CBE32338

Chapter 1.0 Introduction to the Temperature Control Laboratory

1.1 The Temperature Control Laboratory

• 1.1.1 Hardware
• Markdown Links
  • Temperature Control Laboratory
  • TCLab
  • README
  • here
• Figure files used
  • figures/B.00-arduino_lab_kit.png

1.2 The TCLab Python Package

• 1.2.1 Connecting to the Temperature Control Laboratory
  • 1.2.1.1 Installation
  • 1.2.1.2 Importing
  • 1.2.1.3 Using TCLab with Python's with statement
• 1.2.2 Reading Temperatures
• 1.2.3 Setting Heaters
• 1.2.4 Synchronizing with Real Time using clock
  • 1.2.4.1 Using clock with TCLab
• 1.2.5 The TCLab Historian
• 1.2.6 The TCLab Plotter
• 1.2.7 Using TCLab Offline
• 1.2.8 Running Diagnostics
• Markdown Links
  • TCLab
  • TCLab-sketch
  • Arduino IDE
  • Pandas Data Analysis Library
• Figure files used
  • figures/B.00-TCLabOverview.png

1.11 TCLab Lab 1: Coding a relay controller

• 1.11.1 Procedures
• 1.11.2 Exercise 1. Download and install TCLab.py
• 1.11.3 Exercise 2. Verify that your hardware and software are working correctly.
• 1.11.4 Exercise 3. Turn on the heaters for 120 seconds and log temperature response.
• 1.11.5 Exercise 4. Code an on-off controller.
• 1.11.6 Exercise 5. Analysis
• Markdown Links
  • On-Off Control in Section 1.6 of Feedback Control for Scientists and Engineers
  • The TCLab Python Package
  • TCLab Relay Control
  • TCLab Python Package

Chapter 2.0 Model Identification

2.1 Step Testing

• 2.1.1 Executing the Step Test
  • 2.1.1.1 Conduct the Experiment
  • 2.1.1.2 Verify the Experimental Data
  • 2.1.1.3 Convert to a DataFrame
  • 2.1.1.4 Save DataFrame as a .csv file
  • 2.1.1.5 Verify the Data File

2.2 Fitting Step Test Data to Empirical Models

• 2.2.1 Read the Data File
• 2.2.2 Parameter Estimation
  • 2.2.2.1 Fitting the Step Change Data to a First Order Model
  • 2.2.2.2 Reading Saved Data
  • 2.2.2.3 Estimating Gain and Time Constant
• 2.2.3 First Order plus Dead Time
• 2.2.4 Second Order
• 2.2.5 Fitting a Second Order Model by Least Squares

2.3 First Order Model for a Single Heater

• 2.3.1 First-order lumped model for heater/sensor device.
  • 2.3.1.1 Steady State
• 2.3.2 Loading previously saved experimental data
  • 2.3.2.1 Deviation Variables
  • 2.3.2.2 First Order Linear Differential Equations
  • 2.3.2.3 Plotting the Analytical Solution
• 2.3.3 Matching the Model to Experimental Data
  • 2.3.3.1 Does this solution make sense?
• Markdown Figures
  • images/arduino_comsol.png
• Markdown Links
  • specific heat capacity for solids

2.4 Two-Input, Two-Output Model

• 2.4.1 Interacting Heaters
• 2.4.2 Deviation Variables
• 2.4.3 Steady State
• 2.4.4 Estimating $U_a$ and $U_b$
• 2.4.5 Simulation with odeint
• 2.4.6 Fitting the Model to Measured Step Response Data

2.5 Two State Model for a Single Heater

• 2.5.1 Dynamics of the Heater/Sensor System
• 2.5.2 Model in deviation variables
• 2.5.3 Consequences of this Model

2.6 Four State Model

• 2.6.1 Multivariable Heater/Sensor System
• 2.6.2 Deviation variables
• 2.6.3 State space

2.10 TCLab Lab 2: Model Identification

• 2.10.1 Procedures
• 2.10.2 Exercise 1. Verify operation of the temperature control lab.
• 2.10.3 Exercise 2. Check for steady state
• 2.10.4 Exercise 3. Step test.
• 2.10.5 Exercise 4. Verify and save data to a .csv file
• 2.10.6 Exercise 5. Analysis

2.10 TCLab Lab 2: Model Identification

• 2.10.1 Procedures
• 2.10.2 Exercise 1. Verify operation of the temperature control lab.
• 2.10.3 Exercise 2. Check for steady state
• 2.10.4 Exercise 3. Step test.
• 2.10.5 Exercise 4. Verify and save data to a .csv file
• 2.10.6 Exercise 5. Analysis

2.11 Model Identification: Fitting models to data

• 2.11.1 Initializations
  • 2.11.1.1 Reading data
  • 2.11.1.2 Plotting function
• 2.11.2 Empirical Models
  • 2.11.2.1 First-order linear model
  • 2.11.2.2 First-order linear model with time delay
• 2.11.3 First-principles modeling
  • 2.11.3.1 First-order energy balance for one heater
  • 2.11.3.2 Two State Model
• 2.11.4 Two heater, four state model
• 2.11.5 Consequences
• 2.11.6 State-Space Model
• 2.11.7 Putting to work

Chapter 3.0 State Estimation

3.1 Open and Closed Loop Estimation

• 3.1.1 Experiment 1. Open-Loop State Estimation and Relay Control
  • 3.1.1.1 Open Loop Estimation
  • 3.1.1.2 Event Loop
• 3.1.2 Experiment 2. Closed-Loop State Estimation and Relay Control
  • 3.1.2.1 Review of Closed Loop Estimation
  • 3.1.2.2 Choosing $L$
• 3.1.3 Question

Chapter 4.0 Feedback Control

4.1 Relay Control

• 4.1.1 Simple Relay Control
• 4.1.2 Relay Control with Hysteresis
• 4.1.3 Multivariable On-Off Control
• 4.1.4 Exercises

4.3 PID Control

• 4.3.1 PID Simulation
• 4.3.2 PID Implementation
• Markdown Links
  • Web version available

4.10 Lab Assignment: PID Control

• 4.10.1 Part 1. Manual Control
• 4.10.2 Part 2. Implementing a PID Controller
• 4.10.3 Part 3. Tuning the PID Controller

4.11 Lab Assignment 4: PI Control

• 4.11.1 Implementation of a simple PI controller
• 4.11.2 Exercise 1. Tune the PI control for the Temperature Control Lab
• 4.11.3 Exercise 2. Hardware testing the PI controller
• 4.11.4 Exercise 3. Multivariable PI control

Chapter 5.0 Predictive Control and Real Time Optimization

5.1 Simulation, Control, and Estimation using Pyomo

• 5.1.1 Installations
  • 5.1.1.1 Google Colab
  • 5.1.1.2 MacOS
  • 5.1.1.3 Windows PC
• 5.1.2 Process Information
  • 5.1.2.1 Process Parameter Values
  • 5.1.2.2 Process Inputs
• 5.1.3 Pyomo Simulation
• 5.1.4 Optimal Control with Knowledge of Disturbances
  • 5.1.4.1 Exercise
• 5.1.5 Estimation/Observation
• 5.1.6 Coding the Observer as a Python Generator
• 5.1.7 Coding the Controller as a Python Generator
• 5.1.8 MPC Demonstration
• 5.1.9 To be Removed

5.2 Simulation, Control, and Estimation using Pyomo

• 5.2.1 Installations
  • 5.2.1.1 Google Colab
  • 5.2.1.2 MacOS
  • 5.2.1.3 Windows PC
• 5.2.2 Process Information
  • 5.2.2.1 Process Parameter Values
  • 5.2.2.2 Process Inputs
• 5.2.3 Pyomo Simulation
• 5.2.4 Optimal Control with Knowledge of Disturbances
  • 5.2.4.1 Exercise
• 5.2.5 Estimation/Observation
• 5.2.6 Coding the Observer as a Python Generator
• 5.2.7 Coding the Controller as a Python Generator

Appendix A. A.0 Additional Python

A.1 Coding Controllers with Python Generators

• A.1.1 Example: Relay Control with Hysteresis
  • A.1.1.1 Simulation
  • A.1.1.2 Experiment
• A.1.2 Example: Proportional-Integral Control
  • A.1.2.1 Simulation
  • A.1.2.2 Experiment
• Markdown Links
  • here

A.2 Modular Simulation using Python Generators

• Markdown Links
  • Simulation using scipy.integrate.odeint()
  • Typical Usage
  • What's Wrong with That?
  • Python Generators
  • Yield Statement
  • Iterators
  • Two-way communcation with Generators using Send
  • Example Application: Modeling Gravity-Drained Tanks with Python Generators
  • Generator for a Gravity-Drained Tank
  • Simulation of a Single Tank with Constant Inflow
  • Simulation of Two Tanks in Series
  • Simulation of Two Tanks in Series with PI Level Control on the Second Tank
  • Adding a PI Control Generator
  • Implementing Cascade Control for Two Tanks in Series with Unmeasured Disturbance
  • Enhancing Modularity with Class Definitions for Process Units
  • Gravity-Drained Tank Class
  • PI Controller Class
  • Modular Simulation of Cascade Control for Two Tanks in Series
  • generators and iterators

A.3 A Modular Approach to Simulation using Python Generators

• Markdown Links
  • https://github.com/jckantor/CBE30338
  • Simulation using scipy.integrate.odeint()
  • Typical Usage
  • What's Wrong with That?
  • Python Generators
  • Yield Statement
  • Iterators
  • Two-way communcation with Generators using Send
  • Example Application: Modeling Gravity-Drained Tanks with Python Generators
  • Generator for a Gravity-Drained Tank
  • Simulation of a Single Tank with Constant Inflow
  • Simulation of Two Tanks in Series
  • Simulation of Two Tanks in Series with PI Level Control on the Second Tank
  • Adding a PI Control Generator
  • Implementing Cascade Control for Two Tanks in Series with Unmeasured Disturbance
  • Enhancing Modularity with Class Definitions for Process Units
  • Gravity-Drained Tank Class
  • PI Controller Class
  • Modular Simulation of Cascade Control for Two Tanks in Series
  • generators and iterators

A.4 Animation in Jupyter Notebooks

• A.4.1 Summary
• A.4.2 Prerequisites
• A.4.3 Step-by-Step Approach to Animation with Matplotlib
  • A.4.3.1 Step 1. Create the background frame.
  • A.4.3.2 Step 2. Define a function to draw each frame
  • A.4.3.3 Step 3. Create the Animation Object
  • A.4.3.4 Step 4. Render the Animation
• A.4.4 Example: Phase Plane Animation for an Exothermic Stirred-Tank Reactor
• Markdown Links
  • https://github.com/jckantor/CBE30338
  • Animating the Lorenz System in 3D
  • Embedding Matplotlib Animations in Jupyter Notebooks
  • here