Dynamic Modeling, Predictive Control and Performance Monitoring

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1 Biao Huang, Ramesh Kadali Dynamic Modeling, Predictive Control and Performance Monitoring A Data-driven Subspace Approach 4y Spri nnger g<

2 Contents Notation XIX 1 Introduction An Overview of This Book Main Features of This Book Organization of This Book 4 Part I Dynamic Modeling through Subspace Identification 2 System Identification: Conventional Approach Introduction Discrete-time Systems Finite Difference Models Exact Discretization for Linear Systems Backshift Operator and Discrete-time Transfer Functions An Example of System Identification: ARX Modeling Persistent Excitation in Input Signal Model Structures Prediction Error Model (PEM) AutoRegressive with Exogenous Input Model (ARX) AutoRegressive Moving Average with Exogenous Input Model (ARMAX) Box-Jenkins Model (BJ) Output Error Model (OE) MISO (Multi-input and Single-output) Prediction Error Model State Space Model Prediction Error Method Motivation Optimal Prediction Prediction Error Method 24

2.2 Exact Discretization for Linear Systems 10 2.2.3 Backshift Operator and Discrete-time Transfer Functions 11 2.3 An Example of System Identification: ARX Modeling 12 2.

3 XIV Contents 2.7 Closed-loop Identification Identifiability without External Excitations Direct Closed-loop Identification Indirect Closed-loop Identification Joint Input-output Closed-loop Identification Summary 29 3 Open-loop Subspace Identification Introduction Subspace Matrices Description State Space Models Notations and Subspace Equations Open-loop Subspace Identification Methods Regression Analysis Approach Projection Approach and N4SID Projections Non-steady-state Kaiman Filters Projection Approach for Subspace Identification QR Factorization and MOESP Statistical Approach and CVA CVA Approach Determination of System Order Instrument-variable Methods and EIV Subspace Identification Summary 53 4 Closed-loop Subspace Identification Introduction Review of Closed-loop Subspace Identification Methods N4SID Approach Joint Input-Output Approach ARX Prediction Approach An Innovation Estimation Approach An Orthogonal Projection Approach A Solution through Orthogonal Projection The Problem of Biased Estimation and the Solution Model Extraction through Kaiman Filter State Sequence Extension to Error-in-variable (EIV) Systems Simulation Summary 78 5 Identification of Dynamic Matrix and Noise Model Using Closed-loop Data Introduction Estimation of Process Dynamic Matrix and Noise Model Estimation of Dynamic Matrix of the Process Estimation of the Noise Model 85

3 Open-loop Subspace Identification Methods 40 3.4 Regression Analysis Approach 40 3.5 Projection Approach and N4SID 43 3.5.1 Projections 43 3.5.2 Non-steady-state Kaiman Filters 44 3.5.3 Projection Approach for Subspace Identification 46 3.

4 Contents XV 5.3 Some Guidelines for the Practical Implementation of the Algorithm Extension to the Case of Measured Disturbance Variables Closed-loop Simulations Univariate System Multivariate System Identification of the Dynamic Matrix: Pilot-scale Experimental Evaluation Summary 96 Part II Predictive Control 6 Model Predictive Control: Conventional Approach Introduction Understanding MPC Fundamentals of MPC Process and Disturbance Models Predictions Free and Forced Response Objective Function Constraints Control Law Dynamic Matrix Control (DMC) The Prediction Model Unconstrained DMC Design Penalizing the Control Action Handling Disturbances in DMC Multivariate Dynamic Matrix Control Hard Constrained DMC Economic Optimization Generalized Predictive Control (GPC) Summary Data-driven Subspace Approach to Predictive Control Introduction Predictive Controller Design from Subspace Matrices Inclusion of Integral Action Inclusion of Feedforward Control Constraint Handling Tuning the Noise Model Simulations Experiment on a Pilot-scale Process Summary 141

7 Summary 96 Part II Predictive Control 6 Model Predictive Control: Conventional Approach 101 6.1 Introduction 101 6.2 Understanding MPC 102 6.3 Fundamentals of MPC 103 6.3.1 Process and Disturbance Models 103 6.

5 XVI Contents Part III Control Performance Monitoring 8 Control Loop Performance Assessment: Conventional Approach Introduction SISO Feedback Control Performance Assessment MIMO Feedback Control Performance Assessment Summary State-of-the-art MPC Performance Monitoring Introduction MPC Performance Monitoring: Model-based Approach Minimum-variance Control Benchmark LQG/MPC Benchmark Model-based Simulation Approach Designed/Historical vs Achieved Historical Covariance Benchmark MPC Performance Monitoring through Model Validation MPC Performance Monitoring: Model-free Approach Impulse-Response Curvature Prediction-error Approach Markov Chain Approach MPC Economic Performance Assessment and Tuning Probabilistic Inference for Diagnosis of MPC Performance Bayesian Network for Diagnosis Decision Making in Performance Diagnosis Summary Subspace Approach to MIMO Feedback Control Performance Assessment Introduction Subspace Matrices and Their Estimation Revisit of Important Subspace Matrices Estimation of Subspace Matrices from Open-loop Data Estimation of MVC-benchmark from Input/Output Data Closed-loop Subspace Expression of Process Response under Feedback Control Estimation of MVC-benchmark Directly from Input/Output Data Simulations and Application Example Summary 193

2.2 LQG/MPC Benchmark 159 9.2.3 Model-based Simulation Approach 160 9.2.4 Designed/Historical vs Achieved 161 9.2.5 Historical Covariance Benchmark 161 9.2.6 MPC Performance Monitoring through Model Validation 162 9.

6 Contents XVII 11 Prediction Error Approach to Feedback Control Performance Assessment Introduction Prediction Error Approach to Feedback Control Performance Assessment Subspace Algorithm for Multi-step Optimal Prediction Errors Preliminary Calculation of Multi-step Optimal Prediction Errors Case Study Summary Performance Assessment with LQG-benchmark from Closed-loop Data Introduction Obtaining LQG-benchmark from Feedback Closed-loop Data Obtaining LQG-benchmark with Measured Disturbances Controller Performance Analysis Case 1: Feedback Controller Acting on the Process with Unmeasured Disturbances Case 2: Feedforward Plus Feedback Controller Acting on the Process Case 3: Feedback Controller Acting on the Process with Measured Disturbances Summary of the Subspace Approach to the Calculation of LQG-benchmark Simulations Application on a Pilot-scale Process Summary 227 References 229 Index 237

4 Summary 211 12 Performance Assessment with LQG-benchmark from Closed-loop Data 213 12.1 Introduction 213 12.2 Obtaining LQG-benchmark from Feedback Closed-loop Data... 214 12.

Univariate and Multivariate Methods PEARSON. Addison Wesley

Time Series Analysis Univariate and Multivariate Methods SECOND EDITION William W. S. Wei Department of Statistics The Fox School of Business and Management Temple University PEARSON Addison Wesley Boston