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Multivariable Control Systems: An Engineering Approach / Edition 1

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Multivariable control techniques solve issues of complex specification and modelling errors elegantly but the complexity of the underlying mathematics is much higher than presented in traditional single-input, single-output control courses.

Multivariable Control Systems focuses on control design with continual references to the practical aspects of implementation. While the concepts of multivariable control are justified, the book emphasises the need to maintain student interest and motivation over exhaustively rigorous mathematical proof. Tools of analysis and representation are always developed as methods for achieving a final control system design and evaluation.


• design implementation clearly laid out using extensive reference to MATLAB®;

• combined consideration of systems (plant) and signals (mainly disturbances) in a fluent but simple presentation;

• step-by-step approach from the objectives of multivariable control to the solution of complete design problems.

Multivariable Control Systems is an ideal text for masters students, students beginning their Ph.D. or for final-year undergraduates looking for more depth than provided by introductory textbooks. It will also interest the control engineer practising in industry and seeking to implement robust or multivariable control solutions to plant problems in as straightforward a manner as possible.

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Editorial Reviews

From the Publisher
This book is well written and suitable for teaching courses. I was pleased to find that the book devoted so much attention to applications. Many industrial applications are given, which can help teachers to prepare practical works and are equally valuable to students and practising engineers. In particular, there are many case studies implemented with MATLAB.

Automatica 41 (2005) 1665 – 1666 (Reviewer: Mohammed Chadli)

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Product Details

Meet the Author

Pedro Albertos is Professor of Automatic Control (1977-), at the Department of Systems Engineering, Computers, and Control, Universidad Politecnica Valencia, (UPV), Spain, giving courses on Advanced and Intelligent Control Systems, and Systems Theory. This school is very well thought of in the control community. From 1999-2002 he was IFAC President, organising the IFAC World Congress in Spain, 2002. President of the Spanish automatic control association CEA-IFAC, he is promoting a stronger industry collaboration, planning regular meetings-seminars for the various working groups. His contribution will significantly enhance the prestige of Advanced Textbooks in Control and Signal Processing. In tems of level of content, Multivariable Control Systems will sit neatly between the simple one-module course and general compendium textbooks of basic undergraduate control courses and the maths-heavy titles available to senior masters and Ph.D. students. As such it will introduce specialist ideas without demanding excessive mathematical rigour to follow the text. This will make it very suitable for final-year undergraduates needing more coverage than a basic textbook and beginning postgraduates who are not yet in a position to benefit from more advanced mathematics. Professor Albertos and Doctor Sala were the editors of a volume of collected papers entitled: Iterative Identification and Control

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Table of Contents

1 Introduction to Multivariable Control
1.1 Introduction
1.2 Process and Instrumentation
1.3 Process Variables
1.4 The Process Behaviour
1.5 Control Aims
1.6 Modes of Operation
1.7 The Need for Feedback
1.8 Model-free vs. Model-based Control
1.9 The Importance of Considering Modelling Errors
1.10 Multivariable Systems
1.11 Implementation and Structural Issues
1.12 Summary of the Chapters
2 Linear System Representation: Models and Equivalence
2.1 Introduction: Objectives of Modelling
2.2 Types of Models.
2.3 First-principle Models: Components
2.4 Internal Representation: State Variables
2.5 Linear Models and Linearisation
2.6 Input/Output Representations
2.6.1 Polynomial Representation
2.6.2 Transfer Matrix
2.7 Systems and Subsystems: Interconnection
2.7.1 Series, Parallel and Feedback Connection
2.7.2 Generalised Interconnection
2.8 Discretised Models.
2.9 Equivalence of Representations
2.10 Disturbance Models
2.10.1 Deterministic Signals
2.10.2 Randomness in the Signals
2.10.3 Discrete Shastic Processes
2.11 Key Issues in Modelling
2.12 Case Study: The Paper Machine Headbox
2.12.1 Simpli.ed Models
2.12.2 Elaborated Models
3 Linear Systems Analysis
3.1 Introduction
3.2 Linear System Time-response
3.3 Stability Conditions
3.3.1 Relative Degree of Stability
3.4 Discretisation
3.5 Gain
3.5.1 Static Gain
3.5.2 Instantaneous Gain
3.5.3 Directional Gain
3.6 Frequency response
3.7 System Internal Structure
3.7.1 Reachability (State Controllability)
3.7.2 Observability
3.7.3 Output Reachability
3.7.4 Remarks on Reachability and Observability
3.7.5 Canonical Forms
3.8 Block System Structure (Kalman Form)
3.8.1 Minimal Realisation
3.8.2 Balanced Realisation.
3.8.3 Poles and Zeros
3.9 Input/Output Properties
3.9.1 Input/Output Controllability
3.10 Model Reduction
3.10.1 Time Scale Decomposition
3.10.2 Balanced Reduction
3.11 Key Issues in MIMO Systems Analysis
3.12 Case Study: Simple Distillation Column
4 Solutions to the Control Problem
4.1 The Control Design Problem
4.2 Control Goals
4.3 Variables Selection
4.4 Control Structures
4.5 Feedback Control
4.5.1 Closed-loop Stability Analysis
4.5.2 Interactions
4.5.3 Generalised Plant
4.5.4 Performance Analysis
Contents xv
4.6 Feedforward Control
4.6.1 Manual Control
4.6.2 Open-loop Inversion and Trajectory Tracking
4.6.3 Feedforward Rejection of Measurable Disturbances
4.7 Two Degree of Freedom Controller
4.8 Hierarchical Control
4.9 Key Issues in Control Design.
4.10 Case Study: Ceramic Kiln
5 Decentralised and Decoupled Control
5.1 Introduction
5.1.1 Plant Decomposition, Grouping of Variables
5.2 Multi-loop Control, Pairing Selection
5.2.1 The Relative Gain Array Methodology
5.2.2 Integrity (Fault Tolerance)
5.2.3 Diagonal Dominance (Stability Analysis)
5.3 Decoupling
5.3.1 Feedforward Decoupling
5.3.2 Feedback Decoupling
5.3.3 SVD Decoupling
5.4 Enhancing SISO Loops with MIMO Techniques: Cascade Control
5.4.1 Case I: Extra Measurements
5.4.2 Case II: Extra Actuators
5.5 Other Possibilities
5.5.1 Indirect and Inferential Control
5.5.2 Override, Selectors
5.5.3 Split-range Control
5.5.4 Gradual Control, Local Feedback
5.6 Sequential-Hierarchical Design and Tuning
5.6.1 Combined Strategies for Complex Plants
5.7 Key Conclusions
5.8 Case Studies
5.8.1 Steam Boiler
5.8.2 Mixing Process
6 Fundamentals of Centralised Closed-loop Control
6.1 State Feedback
6.1.1 Stabilisation and Pole-placement
6.1.2 State Feedback PI Control
6.2 Output Feedback
6.2.1 Model-based Recurrent Observer
6.2.2 Current Observer
6.2.3 Reduced-order Observer
6.2.4 Separation Principle
6.3 Rejection of Deterministic Unmeasurable Disturbances
6.3.1 Augmented Plan

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