Contents Acknowledgments Preface 1 Introduction 1.1 What''s MPC? 1.2 Why MPC? 1.2.1 Economic Drivers of APC/MPC 1.2.2 Economic Advantages of MPC vs. Other Tools 1.
3 Historical Overview 1.3.1 Early Computer Control 1.3.2 The Pioneers 1.3.3 Adoption Growth 1.4 Impact of MPC on Control Research 1.
4.1 Early Theoretical Developments 1.4.2 State-Space Model Formulation and Stability Results 1.4.3 Other Theoretical Developments 1.4.4 Lessons Learned Along the MPC Journey 1.
5 A Typical Industrial Control Problem 1.6 Organization of This Book Exercises 2 Step Response Modeling and Identification 2.1 Linear Time Invariant Systems 2.2 Impulse / Step Response Models 2.2.1 Impulse Response Models 2.2.2 Step Response Models 2.
3 Multi-Step Prediction 2.3.1 Recursive Multi-Step Prediction Based on FIR Model 2.3.2 Recursive Multi-Step Prediction Based on Step-Response Model 2.3.3 Multivariable Generalization 2.4 Examples 2.
5 Identification 2.5.1 Settling Time 2.5.2 Sampling Time 2.5.3 Choice of the Input Signal for Experimental Identification 2.5.
4 The Linear Least Squares Problem 2.5.5 Linear Least Squares Identification Exercises 3 Dynamic Matrix Control - The Basic Algorithm 3.1 The Concept of Moving Horizon Control 3.2 Multi-Step Prediction 3.3 Objective Function 3.4 Constraints 3.4.
1 Manipulated Variable Constraints 3.4.2 Manipulated Variable Rate Constraints 3.4.3 Output Variable Constraints 3.4.4 Combined Constraints 3.5 Quadratic Programming Solution of the Control Problem 3.
5.1 Quadratic Programs 3.5.2 Formulation as a Quadratic Program 3.6 Implementation 3.6.1 Moving Horizon Algorithm 3.6.
2 DMC Examples 3.6.3 Efficient Solutions to the QP 3.6.4 Proper Constraint Formulation 3.6.5 Choice of Horizon Length 3.6.
6 Input Blocking 3.6.7 Filtering of the Feedback Signal 3.7 Examples: Analysis and Guidelines 3.7.1 Unconstrained SISO Systems 3.7.2 Constrained SISO Systems 3.
7.3 MIMO System with Strong Gain Directionality 3.7.4 Constrained MIMO Systems 3.7.5 Conclusions and General Tuning Guidelines 3.8 Case Study: Control of "Shell Heavy Oil Fractionator" using Dynamic Matrix Control 3.8.
1 Heavy Oil Fractionator: Background 3.8.2 Control Structure Description Exercises 4 Dynamic Matrix Control - Extensions and Variations 4.1 Features Found in Other Industrial Algorithms 4.1.1 Reference Trajectories 4.1.2 Coincidence Points 4.
1.3 The Funnel Approach 4.1.4 Use of Other Norms 4.1.5 Input Parameterization 4.1.6 Model Conditioning 4.
1.7 Prioritization of CVs and MVs 4.2 Connection with Internal Model Control 4.3 Some Possible Enhancements to DMC 4.3.1 Closed-Loop Update of Model State 4.3.2 Integrating Dynamics 4.
3.3 Noise Filter 4.3.4 Bi-Level Optimization 4.3.5 Product Property Estimation Exercises 5 Linear Time Invariant System Models 5.1 Sampling and Reconstruction 5.1.
1 Introduction to Digital Control 5.1.2 Sampling 5.1.3 Aliasing 5.1.4 Reconstruction 5.2 Introduction to z-transform 5.
3 Transfer Function Models 5.3.1 Continuous Time 5.3.2 Discrete Time 5.3.3 Transfer Matrix 5.3.
4 Converting Continuous Transfer Function to Discrete Transfer Function 5.3.5 Stability and Implications of Poles 5.3.6 Gain, Frequency Response 5.4 State-Space Model 5.4.1 Continuous Time 5.
4.2 Discrete Time 5.4.3 Converting Continuous- to Discrete-Time System 5.5 Conversion Between Discrete-Time Models 5.5.1 Representing State-Space System as Transfer Function 5.5.
2 Realization of Transfer Function as State-Space System 5.5.3 Impulse and Step Responses of State-Space System 5.5.4 Derivation of Transfer Matrix from Impulse Response 5.5.5 From Impulse / Step Response to State-Space Model Exercises 6 Discrete-Time State Space Models 6.1 State-Coordinate Transformation 6.
2 Stability 6.2.1 System Poles and Characteristic Equation 6.2.2 Stability 6.2.3 Lyapunov Equation 6.3 Controllability, Reachability, and Stabilizability 6.
3.1 Definitions 6.3.2 Conditions for Reachability 6.3.3 Coordinate Transformation 6.4 Observability, Reconstructability, and Detectability 6.4.
1 Definitions 6.4.2 Conditions for Observability 6.4.3 Coordinate Transformation 6.5 Kalman''s Decomposition and Minimal Realization 6.5.1 Kalman''s Decomposition 6.
5.2 Minimal Realization 6.6 Disturbance Modeling 6.6.1 Linear Stochastic System Model for Stationary Processes 6.6.2 Stochastic System Models for Processes with Nonstationary Behavior 6.6.
3 Models for Estimation and Control Exercises 7 State Estimation 7.1 Linear Estimator Structure 7.2 Observer Pole Placement 7.3 Kalman Filter 7.3.1 Derivation of the Optimal Filter Gain Matrix 7.3.2 Correlated Noise Case 7.
3.3 Stability of Kalman Filter 7.4 Extensions 7.4.1 Inferential Estimation 7.4.2 Non-stationary (Integrating) Noise 7.4.
3 Time-Varying System 7.4.4 Periodically Time-Varying System 7.4.5 Measurement Delays 7.5 Least Squares Formulation of State Estimation 7.5.1 Batch Least Squares Formulation 7.
5.2 Recursive Solution and Equivalence with Kalman Filter 7.5.3 Use of Moving Estimation Window Exercises 8 Unconstrained Quadratic Optimal Control 8.1 Linear State Feedback Controller Design 8.2 Finite Horizon Quadratic Optimal Control 8.2.1 OpenLoop Optimal Solution via Least Squares 8.
2.2 State Feedback Solution via Dynamic Programming 8.2.3 Comparison of the Two Approaches 8.3 Infinite Horizon Quadratic Optimal Control 8.3.1 Optimal State Feedback Law: Asymptotic Solution of the Finite Horizon Problem 8.3.
2 Receding Horizon Implementation of the Finite Horizon Solution 8.3.3 Equivalence Between Finite and Infinite Horizon Problems 8.4 Analysis 8.4.1 State Feedback Case 8.4.2 Output Feedback Case 8.
4.3 Setpoint Tracking and Disturbance Rejection 8.5 Stochastic LQ Control 8.5.1 Finite Horizon Problem 8.5.2 Output Feedback LQ Control Exercises 9 Constrained Quadratic Optimal Control 9.1 Finite Horizon Problem 9.
2 Infinite Horizon Problem 9.2.1 Options for Reformulation as an Equivalent FiniteHorizon Problem 9.2.2 Comparison of Various Options 9.3 Constraint Softening 9.4 Derivation of an Explicit Form of the Optimal Control Law via MultiParametric Programming 9.5 Analysis 9.
5.1 Stability Concepts and Lyapunov''s Direct Method 9.5.2 State Feedback Case 9.5.3 Output Feedback Case 9.6 Stochastic Case (*) Exercises 10 System Identification 10.1 Problem Overview 10.
2 Model Structures 10.2.1 Finite Impulse Response Model 10.2.2 Structures for Parametric Identification 10.2.3 Key Issues in Parametric Models 10.3 Parametric Identification Methods 10.
3.1 Prediction Error Method 10.3.2 Properties of Linear Least Squares Identification 10.3.3 Persistency of Excitation 10.3.4 FrequencyDomain Bias Distribution Under PEM 10.
3.5 Parameter Estimation via Statistical Methods ( ) 10.3.6 Other Methods ( ) 10.4 Nonparametric Identification 10.4.1 Impulse Response Identification 10.4.
2 Frequency Response Identification (*) 10.5 Subspace Identification 10.5.1 The Basic Method 10.5.2 Analysis and Discussion 10.6 Practice of System Identification: A User''s Perspective 10.6.
1 Experiment Design 10.6.2 PRBS Signals 10.6.3 Data PreProcessing 10.6.4 Model Fitting and Validation 10.6.
5 Model Quality Assessment and an Integrated Framework Exercises 11 Linear MPC: State Space Formulation 11.1 Motivation 11.2 Model Construction 11.2.1 Model Structure for StateSpace MPC 11.2.2 Stochastic System Model with Output Disturbance Only 11.2.
3 Stochastic System Model with State and Output Disturbances 11.2.4 Summary 11.3 Deterministic State Space MPC 11.3.1 State Regulation Problem 11.3.2 Constraints 11.
3.3 OffsetFree Output Tracking and Regulation Problem 11.4 MPC with State Estimation 11.4.1 State Estimation Using Kalman Filter 11.4.2 Control Calculation Using State Estimate 11.4.
3 MPC with Output Disturbance Only 11.4.4 MPC with State Disturbance Model 11.4.5 MPC with Full Disturbance Model 11.4.6 Tracking a Setpoint Trajectory 11.4.
7 Constraint Softening 11.5 Inferential Control 11.5.1 Problem Formulation 11.5.2 Infrequent Primary Measurements 11.5.3 Handling Measurement Delays in Primary Measurements 11.
6 Sequential LinearizationBased MPC (.