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Techniques of Model-Based Control

Book Description

The state-of-the-art publication in model-based process control—by leading experts in the field.

In Techniques of Model-Based Control, two leading experts bring together powerful advances in model-based control for chemical-process engineering. Coleman Brosilow and Babu Joseph focus on practical approaches designed to solve real-world problems, and they offer extensive examples and exercises.

Coverage includes:

  • The nature of the process-control problem and how model-based solutions help to solve it

  • Continuous time modeling: time domain, Laplace domain, and FOPDT models

  • Feedforward, cascade, override, and single-variable inferential control approaches

  • One and two degree of freedom Internal Model Control

  • Model State Feedback and PI/PID Implementations of IMC

  • Tuning and synthesis of 1DF and 2DF IMC for process uncertainty

  • Estimation and inferential control using multiple secondary measurements

  • Basic and advanced techniques of model identification and model-predictive control

The appendices review the basics of Laplace transforms, feedback control, frequency response analysis, probability, random variables, and linear least-square regression.

From start to finish, Techniques of Model-Based Control offers the real-world insight that professionals need to identify and implement the best control strategies for virtually any process.

Table of Contents

  1. Copyright
    1. Dedication
  2. Prentice Hall International Series in the Physical and Chemical Engineering Sciences
  3. Preface
  4. Acknowledgements
  5. 1. Introduction
    1. 1.1. Nature of the Process Control Problem
    2. 1.2. Overview of Model-Based Control
    3. 1.3. Summary
      1. Problems
      2. References
        1. Bibliography
  6. 2. Continuous-Time Models
    1. 2.1. Introduction
    2. 2.2. Process Model Representations
    3. 2.3. Time Domain Models
    4. 2.4. Laplace Domain Models
    5. 2.5. The First-Order Plus Dead Time Process
    6. 2.6. Summary
      1. Problems
      2. References
        1. Bibliography
  7. 3. One-Degree of Freedom Internal Model Control
    1. 3.1. Introduction
    2. 3.2. Properties of IMC
      1. 3.2.1. Transfer Functions
      2. 3.2.2. No Offset Property of IMC
    3. 3.3. IMC Designs for No Disturbance Lag
    4. 3.4. Design for Processes with No Zeros Near the Imaginary Axis or in the Right Half of the s-Plane
    5. 3.5. Design for Processes with Zeros Near the Imaginary Axis
    6. 3.6. Design for Processes with Right Half Plane Zeros
    7. 3.7. Problems with Mathematically Optimal Controllers
    8. 3.8. Modifying the Process to Improve Control System Performance
    9. 3.9. Software Tools for IMC Design
    10. 3.10. Summary
      1. Problems
      2. References
        1. Bibliography
  8. 4. Two-Degree of Freedom Internal Model Control
    1. 4.1. Introduction
    2. 4.2. Structure of 2DF IMC
    3. 4.3. Design for Stable Processes
      1. 4.3.1. Design of the Setpoint Filter, q(s,εr)
      2. 4.3.2. Design of the Feedback Controller, qqd(s,ε)
    4. 4.4. Design for Unstable Processes
      1. 4.4.1. Internal Stability
      2. 4.4.2. Single-loop Implementation of IMC for Unstable Processes
    5. 4.5. Software Tools for 2DF IMC Designs
    6. 4.6. Summary
      1. Problems
      2. References
        1. Bibliography
  9. 5. Model State Feedback Implementations of IMC
    1. 5.1. Motivation
    2. 5.2. MSF Implementations of 1DF IMC
      1. 5.2.1. MSF for Models of the Form of Eq. (5.4)
      2. 5.2.2. MSF for Models with Transcendental Numerators
    3. 5.3. SIMULINK Realizations of MSF Implementations of IMC
      1. 5.3.1. Overview
      2. 5.3.2. Model Realization
      3. 5.3.3. Computing MSF Gains
      4. 5.3.4. State Feedback Realizations
    4. 5.4. Finding a Safe Lower Bound on the MSF Filter Time Constant
    5. 5.5. MSF Implementations of 2DF IMC
    6. 5.6. Summary
      1. Problems
      2. References
        1. Bibliography
  10. 6. PI and PID Parameters from IMC Designs
    1. 6.1. Introduction
    2. 6.2. The PID Controller
    3. 6.3. 1DF PID Parameters from 1DF IMC
      1. 6.3.1. 1DF PID Parameters for General Process Models
      2. 6.3.2. 1DF PID Parameters for a First-Order Lag Plus Dead time Model
      3. 6.3.3. Derivation of the 1DF PID Parameters of Eq. (6.14) for a First-Order Lag Plus Dead time Model
    4. 6.4. Algorithms and Software for Computing PID Parameters
    5. 6.5. Accommodating Negative Integral and Derivative Time Constants
    6. 6.6. 2DF PID Parameters from 2DF IMC
    7. 6.7. Saturation Compensation
    8. 6.8. Summary
      1. Problems
      2. References
        1. Bibliography
  11. 7. Tuning and Synthesis of 1DF IMC for Uncertain Processes
    1. 7.1. Introduction
    2. 7.2. Process Uncertainty Descriptions
      1. 7.2.1. Parametric Uncertainty
      2. 7.2.2. Frequency Domain Uncertainty Bounds
    3. 7.3. Mp Tuning
      1. 7.3.1. The Problem Statement
      2. 7.3.2. The IMCTUNE Algorithm for Solving the Mp Tuning Problem
      3. 7.3.3. Interpretation of the Results of Mp Tuning
      4. 7.3.4. Use of Multiple Uncertainty Regions to Account for Uncertain Uncertainty
      5. 7.3.4. The Inverse Tuning Problem
    4. 7.4. Conditions for the Existence of Solutions to the Mp Tuning Problem
      1. 7.4.1. Statement of the Nyquist Stability Criterion
      2. 7.4.2. Integral Controllability
      3. 7.4.3. Necessary and Sufficient Conditions for the Existence of a Solution to the Mp Tuning Problem for Any Mp Specification Greater than One
      4. 7.4.4. Justification for the Choice of Complementary Sensitivity Function in Mp Tuning
    5. 7.5. Robust Stability
      1. 7.5.1. A Frequency Domain Robust Stability Theorem for Infinite Dimensional Systems
      2. 7.5.2. A Heuristic Proof of the Robust Stability Theorem for Inherently Stable Processes
    6. 7.6. MP Synthesis
    7. 7.7. Software for Mp Tuning and Synthesis
    8. 7.8. Summary
      1. Problems
      2. References
        1. Bibliography
  12. 8. Tuning and Synthesis of 2DF IMC for Uncertain Processes
    1. 8.1. Introduction
    2. 8.2. Mp Tuning for Stable, Overdamped Uncertain Processes
      1. 8.2.1. Tuning the Feedback Loop via the Partial Sensitivity Function
    3. 8.3. Mp Synthesis for Stable, Overdamped Processes
    4. 8.4. Tuning for Underdamped and Unstable Processes
      1. 8.4.1. Introduction
      2. 8.4.2. Underdamped Stable Processes
      3. 8.4.3. Unstable Processes
    5. 8.5. Mp Synthesis for Underdamped and Unstable Processes
      1. 8.5.1. Introduction
    6. 8.6. Summary
      1. Problems
      2. References
        1. Bibliography
  13. 9. Feedforward Control
    1. 9.1. Introduction
    2. 9.2. Controller Design when Perfect Compensation is Possible
    3. 9.3. Controller Design when Perfect Compensation Is Not Possible
    4. 9.4. Controller Design for Uncertain Processes
      1. 9.4.1. Gain Variations
      2. 9.4.2. Dead time Variations
    5. 9.5. Summary
      1. Problems
      2. References
        1. Bibliography
  14. 10. Cascade Control
    1. 10.1. Introduction
    2. 10.2. Cascade Structures and Controller Designs
    3. 10.3. Saturation Compensation
      1. 10.3.1. IMC Cascade
      2. 10.3.2. IMC/PID Cascade
      3. 10.3.3. PID Cascade
    4. 10.4. Summary
      1. Problems
      2. References
        1. Bibliography
  15. 11. Output Constraint Control (Override Control)
    1. 11.1. Introduction
    2. 11.2. Override and Cascade Constraint Control Structures
    3. 11.3. Cascade Constraint Control
    4. 11.4. Summary
      1. Problems
      2. References
        1. Bibliography
  16. 12. Single Variable Inferential Control (IC)
    1. 12.1. Introduction
    2. 12.2. Classical Control Strategies
      1. 12.2.1. Feedback Control of Secondary Variable
      2. 12.2.2. Cascade Control on the Secondary Variable
      3. 12.2.3. Feedforward Control
      4. 12.2.4. Feedback Control Using an Output Estimator for y
    3. 12.3. Inferential Control
      1. 12.3.1. Structure
      2. 12.3.2. Design of the Inferential Controller for Perfect Models
      3. 12.3.3. Combining Inferential and Feedback Control
      4. 12.3.4. Design of the Inferential Controller for Uncertain Processes
    4. 12.4. Summary
      1. Problems
      2. References
        1. Bibliography
  17. 13. Inferential Estimation Using Multiple Measurements
    1. 13.1. Introduction and Motivation
    2. 13.2. Derivation of the Steady-State Estimator
      1. 13.2.1. Noise in Measurements
    3. 13.3. Selection of Secondary Measurements
      1. 13.3.1. Effect of Measurement Selection on Accuracy of Estimators
      2. 13.3.2. Robustness of Estimators
    4. 13.4. Adding Dynamic Compensation to the Estimators
      1. 13.4.2. Design of Suboptimal Compensators
    5. 13.5. Optimal Estimation
      1. 13.5.1. Application of the Kalman Filter to Inferential Estimation Problem
      2. 13.5.2. Difficulties with the Kalman Filter
    6. 13.6. Summary
      1. Problems
      2. References
        1. Bibliography
  18. 14. Discrete-Time Models
    1. 14.1. The Z-Transform Representation
    2. 14.2. Models of Computer-Controlled Systems
    3. 14.3. Discrete-Time FIR Models
    4. 14.4. Discrete-Time FSR Models
    5. 14.5. Summary
      1. Problems
      2. References
        1. Bibliography
  19. 15. Identification: Basic Concepts
    1. 15.1. Introduction
    2. 15.2. Least-Squares Estimation of Parameters
      1. 15.2.1. Formulation of the General SISO Identification Problem (Known Time Delay Case)
      2. 15.2.2. Determining the Time Delay
      3. 15.2.3. Recovering Continuous-Time Models from Discrete-Time Models
    3. 15.3. Properties of the Least-Squares Estimator
      1. 15.3.1. Existence of the Parameters
      2. 15.3.2. Accuracy of Model
      3. 15.3.3. Accuracy of Parameters
    4. 15.4. General Procedure for Process Identification
    5. 15.5. Summary
      1. Problems
      2. References
        1. Bibliography
  20. 16. Identification: Advanced Concepts
    1. 16.1. Design of Input Signals: PRBS Signals
      1. 16.1.1. Clock Tick Versus Sample Time
      2. 16.1.2. Choice of Amplitude, a
      3. 16.1.3. Duration of the Test
    2. 16.2. Noise Prefiltering
      1. 16.2.1. Prefiltering Using Noise Models
    3. 16.3. Modifications to the Basic Least-Squares Identification
    4. 16.4. Multiple Input, Multiple Output (MIMO) Systems
    5. 16.5. A Comprehensive Example
    6. 16.6. Effect of Prefilter on Parameter Estimates
    7. 16.7. Software for Identification
    8. 16.8. Summary
      1. Problems
      2. References
        1. Bibliography
  21. 17. Basic Model-Predictive Control
    1. 17.1. Introduction
    2. 17.2. SISO MPC
      1. 17.2.1. Dynamic Matrix Model
      2. 17.2.2. Description of the Algorithm
      3. 17.2.2. Tuning Parameters
      4. 17.2.3. Discussion
      5. 17.2.4. Feedforward MPC
    3. 17.3. Unconstrained Multivariable Systems
      1. 17.3.1. Development of the Algorithm for MIMO Case
      2. 17.3.2. Tuning
    4. 17.4. State-Space Formulation of Unconstrained SOMPC
      1. 17.4.1. Step Response Model
      2. 17.4.2. Prediction
      3. 17.4.3. Control Law
      4. 17.4.4. Observer Equation
      5. 17.4.5. Observer-Error Equation
      6. 17.4.6. Observer-Controller Closed-Loop Equation
    5. 17.5. Summary
      1. Problems
      2. References
        1. Bibliography
  22. 18. Advanced Model-Predictive Control
    1. 18.1. Incorporating Constraints
      1. 18.1.1. Constraint Types
        1. 18.1.1.1. Manipulated Variable Constraints
        2. 18.1.1.2. Constraints on Output Variables
        3. 18.1.1.3. Constraints on Associated Process Outputs
      2. 18.1.2. Effect of Input Constraints on Steady-State Regulation
      3. 18.1.3. Formulation of the Constrained MPC Algorithm
        1. 18.1.3.1. Constraint Softening
      4. 18.1.4. Stability of the Constrained MPC Algorithm
      5. 18.1.5. Discussion
    2. 18.2. Incorporating Economic Objectives: The LP-MPC Algorithm
      1. 18.2.1. General Formulation of the QP-MPC (LP-MPC) Algorithm
      2. 18.2.2. Discussion
    3. 18.3. Extension to Nonlinear Systems
      1. 18.3.1. The Two-phase MPC (TP-MPC) Algorithm
      2. 18.3.2. Discussion
    4. 18.4. Extension to Batch Processes
      1. 18.4.1. The Shrinking Horizon MPC (SH-MPC) Algorithm
      2. 18.4.2. Discussion
    5. 18.5. Summary
      1. Problems
      2. References
        1. Bibliography
  23. 19. Inferential Model-Predictive Control
    1. 19.1. Inferential Model-Predictive Control (IMPC)
      1. 19.1.1. Derivation of the Inferential MPC Algorithm
    2. 19.2. Simple Regression Estimators
      1. 19.2.1. Scaling
    3. 19.3. Data-Driven Dynamic Estimators
    4. 19.4. Nonlinear Data-Driven Estimators
      1. 19.3.1. Discussion
    5. 19.5. Summary
      1. Problems
      2. References
        1. Bibliography
  24. A. Review of Basic Concepts
    1. A.1. Block Diagrams
    2. A.2. Laplace Transform and Transfer Functions
      1. A.2.1. Common Transfer Functions
    3. A.3. P, PI, and PID Controller Transfer Functions
    4. A.4. Stability of Systems
    5. A.5. Stability of Closed-Loop Systems
    6. A.6. Controller Tuning
      1. A.6.1. Tuning Correlations
      2. A.6.2. Tuning of Integrating Processes
    7. A.7. Regulatory Issues Introduced by Constraints
      1. A.7.1. Scaling and Nondimensionalization of Process Variables
      2. A.7.2. Steady-State Suppression of Disturbances for SISO Systems
    8. Problems
    9. References
      1. Bibliography
  25. B. Review of Frequency Response Analysis
    1. B.1. Introduction
    2. B.2. Frequency Response from Transfer Functions
    3. B.3 . Disturbance Suppression in SISO Systems: Effect of Constraints
    4. B.4. Stability in the Frequency Domain
    5. B.5. Closed-Loop Frequency Response Characteristics
    6. Problems
    7. References
      1. Bibliography
  26. C. Review of Linear Least-Squares Regression
    1. C.1. Derivation of the Linear Least-Squares Estimate
    2. C.2. Properties of the Linear Least-Squares Estimate
    3. C.3. Measures of Model Fit
    4. C.4. Weighted Least-Squares
    5. C.5. Robustness
    6. C.6. Principal Component Regression
    7. Problems
    8. References
      1. Bibliography
  27. D. Review of Random Variables and Random Processes
    1. D.1. Introduction to Random Variables
      1. D.1.1. The Normal Distribution
      2. D.1.2. Sampling from a Population
    2. D.2. Random Processes and White Noise
    3. D.3. Spectral Decomposition of Random Processes
    4. D.4. Multidimensional Random Variables
  28. E. MATLAB and Control Toolbox Tutorial
    1. E.1. MATLAB Resources
    2. E.2. Basic Commands
      1. E.2.1. Creating Matrices
      2. E.2.2. Manipulating Matrices
      3. E.2.3. Creating Matrices
      4. E.2.4. Operations on Matrix Elements
      5. E.2.5. Programming in MATLAB
      6. E.2.6. File Management, Search Paths
      7. E.2.7. Storing MATLAB Statements in a File: m-files
      8. E.2.8. Creating New Functions
      9. E.2.9. Graphics
      10. E.2.10. Demonstrations
      11. E.2.11. Numerical Analysis
      12. E.2.12. Solution of Ordinary Differential Equations
    3. E.3. Control System Toolbox Tutorial
      1. E.3.1. Entering a System Transfer Function Model
      2. E.3.2. Conversion to Other Representations
      3. E.3.3. Analysis of Control Systems
      4. E.3.4. Block Diagram Analysis
      5. E.3.5. Root Locus Analysis
      6. E.3.6. Phase and Gain Margins
      7. E.3.7. Approximating Time Delays
      8. E.3.8. Discrete System Modeling
      9. E.3.9. Analysis of Discrete Systems
      10. E.3.10. Multivariable System Modeling
      11. E.3.11. Parallel Connections
      12. E.3.12. Closed-Loop Systems
    4. Problems
  29. F. SIMULINK Tutorial
    1. F.1. Basics
    2. F.2. Creating a Block Diagram in SIMULINK
    3. F.3. Laplace Transform Models
    4. F.4. Simulation of Discrete Systems Using SIMULINK
      1. F.4.1. Use of Discrete Transfer Functions
      2. F.4.2. Subsystems and Masks
    5. Problems
  30. G. Tutorial on IMCTUNE Software
    1. G.1. Introduction
    2. G.2. Getting Started on 1DF Systems
      1. G.2.1. Data Input
      2. G.2.2. Entering General Numerator and Denominator Polynomials for a Process or Model
        1. G.2.2.1. Expanded Form
        2. G.2.2.2. Factored Form
        3. G.2.1.3. Parallel Processes
        4. G.2.1.4. Uncertainty Bounds
        5. G.2.1.5. Entering the Model
        6. G.2.1.6. Controller
    3. G.3. Menu Bar for 1DF Systems
    4. G.4. Getting Started on 2DF Systems
      1. G.4.1. The Model
    5. G.5. Menu Bar for 2DF Systems
    6. G.6. Getting Started on Cascade Control Systems
    7. G.7. Menu Bar for Cascade Systems
    8. G.8. Other Useful .m Files Included with IMCTUNE
      1. G.8.1. TFN.m: Create Transfer Functions as Products of Polynomials Cascaded with a Deadtime
      2. G.8.2. TCF.m Time Constant Form
  31. H. Identification Software
    1. H.1. Introduction
    2. H.2. POLYID: Description
      1. H.2.1. System Requirements
      2. H.2.2. Input Requirements
      3. H.2.3. Subroutines Used
        1. Function est1
        2. Function estn
        3. Function id1
        4. Function polyid
        5. Function polyid1
        6. Function polyid11
        7. Function timest
    3. H.3. MODELBUILDER
    4. H.4. PIDTUNER
    5. Reference
      1. Bibliography
  32. I. Simulink Models for Projects
    1. I.1. Naphtha Cracker
      1. I.1.1. Process Description
      2. I.1.3. Control Objectives
      3. I.1.4. Control Constraints
      4. I.1.5. SIMULINK Model
      5. I.1.6. Suggested Project Work
    2. I.2. Shell Heavy Oil Fractionator
      1. I.2.1. Introduction
      2. I.2.2. Process Description
      3. I.2.3. Control Constraints
      4. I.2.4. Economic Objective
      5. I.2.5. Simulink Model
      6. I.2.6. Prototype Test Cases
      7. I.2.7. Suggested Project Assignments
    3. I.3. Temperature and Level Control in a Mixing Tank
      1. I.3.1. Process Description
      2. I.3.2. Suggestions for Projects
    4. I.4. Pressure and Level Control Experiment
      1. I.4.1. Process Description
      2. I.4.2. Suggested Projects
    5. I.5. Temperature and Level Control
      1. I.5.1. Process Description
      2. I.5.2. Suggested Projects
    6. I.6. Heat Exchanger
      1. I.6.1. Process Description
      2. I.6.2. Implementation
      3. I.6.3. Suggested Projects
    7. I.7. The Tennessee Eastman Project
      1. I.7.1. SIMULINK Model Description
      2. I.7.2. Suggested Project Work
    8. References
      1. Bibliography