic Control.- 16.4 Controllers Driven by Sensors.- 16.4.1 Proximity Measurement Feedback.- 16.4.2 Force Feedback.- 16.4.3 Hybrid Control.- 16.5 Conclusion.- References.- A.1 Polynomial Matrices.- A.1.1 Basic Definitions Concerning the Matrices.- A.1.2 Principal Transformations.- A.1.3 Divisibility.- A.1.4 Applications.- A.2 Problems of Inverses.- A.2.1 Generalised Inverse.- A.2.2 Inverses of Polynomial Matrices.- A.2.3 The Equation M.D = Y.- A.3 Spectral Factorisation.

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