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. Features: • 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.
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)
Multivariable Control Systems will sell because it teaches a very important form of control without burdening the subject with an overdependence on heavy and complicated mathematics
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.Features: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.
This book focuses on control design with continual references to the practical aspects of implementation. While the concepts of multivariable control are justified, the book emphasizes the need to maintain student interest and motivation over exhaustively rigorous mathematical proof.
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
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 Stochastic 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 Plants: Process and Disturbance Models
6.3.2 Disturbance rejection
6.4 Summary and Key Issues
6.5 Case Study: Magnetic Suspension
7 Optimisation-based Control
7.1 Optimal State Feedback
7.1.1 Linear Regulators
7.2 Optimal Output Feedback
7.2.1 Kalman Observer
7.2.2 Linear Quadratic Gaussian Control
7.3 Predictive Control
7.3.1 Calculating Predictions
7.3.2 Objective Function
7.3.3 Constraints
7.3.4 Disturbance rejection
7.4 A Generalised Optimal Disturbance-rejection Problem
7.4.1 Design Guidelines: Frequency Weights
7.5 Summary and Key Issues
7.6 Case Study: Distillation Column.
8 Designing for Robustness
8.1 The Downside of Model-based Control
8.1.1 Sources of Uncertainty in Control
8.1.2 Objectives of Robust Control Methodologies
8.2 Uncertainty and Feedback
8.2.1 Model Validity Range
8.2.2 High Gain Limitations
8.3 Limitations in Achievable Performance due to Uncertainty
8.3.1 Amplitude and Frequency of Actuator Commands
8.3.2 Unstable and Non-minimum-phase Systems
8.4 Trade-offs and Design Guidelines
8.4.1 Selection of Design Parameters in Controller Synthesis
8.4.2 Iterative Identification and Control
8.4.3 Generalised 2-DoF Control Structure
8.5 Robustness Analysis Methodologies
8.5.1 Sources and Types of Uncertainty
8.5.2 Determination of Uncertainty Bounds
8.5.3 Unstructured Robust Stability Analysis
8.5.4 Structured Uncertainty
8.6 Controller Synthesis
8.6.1 Mixed Sensitivity
8.7 Conclusions and Key Issues
8.8 Case Studies
8.8.1 Cascade Control
8.8.2 Distillation Column
9 Implementation and Other Issues
9.1 Control Implementation: Centralised vs. Decentralised
9.2 Implementation Technologies.
9.2.1 Analog Implementation
9.2.2 Digital Implementation
9.2.3 User Interface
9.3 Bumpless Transfer and Anti-windup
9.4 Non-conventional Sampling
9.5 Coping with Non-linearity
9.5.1 Basic Techniques
9.5.2 Gain-scheduling
9.5.3 Global Linearisation
9.5.4 Other Approaches
9.6 Reliability and Fault Detection
9.7 Supervision, Integrated Automation, Plant-wide Control
A Summary of SISO System Analysis
A.1 Signals
A.2 Continuous Systems
A.2.1 System Analysis
A.2.2 Frequency response
A.3 Discrete Systems
A.3.1 System Analysis
A.4 Experimental Modelling
A.5 Tables of Transforms
B Matrices
B.1 Column, Row and Null Spaces
B.2 Matrix Inversion
B.3 Eigenvalues and Eigenvectors
B.4 Singular Values and Matrix Gains
B.4.1 Condition number
B.5 Matrix Exponential
B.6 Polynomial Fraction Matrices
C Signal and System Norms
C.1 Normed Spaces
C.2 Function Spaces
C.3 Signals and Systems Norms
C.3.1 Signal Norms
C.3.2 System Norms
C.4 BIBO Stability and the Small-gain Theorem
D Optimisation
D.1 Static Optimisation
D.2 Discrete Linear Quadratic Regulator
D.2.1 Multi-step Optimisation (Dynamic Programming)
D.2.2 Stationary Regulator
E Multivariable Statistics
E.1 Random Variables
E.1.1 Linear Operations with Random Variables
E.2 Multi-dimensional Random Variables
E.3 Linear Predictors (Regression)
E.4 Linear Systems
E.4.1 Simulation.
E.4.2 Prediction: The Kalman Filter
F Robust Control Analysis and Synthesis
F.1 Small-gain Stability Analysis
F.2 Structured Uncertainty
F.2.1 Robust Performance
F.3 Additional Design Techniques
F.3.1 Robust Stabilisation
F.3.2 McFarlane-Glover Loop Shaping
References
Index