CBE30338

Chapter 1.0 Getting Started

1.1 Getting Started with Python and Jupyter Notebooks

• 1.1.1 Summary
• 1.1.2 Step 0: Gain Executable Access to Jupyter Notebooks
  • 1.1.2.1 Using Jupyter/Python in the Cloud
  • 1.1.2.2 Installing Jupyter/Python on your Laptop
• 1.1.3 Step 1: Start a Jupyter Notebook Session
• 1.1.4 Step 2: Simple Calculations with Python
  • 1.1.4.1 Basic Arithmetic Operations
  • 1.1.4.2 Python Libraries
  • 1.1.4.3 Working with Lists
  • 1.1.4.4 Working with Dictionaries
  • 1.1.4.5 Plotting with Matplotlib
  • 1.1.4.6 Solve Equations using Sympy Library
• 1.1.5 Step 3: Where to Learn More
  • 1.1.5.1 Introduction to Python for Science
  • 1.1.5.2 Tutorial Introduction to Python for Science and Engineering
  • 1.1.5.3 Interative learning and on-line tutorials
  • 1.1.5.4 Official documentation, examples, and galleries
• Markdown Figures
  • Screen Shot Jupyter Session
• Markdown Links
  • Jupyter Notebook
  • Wakari.io
  • SageMathCloud
  • tmpnb.org
  • Anaconda
  • Continuum Analytics
  • this Khan Academy video
  • Sympy
  • Introduction to Python for Science
  • acceptable use policy
  • Springer
  • Amazon
  • github
  • A Primer on Scientific Programming with Python (Fourth Edition)
  • github
  • pycse - Python Computations in Science and Engineering
  • github repository for pycse
  • Code Academy on Python
  • Khan Academy Videos on Python Programming
  • Python Tutorial
  • Think Python: How to Think Like a Computer Scientist
  • Engineering with Python
  • Notebook Examples
  • Notebook Gallery
  • Official Notebook Documentation
  • Matplotlib
• Figure files used
  • figures/Screen-Shot-Jupyter-Session.png

1.2 Python Basics

• 1.2.1 What I hope you'll get out of this tutorial
  • 1.2.1.1 Why Python?
  • 1.2.1.2 Markdown Sidenote
  • 1.2.1.3 LaTeX Sidenote
• 1.2.2 Python Basics
  • 1.2.2.1 Variables
  • 1.2.2.2 More Complicated Data Types
  • 1.2.2.3 Using Variables
  • 1.2.2.4 Importing in Python: Math and plotting
  • 1.2.2.5 Loops in Python
• 1.2.3 Additional Resources
• Markdown Links
  • Code Academy
  • Official Python Reference
  • Learn Python the Hard Way

1.3 Python Conditionals and Libraries

• 1.3.1 A Tutorial by Jacob Gerace
• 1.3.2 Conditionals in Python
• 1.3.3 Functions in Python
• 1.3.4 Numpy - "The Fundamental Package for Scientific Computing with Python"
• 1.3.5 Additional Resources
• Markdown Links
  • Code Academy
  • Official Python Reference
  • Learn Python the Hard Way

1.4 Python Numeric Integration Revisited

• 1.4.1 Sidenotes
  • 1.4.1.1 Code Academy Sidenote
  • 1.4.1.2 Markdown/Latex Sidenote
• 1.4.1 Second Header
  • 1.4.1.1 Tertiary Header
    • 1.4.1.1.1 Etc
  • 1.4.1.2 Latex Side Note
• 1.4.2 Hare and Lynx Example
  • 1.4.2.1 Adapted from Dr. Kantor's Notes)
  • 1.4.2.2 Introduction
  • 1.4.2.3 Modeling
    • 1.4.2.3.1 Relevant Parameters
    • 1.4.2.3.2 Model Equations
  • 1.4.2.4 Programming and Plotting
    • 1.4.2.4.1 Step 1: Initialization
    • 1.4.2.4.2 Step 2: Default Parameter Values
    • 1.4.2.4.3 Step 3: Define the differential equations
    • 1.4.2.4.4 Step 4: Integrate Differential Equations
    • 1.4.2.4.5 Step 5: Plot
• Markdown Figures
  • http://boredomtherapy.com/wp-content/uploads/2015/12/14-canadian-lynx-paws-cute.jpg
  • http://www.cbc.ca/kidscbc2/content/contests/cute_snowshoe1.jpg
  • MainLynx.jpg
• Markdown Links
  • Github's Markdown Guide
  • Dr. Kantor's Notes

Chapter 2.0 Process Modeling

2.1 Process Variables

• 2.1.1 Intensive and Entensive Variables
  • 2.1.1.1 Exercises
• 2.1.2 Thermodynamic State
  • 2.1.2.1 Conjugate Variables
    • 2.1.2.1.1 Pressure/Volume
    • 2.1.2.1.2 Temperature/Entropy
    • 2.1.2.1.3 Chemical Potential/Molar Amount
    • 2.1.2.1.4 Conjugate Variables
• 2.1.3 Homogeneous Equations
• Markdown Links
  • brake specific fuel consumption (BSFC)

2.2 Gravity Drained Tank

• 2.2.1 Summary
• 2.2.2 Torricelli's law
• 2.2.3 Mass Balance for Tank with Constant Cross-Sectional Area
• 2.2.4 Step-by-Step Approach to Nonlinear Simulation
  • 2.2.4.1 Step 1. Initialize Jupyter and Python
  • 2.2.4.2 Step 2. Define parameters
  • 2.2.4.3 Step 3. Write Functions for the RHS of the Differential Equations
  • 2.2.4.4 Step 4. Choose an Initial Condition, a Time Grid, and Integrate the Differential Equation
  • 2.2.4.5 Step 5. Visualize and Analyze Results
  • 2.2.4.6 Step 6. Adjust and Repeat as Needed

2.3 Blending Tank Simulation

• 2.3.1 Summary
• 2.3.2 Basic Simulation of the Blending Tank
  • 2.3.2.1 Step 1. Initialize Python Workspace
  • 2.3.2.2 Step 2. Establish Parameter Values
  • 2.3.2.3 Step 3. Write a function to compute the RHS's of the Differential Equations
  • 2.3.2.4 Step 4. Set the Initial Conditions, Time Grid, and Integrate
  • 2.3.2.5 Step 5. Visualize the Solution
• 2.3.3 Steady State Analysis

2.4 Continuous Product Blending

• 2.4.1 Preliminary Control Analysis
  • 2.4.1.1 Parameters
  • 2.4.1.2 Control Objectives
  • 2.4.1.3 Classification of Variables
  • 2.4.1.4 Degrees of Freedom Analysis
  • 2.4.1.5 Steady State
  • 2.4.1.6 Exercise 1. Determine Operating Range
• 2.4.2 Modeling
• 2.4.3 Simulation
  • 2.4.3.1 Step 1. Imports
  • 2.4.3.2 Step 2. Parameter Values
  • 2.4.3.3 Step 3. Computing Steady State
  • 2.4.3.4 Step 4. Process Model Equations
  • 2.4.3.5 Step 5. Numerical Solution of the Process Model
  • 2.4.3.6 Step 6. Visualization and Analysis
  • 2.4.3.7 Exercise 2. Explore Dynamical Behavior
• 2.4.4 Control Residence Time
• 2.4.5 Control Concentration
• 2.4.6 Exercise 3.
• 2.4.7 Proportional-Integral Control
• 2.4.8 Exercise 4.
• Markdown Figures
  • figures/Continuous-Mixed-Tank.png
• Tags: exercise
• Figure files used
  • figures/Continuous-Mixed-Tank.png

2.5 Hare and Lynx Population Dynamics

• 2.5.1 Summary
• 2.5.2 Introduction
• 2.5.3 Historical Data
• 2.5.4 Population Dynamics
  • 2.5.4.1 Model Equations
  • 2.5.4.2 Parameter Values
• 2.5.5 Simulation using the scipy.odeint())
  • 2.5.5.1 Step 1. Initialization
  • 2.5.5.2 Step 2. Establish Parameter Values
  • 2.5.5.3 Step 3. Write function for the RHS of the Differential Equations
  • 2.5.5.4 Step 4. Choose Time Grid, Initial Conditions, and Integrate
  • 2.5.5.5 Step 5. Visualize and Analyze the Solution
    • 2.5.5.5.1 Phase Plane
• 2.5.6 Nullclines
• 2.5.7 Interactive Simulation
  • 2.5.7.1 Visualization Function
  • 2.5.7.2 Simulation Function
• 2.5.8 Stability of a Steady State
  • 2.5.8.1 1. Unstable Focus
  • 2.5.8.2 2. Stable Focus
  • 2.5.8.3 3. Stable and Unstable Nodes
• 2.5.9 Summary
• 2.5.10 Suggested Exercise
• Markdown Figures
  • Canadian lynx by Keith Williams
  • Snowshoe Hare, Shirleys Bay
  • https://commons.wikimedia.org/wiki/File:Figure_45_06_01.jpg
• Markdown Links
  • Snowshoe hare
  • Canadian lynx
  • CC BY 2.0
  • via Wikimedia Commons
  • CC BY-SA 3.0
  • via Wikimedia Commons
  • Stenseth, 1997
  • CC BY 4.0
  • via Wikimedia Commons
  • Zhang, 2007
  • D. R. Hundley at Whitman College
  • here
  • here

2.6 Exothermic Continuous Stirred Tank Reactor

• 2.6.1 Description
• 2.6.2 Reaction Kinetics
• 2.6.3 Model Equations and Parameter Values
• 2.6.4 Transient Behavior
• 2.6.5 Effect of Cooling Temperature
• 2.6.6 Interactive Simulation
• 2.6.7 Nullclines
• 2.6.8 Phase Plane Analysis
• 2.6.9 Suggested Exercises
• Markdown Figures
  • Exothermic Reactor
• Markdown Links
  • Daniele Pugliesi
  • CC BY-SA 3.0
  • Link
• Tags: exercise

2.7 Fed-Batch Bioreactor

• 2.7.1 Model Development
  • 2.7.1.1 Dilution Effect
• 2.7.2 Python Implementation
• 2.7.3 Simulation

2.8 Model Library

Chapter 3.0 Linearization

3.1 Step Response of a Gravity Drained Tank

• 3.1.1 Summary
• 3.1.2 Mass Balance for Tank with Constant Cross-Sectional Area
• 3.1.3 Nonlinear Step Response
• 3.1.4 Linear Approximation of the Step Response
  • 3.1.4.1 Fit for $K$
  • 3.1.4.2 Fit for $\tau$
  • 3.1.4.3 Comparing the linear approximation to the nonlinear simulation
• Markdown Links
  • https://github.com/jckantor/CBE30338

3.2 Linear Approximation of a Process Model

• 3.2.1 Key Idea
• 3.2.2 Why is this Important?
• 3.2.3 Procedure for a Single Variable System
  • 3.2.3.1 Step 1. Find a Nominal Steady State Operating Condition
  • 3.2.3.2 Step 2. Define deviation variables
  • 3.2.3.3 Step 3. Taylor Series Expansion
  • 3.2.3.4 Step 4. Linear Approximation
  • 3.2.3.5 Example: Gravity Drained Tank
  • 3.2.3.6 Exercises

3.3 Linear Approximation of a Multivariable Model

• 3.3.1 Multivariable Systems
  • 3.3.1.1 Example: Gravity Drained Tanks
    • 3.3.1.1.1 Model
    • 3.3.1.1.2 Nominal Inputs
    • 3.3.1.1.3 Steady State for nominal input
    • 3.3.1.1.4 Deviation Variables
    • 3.3.1.1.5 Linearization
    • 3.3.1.1.6 Summary of the linear model using matrix/vector notation
• 3.3.2 Exercises
  • 3.3.2.1 First Order Reaction in a CSTR
  • 3.3.2.2 Two Gravity Drained Tanks in Series
  • 3.3.2.3 Isothermal CSTR with second-order reaction
• Markdown Figures
  • Gravity Drained Tanks
• Figure files used
  • figures/GravityDrainedTanks.png

3.4 Fitting First Order plus Time Delay to Step Response

• 3.4.1 Summary
• 3.4.2 Initializations
• 3.4.3 First Order plus Time Delay Models
  • 3.4.3.1 First Order Models
  • 3.4.3.2 Time Delay
  • 3.4.3.3 First Order plus Time Delay (FOPTD))
  • 3.4.3.4 Visualization
• 3.4.4 Fitting an FOPTD model
  • 3.4.4.1 Sample Problem Statement
  • 3.4.4.2 Step 1. Shift and scale the experimental data to correspond to a unit step input at time t = 0.
  • 3.4.4.3 Step 2. Create a function to compute the response of an FOPTD model.
  • 3.4.4.4 Step 3. Create a function to measure the error between an FOPTD model and the experimental data.
  • 3.4.4.5 Step 4. Use scipy.optimize.minimize() to find the best fitting FOPTD model.-to-find-the-best-fitting-FOPTD-model.)
  • 3.4.4.6 Step 5. Rescale FOPTD output and compare to experimental data.

3.5 One Compartment Pharmacokinetics

• 3.5.1 Summary
• 3.5.2 Antibiotics
• 3.5.3 Model Description
• 3.5.4 Problem Statement 1
• 3.5.5 Solution Strategy 1: Simulation from a Known Initial Condition
  • 3.5.5.1 Step 1. Initialization
  • 3.5.5.2 Step 2. Enter Parameter Values
  • 3.5.5.3 Step 3. A Function the RHS of the Differential equation
  • 3.5.5.4 Step 4. Solution and Visualization
  • 3.5.5.5 Step 5. Analysis of the Results
• 3.5.6 Solution Strategy 2: Time-Dependent Input
  • 3.5.6.1 Analysis of the Results
• 3.5.7 Problem Statement 2
• 3.5.8 Solution Strategy 3: Periodic Dosing
• Markdown Figures
  • ./figures/Pharmaockinetics1.png
  • figures/nihms-475924-f0001.jpg
  • ./figures/Pharmaockinetics2.png
  • ./figures/nihms-475924-f0001.jpg
• Markdown Links
  • antibiotic resistance
  • Levison, Matthew E., and Julie H. Levison. “Pharmacokinetics and Pharmacodynamics of Antibacterial Agents.” Infectious disease clinics of North America 23.4 (2009): 791–vii. PMC. Web. 8 May 2017.
  • Levison, Matthew E., and Julie H. Levison. “Pharmacokinetics and Pharmacodynamics of Antibacterial Agents.” Infectious disease clinics of North America 23.4 (2009): 791–vii. PMC. Web. 8 May 2017.
• Figure files used
  • figures/Pharmaockinetics2.png
  • figures/nihms-475924-f0001.jpg
  • figures/Pharmaockinetics1.png

3.6 Second Order Models

• 3.6.1 Step Response
  • 3.6.1.1 Overdamped ($\zeta > 1$))
  • 3.6.1.2 Critically Damped ($\zeta = 1$))
  • 3.6.1.3 Underdamped ($0 \lt \zeta \lt 1$))
  • 3.6.1.4 Undamped ($\zeta = 0$))
• 3.6.2 Simulation
• 3.6.3 Performance Indicators for Underdamped Systems
• 3.6.4 Estimating Parameters for an Underdamped System
  • 3.6.4.1 Starting with a Physical Model
  • 3.6.4.2 Starting with a Step Response
• Markdown Figures
  • 2ndOrder.png

3.7 Interacting Tanks

• 3.7.1 Problem Statement
• 3.7.2 Solution
  • 3.7.2.1 Part a.
  • 3.7.2.2 Part b.
  • 3.7.2.3 Further Calculations
• Markdown Figures
  • Image of a two interacting tanks
• Figure files used
  • figures/InteractingTanks.png

3.8 Manometer Models and Dynamics

• 3.8.1 Summary
• 3.8.2 Learning Goals
• 3.8.3 Initializations
• 3.8.4 Model 1. Steady State Response to a Pressure Differential
• 3.8.5 Model 2. Dynamic Response with Negligible Viscosity
• 3.8.6 Model 3. Dynamic Response with Viscous Dissipation
• 3.8.7 Model 4. Second Order System in Standard Form

    - [3.8.7.1 Undamped ($\zeta = 0$)](https://jckantor.github.io/CBE30338/03.08-Manometer-Models-and-Dynamics.html#3.8.7.1-Undamped-($\zeta-=-0$))
    - [3.8.7.2 Underdamped ($\zeta < 1$)](https://jckantor.github.io/CBE30338/03.08-Manometer-Models-and-Dynamics.html#3.8.7.2-Underdamped-($\zeta-<-1$))
    - [3.8.7.3 Critically damped ($\zeta = 1$)](https://jckantor.github.io/CBE30338/03.08-Manometer-Models-and-Dynamics.html#3.8.7.3-Critically-damped-($\zeta-=-1$))
    - [3.8.7.4 Overdamped ($\zeta > 1$)](https://jckantor.github.io/CBE30338/03.08-Manometer-Models-and-Dynamics.html#3.8.7.4-Overdamped-($\zeta->-1$))

• 3.8.8 Model 5. Dynamic Response to Sinusoidal Input
• 3.8.9 Model 6. State Space Representation
• Markdown Figures
  • https://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Schlauchwaage_Schematik.svg/250px-Schlauchwaage_Schematik.svg.png
• Markdown Links
  • Bd
  • German language Wikipedia
  • CC BY-SA 3.0
  • Link

3.9 Modeling and Control of a Campus Outbreak of Coronavirus COVID-19

• 3.9.1 1. Brief background on the SARS-CoV-2 Coronavirus and COVID-19
• 3.9.2 Model 1. SIR model for an infectious disease
  • 3.9.2.1 Readings
  • 3.9.2.2 Introduction to SIR models
  • 3.9.2.3 Key Properties of the SIR Model
  • 3.9.2.4 Simulation
  • 3.9.2.5 How many people will be infected following an outbreak?
• 3.9.3 Model 2. SEIR model
• 3.9.4 Model 3. Mitigation and Social Distancing
  • 3.9.4.1 Social Distancing Strategies for the Campus
• 3.9.5 Model 4. Improving the fidelity of the model.
• 3.9.6 Additional Modeling Opportunities. Transportation, power law kinetics, etc.
• Markdown Links
  • COVID-19
  • global health emergency by the World Health Organization (WHO)
  • Coronavirus COVID-19 Global Cases by Johns Hopkins CSSE
  • WHO Novel Coronavirus (COVID-19) Situation
  • Cell Press Coronavirus Resource Hub
  • Lancet COVID-19 Resource Centre
  • medRxiv preprint server search on COVID-19
  • New England Journal of Medicine Coverage on Coronavirus (COVID-19)
  • WHO Database of publications on coronavirus disease (COVID-19)
  • CDC Social Distancing

Chapter 4.0 PID Control

• 4.0.1 PID Control Formulations
  • 4.0.1.1 Non-interacting Form
  • 4.0.1.2 ISA Form
• 4.0.2 Implementation

4.1 Implementing PID Controllers with Python Yield Statement

• 4.1.1 Python Yield Statement
• 4.1.2 PID Control Implementation
• 4.1.3 Simulation
• 4.1.4 Analysis
• Markdown Links
  • here

4.2 PID Control with Setpoint Weighting

• 4.2.1 Setpoint 'Kick'
• 4.2.2 Setpoint Weighting
• 4.2.3 Implementation of Setpoint Weighting
• 4.2.4 Simulation

4.3 PID Control with Bumpless Transfer

• 4.3.1 Switching from Manual to Automatic Control
• 4.3.2 Bumpless Transfer
  • 4.3.2.1 Tracking the Manipulated Variable
  • 4.3.2.2 Setpoint Tracking
  • 4.3.2.3 Steady State

4.4 PID Control with Anti-Reset-Windup

• 4.4.1 Additional Benefits of Tracking the Manipulated Variable
• 4.4.2 Embedding Anti-Reset Windup inside the Controller

4.5 Realizable PID Control

• 4.5.1 Example: PID Control with Significant Measurement Noise
• 4.5.2 Modifying the Derivative Term
• 4.5.3 Example Revisited

4.6 PID Controller Tuning

- [4.6.1 Empirical Methods](https://jckantor.github.io/CBE30338/04.06-PID-Controller-Tuning.html#4.6.1-Empirical-Methods)

• 4.6.1 PID Reference Implementation
• 4.6.2 AMIGO Tuning
  • 4.6.2.1 KLT Model - First Order with Dead Time
  • 4.6.2.2 Tuning Rules
• 4.6.3 Ziegler Nichols Tuning
• 4.6.4 Relay Tuning
• 4.6.5 Exercise: Compare the performance of these tuning rules.
• Tags: exercise

4.10 PID Control - Laboratory

• 4.10.1 PID Control
• 4.10.2 Exercise 1. Is the transfer from manual to automatic bumpless?
• 4.10.3 Exercise 2
• Tags: exercise

4.11 Implementing PID Control in Nonlinear Simulations

• 4.11.1 Model
• 4.11.2 Simulation 1. Same Initial Condition, different values of $q_c$
• 4.11.3 Simulation 2. Fixed Time Grid
• 4.11.4 Simulation 3. Proportional-Integral-Derivative Control
  • 4.11.4.1 Independent Parameters
  • 4.11.4.2 Setpoint Weighting
  • 4.11.4.3 Discrete Time Implementation
  • 4.11.4.4 Bounded Control
• 4.11.5 Simulation 4. Interactive Controller Tuning
• 4.11.6 Simulation 5. Using the PIDsim Controller Class
  • 4.11.6.1 Contents of PIDsim.py
• Markdown Figures
  • Exothermic Reactor
• Markdown Links
  • Daniele Pugliesi
  • CC BY-SA 3.0
  • Link
  • DISCRETE PID CONTROLLER (PYTHON RECIPE)
  • ivPID
  • python-pid_controller
  • PID Controller
  • pypid 0.4
  • PIDController
  • PID.py
  • APMonitor.com
• Figure files used
  • figures/408px-Agitated_vessel.png

4.12 Interactive PID Control Tuning with Ziegler-Nichols

• 4.12.1 Summary
• 4.12.2 Notebook Initialization
• 4.12.3 Block Diagram of the Closed-Loop Control System
  • 4.12.3.1 Process Transfer Functions
  • 4.12.3.2 Measurement Transfer Function
  • 4.12.3.3 Proportional-Integral (PI) Control-Control)
• 4.12.4 Closed-Loop Transfer Functions
  • 4.12.4.1 Definitions
  • 4.12.4.2 Interactive Simulation
• 4.12.5 3. Control Tuning Procedures
  • 4.12.5.1 Ziegler-Nichols
  • 4.12.5.2 Tyreus-Luyben
• 4.12.6 Exercises
  • 4.12.6.1 Exercise: PID Control
  • 4.12.6.2 Exercise: Alternative Tuning Rules
• 4.12.7 References
• Markdown Figures
  • figures/controlloop.png
• Markdown Links
  • Wikipedia page describing the Ziegler-Nichols method

Chapter 5.0 Frequency Domain Control Design

5.1 Getting Started with Transfer Functions

• 5.1.1 Installation
• 5.1.2 Library Usage
• 5.1.3 Demonstration
  • 5.1.3.1 Step Response of Transfer Functions
  • 5.1.3.2 Transfer Functions in Series
  • 5.1.3.3 Second Order Transfer Functions
• Markdown Links
  • Python Control Systems Library
  • Python Control Systems Documentation
  • Python Control Systems Library

5.2 Closed-Loop Transfer Functions for Car Cruise Control

• 5.2.1 Summary
• 5.2.2 Block Diagram for Car Cruise Control
• 5.2.3 Closed-Loop Transfer Functions
• 5.2.4 Step Responses
• 5.2.5 Additional Examples
  • 5.2.5.1 Internal Model Control
  • 5.2.5.2 SEMD Figure 11-14
• Markdown Figures
  • Cruise Control Block Diagram
  • Cruise Control Block Diagram
  • Internal Model Control
  • Internal Model Control
• Figure files used
  • figures/E11-10.png
  • figures/CruiseControl2.png
  • figures/CruiseControl.png
  • figures/Internal_Model_Control.png

5.3 Creating Bode Plots

• 5.3.1 Initializations
• 5.3.2 Creating Bode Plots
  • 5.3.2.1 Specify a Transfer Function
  • 5.3.2.2 Adding Time Delay
  • 5.3.2.3 Bode Plot using Default Options
  • 5.3.2.4 Specify Frequency Range
  • 5.3.2.5 Setting Other Plotting Options
• 5.3.3 Adding Features to the Bode Plot
  • 5.3.3.1 Crossover Frequency and Gain at Crossover
• Markdown Links
  • Python Control Systems Library
  • here
  • Python Control Systems Library

5.4 Controller Tuning Rules in Frequency Domain

• 5.4.1 Closed-Loop Transfer Functions
  • 5.4.1.1 Process Transfer Functions
  • 5.4.1.2 Control Transfer Functions
  • 5.4.1.3 Closed Loop Transfer Functions
• 5.4.2 Example
  • 5.4.2.1 Entering Process Transfer Functions
  • 5.4.2.2 Finding Cross-Over Frequency and Gain at Cross-Over
  • 5.4.2.3 Computing Ultimate Gain and Period
• 5.4.3 Ziegler-Nichols Tuning Rules
  • 5.4.3.1 Interactive Tuning of a PID Controller
• Markdown Links
  • Python Control Systems Library

5.5 Baroreflex as a Linear Control System

• 5.5.1 Peripheral Arc
• 5.5.2 P, PI, PD, and PID Control
  • 5.5.2.1 Ziegler-Nichols Tuning
  • 5.5.2.2 Proportional-Derivative Control
  • 5.5.2.3 Internal Model Control Tuning
• 5.5.3 Measured Physiological Response of Neural Arc
• 5.5.4 Comparison of ZN Tuned PD Control to the Observed Physiological Response of the Neural arc
• 5.5.5 Modifications to the PD Controller
• 5.5.6 Conclusions
  • 5.5.6.1 References
• Markdown Figures
  • baroreflex system
  • baroreflex control diagram
• Markdown Links
  • baroreflex
  • baroreceptors
  • Python Control Systems Library
  • Ziegler-Nichols tuning
• Figure files used
  • figures/nrcardio.2015.96-f2.jpg
  • figures/baroreflex.png

Chapter 6.0 Optimization

6.1 Unconstrained Scalar Optimization

• 6.1.1 Example: Reactor for a Series Reaction
• 6.1.2 Continuous Stirred Tank Reactor
• 6.1.3 Analytical Solution using Calculus
• 6.1.4 Numerical Solution using scipy.minimize_scalar
• 6.1.5 [Bonus Discussion] Batch Reactor

6.2 Linear Production Model

• 6.2.1 Example: Production Plan for a Single Product Plant
  • 6.2.1.1 Mathematical Model
  • 6.2.1.2 Exercises
• 6.2.2 Production Plan: Product Y
  • 6.2.2.1 Exercises
• 6.2.3 Production Plan: Mixed Product Strategy
• 6.2.4 Solution using scipy.optimize.linprog
• 6.2.5 What are the active constraints?
• 6.2.6 What is the incremental value of labor?
  • 6.2.6.1 Exercise
• 6.2.7 Theory of Constraints
• Markdown Figures
  • LP_ProductX.png
  • LP_ProductY.png
  • LP_ProductXY.png
• Markdown Links
  • Pyomo
  • glpk
  • scipy.optimize library
• Figure files used
  • figures/LP_ProductXY.png
  • figures/LP_ProductX.png
  • figures/LP_ProductY.png
  • figures/LPprob01.png

6.3 Linear Programming

• 6.3.1 Matrix/Vector format
• 6.3.2 Example 19.3: Refinery Blending Problem

6.4 Linear Production Model in Pyomo

• 6.4.1 Installation
  • 6.4.1.1 Anaconda
  • 6.4.1.2 Google Colab
• 6.4.2 Algebraic Modeling Languages
• 6.4.3 Key Concepts in Pyomo
• 6.4.4 Example: Linear Production Model with Constraints
  • 6.4.4.1 Step 1. Import Pyomo.
  • 6.4.4.2 Step 2. Create the model object.
  • 6.4.4.3 Step 3. Add the Decision Variables, Objective, and Constraints to the model object.
  • 6.4.4.4 Step 4. Create a solver object and solve.
  • 6.4.4.5 Step 5. Display the solution.
• 6.4.5 Python Lists, Sets, Dictionaries, and Iterators
  • 6.4.5.1 Data in Matrix/Vector Format
• Markdown Links
  • Pyomo
  • Anaconda package for Python 3.x
  • glpk
  • ipopt
  • cbc
  • GAMS
  • AIMMS
  • AMPL
  • FICO XPRESS
  • YALMIP
  • CVX
  • JuMP
  • Pyomo

6.5 Linear Programming in Pyomo

• 6.5.1 Starting the Model

6.6 Linear Blending Problem

• 6.6.1 Problem Statement (Jenchura, 2017))
  • 6.6.1.1 Solution
    • 6.6.1.1.1 Representing Problem Data as a Python Dictionary
    • 6.6.1.1.2 Objective Function
    • 6.6.1.1.3 Volume Constraint
    • 6.6.1.1.4 Product Composition Constraint
    • 6.6.1.1.5 Pyomo Model

6.7 Design of a Cold Weather Fuel

• 6.7.1 Data
• 6.7.2 Denatured Alcohol
• 6.7.3 Cold Weather Product Requirements
• 6.7.4 Optimization Model
• 6.7.5 Display Composition
• Markdown Figures
  • ./figures/alcohol_stove.jpeg
• Markdown Links
  • manufacturer's product
• Figure files used
  • figures/alcohol_stove.jpeg

6.8 Gasoline Blending

• 6.8.1 Gasoline Product Specifications
• 6.8.2 Stream Specifications
• 6.8.3 Blending Model
• 6.8.4 Display Results
  • 6.8.4.1 Results for each Stream
  • 6.8.4.2 Results for each Product
• 6.8.5 Exercise 1.
• 6.8.6 Exercise 2.
• 6.8.7 Exercise 3.
• Tags: exercise

6.99 Pyomo Examples

• 6.99.1 Example: Nonlinear Optimization of Series Reaction in a Continuous Stirred Tank Reactor
• 6.99.2 Example 19.3: Linear Programming Refinery
• 6.99.3 Example: Making Change
• 6.99.4 Example: Linear Production Model with Constraints with Duals

Chapter 7.0 Simulation and Optimal Control

• 7.0.1 Available Solvers
• Markdown Links
  • ampl.com

7.1 Simulation and Optimal Control in Pharmacokinetics

• 7.1.1 Installations and Initialization
• 7.1.2 A Pharmacokinetics Example
• 7.1.3 Simulation of Fixed Infusion Rate Strategy
• 7.1.4 Optimizing the Infusion Strategy
• 7.1.5 Alternative Objectives
• Markdown Figures
  • Infusionspumpe
• Markdown Links
  • Google Colaboratory
  • Pflegewiki-User Würfel
  • CC BY-SA 3.0

7.2 Soft Landing a Rocket

• 7.2.1 Required Installations
  • 7.2.1.1 Google Colab
  • 7.2.1.2 Windows PC
• 7.2.2 Python Initializations
• 7.2.3 Version 1: Vertical Dynamics of a Rocket with Constant Mass
  • 7.2.3.1 First attempt at a solution
  • 7.2.3.2 Land on the surface, not above or below the surface.
  • 7.2.3.3 Make that a soft landing.
  • 7.2.3.4 Restrict fuel flow to engine capacity.
• 7.2.4 Version 2: Rescaled Model
  • 7.2.4.1 How much fuel is burned?
  • 7.2.4.2 Minimize fuel consumption.
• 7.2.5 Version 3: Rocket Model
• Markdown Figures
  • Eagle In Lunar Orbit - GPN-2000-001210
  • LM illustration 02-IT
• Markdown Links
  • NASA Michael Collins [Public domain] via Wikimedia Commons
  • Apollo 11 Landing on the Moon, July 20, 1969
  • SpaceX Falcon Heavy Side Boosters Landing at Kennedy Space Center, February 6, 2018
  • Blue Origin, November 24, 2014
  • ampl.com
  • NASA Marshall Space Flight Center (NASA-MSFC)derivative work: Adert [Public domain]
  • Apollo 11 Lunar Module

7.3 Simulation in Pyomo

7.4 Simulation of an Exothermic CSTR

• 7.4.1 Description
• 7.4.2 Imports
• 7.4.3 Arrehenius Law Kinetics for a First-Order Reaction
• 7.4.4 Modeling and Parameter Values
  • 7.4.4.1 Mathematical Model
  • 7.4.4.2 Pyomo Model
• 7.4.5 Simulation and Visualization
  • 7.4.5.1 Simulation
  • 7.4.5.2 Visualization Functions
• 7.4.6 Effect of Cooling Temperature
• Markdown Figures
  • Exothermic Reactor
• Markdown Links
  • Daniele Pugliesi
  • Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0)
  • Link

7.5 First Order System in Pyomo

• 7.5.1 First-Order Differential Equation with Initial Condition

7.6 Path Planning for a Simple Car

• 7.6.1 Required Installations
• 7.6.2 Kinematic Model
• 7.6.3 Pyomo Model
• 7.6.4 Accessing Solution Data
• 7.6.5 Visualizing Car Path

7.7 Transient Heat Transfer in Various Geometries

• 7.7.1 Rescaling
  • 7.7.1.1 Dimensionless Model
• 7.7.2 Preliminary Code
• 7.7.3 Planar Coordinates
• 7.7.4 Cylindrical Coordinates
• 7.7.5 Spherical Coordinates

7.8 Path Constraints

• 7.8.1 Recoding for Compact Style
• 7.8.2 Subscripting Equations

Chapter 8.0 Predictive Control

8.1 Zero-Order Hold and Interpolation

• 8.1.1 Interpolation Function
• 8.1.2 Demonstration

Chapter 9.0 Discrete Events

9.1 Scheduling State-Task Networks

• 9.1.1 Example (Kondili, et al., 1993))
• 9.1.2 Encoding the STN data
  • 9.1.2.1 Setting a Time Grid
• 9.1.3 Creating a Pyomo Model
  • 9.1.3.1 Characterization of Tasks
  • 9.1.3.2 Characterization of States
  • 9.1.3.3 Characterization of Units
  • 9.1.3.4 Pyomo Model
• 9.1.4 Analysis
  • 9.1.4.1 Profitability
  • 9.1.4.2 State Inventories
  • 9.1.4.3 Unit Assignment
  • 9.1.4.4 Unit Batch Inventories
  • 9.1.4.5 Gannt Chart
• 9.1.5 Trace of Events and States
• Markdown Figures
  • Kondili_1993
• Figure files used
  • figures/Kondili_1993.png

9.2 State-Task Networks

• 9.2.1 Description
• 9.2.2 Exercise
• 9.2.3 References
• Markdown Figures
  • figures/Konsili_1993.png
• Figure files used
  • figures/Kondili_1993.png

9.3 Machine Bottleneck

• 9.3.1 Example
• 9.3.2 Modeling
  • 9.3.2.1 Data
  • 9.3.2.2 Decision Variables
• 9.3.3 Pyomo Model
• 9.3.4 Visualization
• 9.3.5 Multiple Machines

Appendix A. A.0 Additional Python

A.1 Python Library for CBE 30338

• A.1.1 Some Python basics
  • A.1.1.1 Python functions
    • A.1.1.1.1 Functions are Python objects
    • A.1.1.1.2 Create simple functions with lambda
    • A.1.1.1.3 Create complex functions with def
  • A.1.1.2 Comprehensions
  • A.1.1.3 map, filter, reduce
• A.1.2 CBE30338.plotter()`)

A.2 Modular Simulation using Python Generators

• A.2.1 Simulation using scipy.integrate.odeint())
  • A.2.1.1 Typical Usage
• A.2.2 What's Wrong with That?
• A.2.3 Python Generators
  • A.2.3.1 Yield Statement
  • A.2.3.2 Iterators
  • A.2.3.3 Two-way communcation with Generators using Send
• A.2.4 Example Application: Modeling Gravity-Drained Tanks with Python Generators
  • A.2.4.1 Generator for a Gravity-Drained Tank
  • A.2.4.2 Simulation of a Single Tank with Constant Inflow
  • A.2.4.3 Simulation of Two Tanks in Series
  • A.2.4.4 Simulation of Two Tanks in Series with PI Level Control on the Second Tank
  • A.2.4.5 Adding a PI Control Generator
  • A.2.4.6 Implementing Cascade Control for Two Tanks in Series with Unmeasured Disturbance
• A.2.5 Enhancing Modularity with Class Definitions for Process Units
  • A.2.5.1 Gravity-Drained Tank Class
  • A.2.5.2 PI Controller Class
  • A.2.5.3 Modular Simulation of Cascade Control for Two Tanks in Series
• Markdown Links
  • generators and iterators

A.3 Animation in Jupyter Notebooks

• A.3.1 Summary
• A.3.2 Prerequisites
• A.3.3 Step-by-Step Approach to Animation with Matplotlib
  • A.3.3.1 Step 1. Create the background frame.
  • A.3.3.2 Step 2. Define a function to draw each frame
  • A.3.3.3 Step 3. Create the Animation Object
  • A.3.3.4 Step 4. Render the Animation
• A.3.4 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

Appendix B. B.0 Student Projects

B.1 Diabetes: Controlling Blood Glucose Concentrations

• B.1.1 Problem Statement
  • B.1.1.1 Introduction and Problem
  • B.1.1.2 Technology Challenge
  • B.1.1.3 Goals and Objectives:
• B.1.2 Theoretical Development
  • B.1.2.1 The Bergman Model for Type I Diabetes
  • B.1.2.2 Exercise Model
  • B.1.2.3 Core Model Assumptions
• B.1.3 Results and Executable Elements
  • B.1.3.1 Import Libraries
  • B.1.3.2 Define Model Function for Bergman Model
  • B.1.3.3 Define Model Function for Exercise Model
  • B.1.3.4 Disturbance Function
  • B.1.3.5 Injection Function
  • B.1.3.6 Solver Functions for Bergman Model and Exercise Model
  • B.1.3.7 Plotting Function
  • B.1.3.8 Parameter Values for Bergman Model
  • B.1.3.9 Parameter Values for Exercise Model
  • B.1.3.10 Parameter Values for the Disturbance Function for Meals
  • B.1.3.11 Time and Initial Conditions for the Bergman Minimal Model
  • B.1.3.12 Time and Initial Conditions for the Exercise Model
• B.1.4 Simulation 1: No Controller Input
• B.1.5 Simulation 2: Basal Dose
  • B.1.5.1 Simulation 3: High-Concentration Injection Prior to Meal
  • B.1.5.2 Simulation 4: High-Concentration Injection and Basal Dose
• B.1.6 Simulation 5: PID Control
• B.1.7 Simulation 6: PID Control with Basal Dose
  • B.1.7.1 Simulation 7: PID Control with Basal Dose and Injection
  • B.1.7.2 Simulation 8: Exercise and Meal with no Control
  • B.1.7.3 Simulation 9: Exercise and Meal with only Basal Dose
  • B.1.7.4 Simulation 10: Exercise and Meal with PID Controller
  • B.1.7.5 Simulation 11: Exercise and Meal with PID Controller and Basal Dose
• B.1.8 Summary and Conclusion
• B.1.9 Appendices
  • B.1.9.1 References
• B.1.10 Statement of Contributions

B.2 Visual Tracking of an Object with a Drone

• B.2.1 Problem Statement
  • B.2.1.1 Technology Challenge
  • B.2.1.2 Project Goal
• B.2.2 Results and Theory
  • B.2.2.1 Controller
  • B.2.2.2 Image Recognition
  • B.2.2.3 PID Control for Object Tracking
• B.2.3 Executable Element
• B.2.4 Conclusion and Summary
• B.2.5 Appendices
  • B.2.5.1 A.) TelloCV.py-TelloCV.py)
  • B.2.5.2 B.) Tracker.py-Tracker.py)