Multivariable control systems - an engineering approach

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 Plan