cbe30338-2021

Chapter 1.0 Introduction

1.1 Schedule and Course Organization

• 1.1.1 Getting Started
• 1.1.2 Introduction to the Course and Process Control
  • 1.1.2.1 Week 1
• 1.1.3 Modeling and Parameter Estimation
  • 1.1.3.1 Week 2
  • 1.1.3.2 Week 3
• 1.1.4 Feedback Control
  • 1.1.4.1 Week 4
  • 1.1.4.2 Week 5
  • 1.1.4.3 Week 6
• 1.1.5 Process Analytics
  • 1.1.5.1 Week 7
  • 1.1.5.2 Week 8
• 1.1.6 Optimization
  • 1.1.6.1 Week 9
  • 1.1.6.2 Week 10
• 1.1.7 Predictive Control
  • 1.1.7.1 Week 11
  • 1.1.7.2 Week 12
• 1.1.8 Final Project
  • 1.1.8.1 Week 13
  • 1.1.8.2 Week 14
  • 1.1.8.3 Finals Week
• Markdown Links
  • https://zoom.us/test
  • Anaconda.com
  • Amazon
  • apmonitor.com
  • such as this device for an Apple Mac
  • such as this
  • Class Meeting
  • Syllabus
  • FBS 1.2-1.4
  • cbe30338-2021 Section 1.1
  • Class Meeting
  • FBS 3.1, 3.2
  • cbe30338-2021 Section 2.1
  • Class Meeting
  • cbe30338-2021 Section 2.2
  • cbe30338-2021 Section 1.3
  • cbe30338-2021 Section 1.4
  • Class Meeting
  • cbe30338-2021 Section 2.3
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  • cbe30338-2021 Section 2.4
  • Class Meeting
  • cbe30338-2021 Section 3.1 & 3.2
  • Class Meeting
  • cbe30338-2021 Section 3.3
  • cbe30338-2021 Section 3.6
  • Class Meeting
  • cbe30338-2021 Section 3.4
  • Class Meeting
  • cbe30338-2021 Section 3.5
  • Class Meeting
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1.2 What is Process Control?

• 1.2.1 Examples
  • 1.2.1.1 Refineries: Fluidized Catalytic Cracking Unit (FCCU))
  • 1.2.1.2 Manufacturing: Tesla Shanghai Gigafactory
  • 1.2.1.3 Biomedical: Automated Insulin Therapy
• 1.2.2 Elements of Feedback Control
  • 1.2.2.1 Discussion Questions
• Markdown Figures
  • https://www.medtronicdiabetes.com/res/img/770g/770g-img1a.jpg
  • ./figures/FeedbackControlDiagram.png
• Markdown Links
  • 2005 incident at the BP Texas City Refinery
  • Medtronic MiniMed 770G System
• Figure files used
  • figures/FeedbackControlDiagram.png

1.3 The Temperature Control Laboratory

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

1.4 The TCLab Python Package

• 1.4.1 Connecting to the Temperature Control Laboratory
  • 1.4.1.1 Installing the tclab library
  • 1.4.1.2 Creating a TCLab instance
  • 1.4.1.3 Using the LED
  • 1.4.1.4 Using TCLab and Python's with statement
• 1.4.2 Reading Temperatures
• 1.4.3 Setting Heater Power
  • 1.4.3.1 Setting maximum power with .P1 and .P2
  • 1.4.3.2 Setting heater power with .Q1() and .Q2()-and-.Q2()`)
  • 1.4.3.3 Setting heater power with .U1 and .U2
• 1.4.4 Synchronizing with Real Time using clock
  • 1.4.4.1 Using clock with TCLab
• 1.4.5 The TCLab Historian
• 1.4.6 The TCLab Plotter
• 1.4.7 Using TCLab Offline
• 1.4.8 Running Diagnostics
• 1.4.9 Lab Assignment 1
  • 1.4.9.1 Exercise 1.
  • 1.4.9.2 Exercise 2.
• 1.4.10 Exercise 3.
• 1.4.11 Exercise 4.
• Markdown Links
  • TCLab
  • TCLab-sketch
  • Arduino IDE
  • Pandas Data Analysis Library
• Figure files used
  • figures/B.00-TCLabOverview.png

1.5 Assignment 1

• Markdown Links
  • Amazon
  • apmonitor.com
  • https://fbswiki.org/wiki/index.php/Main_Page

Chapter 2.0 Linear Process Models

2.1 One Compartment Pharmacokinetics

• 2.1.1 Learning Goals
• 2.1.2 Pharamacokinetics
  • 2.1.2.1 One-Compartment Model
  • 2.1.2.2 Antimicrobials
  • 2.1.2.3 What questions can we ask and answer with this model?
• 2.1.3 Simulation
  • 2.1.3.1 Simulation from a Known Initial Condition
    • 2.1.3.1.1 Problem Statement
    • 2.1.3.1.2 Step 1. Import libraries
    • 2.1.3.1.3 Step 2. Enter Parameter Values
    • 2.1.3.1.4 Step 3. Write the differential equation in standard form
    • 2.1.3.1.5 Step 4. Solution and Visualization
    • 2.1.3.1.6 Step 5. Analysis of the Results
  • 2.1.3.2 Example 2: Improving Simulation using Time-Dependent Input
    • 2.1.3.2.1 Analysis of the Results
  • 2.1.3.3 Example 2: Periodic Dosng
    • 2.1.3.3.1 Solution
• 2.1.4 Assignment 2
  • 2.1.4.1 Exercise 1
  • 2.1.4.2 Exercise 2
• Markdown Figures
  • ./figures/PK-one-compartment.png
  • ./figures/Pharmaockinetics1.png
  • figures/nihms-475924-f0001.jpg
  • ./figures/Pharmaockinetics2.png
  • ./figures/nihms-475924-f0001.jpg
• Markdown Links
  • antimicrobrial resistance
  • solve_ivp
  • 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/Pharmaockinetics3.png
  • figures/Pharmaockinetics2.png
  • figures/nihms-475924-f0001.jpg
  • figures/Pharmaockinetics1.png
  • figures/PK-one-compartment.png
  • figures/Pharmaockinetics4.png

2.2 Properties of Scalar First Order Linear Systems

• 2.2.1 First order linear systems
• 2.2.2 Steady-State Gain
• 2.2.3 Dynamic Response
  • 2.2.3.1 Response to an Initial Condition
  • 2.2.3.2 Time constant
  • 2.2.3.3 Half-life
  • 2.2.3.4 Step Inputs
• 2.2.4 Response to a step input
• 2.2.5 Alternative forms for scalar first-order linear systems

2.3 First Order Model for a Single Heater

• 2.3.1 Learning Goals
• 2.3.2 First-order model for one heater/sensor assembly
  • 2.3.2.1 Energy Balance
  • 2.3.2.2 Energy inflow
  • 2.3.2.3 Energy Outflow
  • 2.3.2.4 One-state model
  • 2.3.2.5 Estimating $\alpha$
  • 2.3.2.6 Steady State
  • 2.3.2.7 Deviation Variables
  • 2.3.2.8 First Order Linear Differential Equations
  • 2.3.2.9 Plotting the Analytical Solution
• 2.3.3 Matching the Model to Experimental Data
• 2.3.4 Assignment 3
• Markdown Figures
  • Comsol model of Temperature Control Laboratory
  • https://jckantor.github.io/cbe30338-2021/figures/Model_Data_Image.jpg
• Markdown Links
  • specific heat capacity for solids
• Figure files used
  • figures/arduino_comsol.png
  • figures/Model_Data_Image.jpg

2.4 Model Identification for the Temperature Control Lab

• 2.4.1 Accessing experimental data
  • 2.4.1.1 Read data into a Pandas DataFrame
• 2.4.2 Comparing experimental data to model predictions
• 2.4.3 Empirical Modeling
  • 2.4.3.1 First order gain and time constant
  • 2.4.3.2 First order with time delay
• 2.4.4 First order Energy balance model
• 2.4.5 Find the best fit
• 2.4.6 Second-order model
  • 2.4.6.1 Dynamics of the Heater/Sensor System
  • 2.4.6.2 Best fit
• 2.4.7 Fourth-Order Multi-Input Multi-Output Model
  • 2.4.7.1 Model derivation
  • 2.4.7.2 Standard form
• 2.4.8 Lab Assignment 2: Identification of a Multi-input, Multi-output Model for the Temperature Control Laboratory
  • 2.4.8.1 Exercise 1.
  • 2.4.8.2 Exercise 2.
  • 2.4.8.3 Exercise 3.
• Markdown Links
  • Pandas
  • data stored in a Google Sheet
  • least_squares

Chapter 3.0 Feedback Control

3.1 Case Study: Thermal Cycling for PCR

• 3.1.1 Pre-reads
• 3.1.2 Coronavirus Diagnostics
• 3.1.3 Polymerase Chain Reaction (PCR))
• 3.1.4 Examples of low-cost and open-source PCR thermal cyclers
• 3.1.5 The Challenge: Prototyping a Control System for a PCR Thermal Cycler
• 3.1.6 What will this project entail?
• Markdown Figures
  • http://media.biocompare.com/m/37/Product/239450-400x300.jpg
  • figures/B.01-FeedbackControlDiagram.png
• Markdown Links
  • Notre Dame Center for Advanced Diagnostics and Therapeutics
  • miniPCR Thermal Cycler
  • https://commons.wikimedia.org/wiki/File:Vaccines-08-00587-g002-A.png
  • https://commons.wikimedia.org/wiki/File:Polymerase_chain_reaction-en.svg
  • miniPCR Thermal Cycler
• Figure files used
  • figures/FeedbackControlDiagram.png
  • figures/B.01-FeedbackControlDiagram.png

3.2 Setpoints

• 3.2.1 Setpoint profiles
• 3.2.2 Creating setpoint functions
  • 3.2.2.1 Specifying piecewise linear setpoint profiles
  • 3.2.2.2 A functon to create functions
  • 3.2.2.3 Example of a setpoint function
  • 3.2.2.4 Creating multiple setpoint functions
• 3.2.3 Case Study: PCR Thermal Cycler Protocols
  • 3.2.3.1 Typcial PCR thermal cycler protocols
  • 3.2.3.2 Representing PCR protocols in Python
  • 3.2.3.3 Converting to ramp, soak specifications
  • 3.2.3.4 Finding the start and finish of each segment
  • 3.2.3.5 Finding the setpoint function by interpolating the start and end of each segment
  • 3.2.3.6 Creating a setpoint function for PCR thermal cycler
• Markdown Links
  • West Control Solutions: Understanding Setpoint Ramping and Ramp/Soak Temperature Control
  • Eurotherm: Ramp and Soak Applications
  • Allen-Bradley: Introduction to the Allen Bradley Ramp/Soak Controller
  • Wikipedia: Thermal Profiling
  • numpy.interp
  • nested functions

3.3 Relay Control

• 3.3.1 Relay Control for the Temperature Control Lab
• 3.3.2 Relay Control with Deadzone (Hysteresis) or Deadtime-or-Deadtime)

3.4 Implementing Controllers in Python

• 3.4.1 The problem with coding controllers as simple functions
• 3.4.2 What we seek in a controller implementation
• 3.4.3 Implementating relay control as nested function
• 3.4.4 Implementing relay control as a Python generator
  • 3.4.4.1 What is a Python generator?
  • 3.4.4.2 Coding a relay controller as a Python generator
• 3.4.5 Implementing relay control as a Python class

3.5 Practical Proportional (P) and Proportional-Integral (PI) Control

• 3.5.1 Learning Goals
• 3.5.2 Negative Feedback
• 3.5.3 Proportional Control
  • 3.5.3.1 Descripton
  • 3.5.3.2 Implementation
  • 3.5.3.3 Controller Testing
  • 3.5.3.4 Steady-State Offset
• 3.5.4 Proportional-Integral (PI) Control-Control)
  • 3.5.4.1 Position form
  • 3.5.4.2 Velocity form
• 3.5.5 Empirical Tuning Rules
• Markdown Figures
  • https://www.biologycorner.com/resources/feedback-loop-glucose.png

3.6 Lab Assignment 3: Relay and PI Control

• 3.6.1 Exercise 1. Relay (or On-Off) control-control)
• 3.6.2 Exercise 2. Implementing a PI Controller

3.7 Integral Windup and Bumpless Transfer

• 3.7.1 Learning Goals
• 3.7.2 PI Control
• 3.7.3 What is Integral Windup?
  • 3.7.3.1 Anti-reset windup - Version 1
  • 3.7.3.2 Anti-reset Windup - Version 2
  • 3.7.3.3 Anti-reset Windup - Complete
• 3.7.4 Manual Operation
• 3.7.5 Bumpless Transfer
  • 3.7.5.1 Bumpless Transfer
• Markdown Figures
  • https://jckantor.github.io/cbe30338-2021/figures/controller-coroutine.png
  • https://www.portescap.com/-/media/project/automation-specialty/portescap/portescap/products/workings-of-encoders/encoder_chart_720x450_1_0.jpg
  • https://jckantor.github.io/cbe30338-2021/figures/valve-position-feedback.png
• Figure files used
  • figures/valve-position-feedback.png
  • figures/controller-coroutine.png

3.8 Lab Assignment 4: Cascade Control

• 3.8.1 Learning Goals
• 3.8.2 Background: What is Cascade Control?
• 3.8.3 General Advice
• 3.8.4 Exercise 1. PI Control for T2 using heater Q1
• 3.8.5 Exerise 2. Cascade Control for the Temperature Control Lab
• Markdown Figures
  • https://cdn.instrumentationtools.com/wp-content/uploads/2016/03/instrumentationtools.com_single-loop-control.png
  • https://cdn.instrumentationtools.com/wp-content/uploads/2016/03/instrumentationtools.com_cascade-control.png
  • https://jckantor.github.io/cbe30338-2021/figures/cascade_control_1.png
  • https://jckantor.github.io/cbe30338-2021/figures/cascade_control_2.png
• Figure files used
  • figures/cascade_control_2.png
  • figures/cascade_control_1.png

3.9 Lab Assignment 4: Solution

• 3.9.1 Exercise 1. PI Control for T2 using Q1
  • 3.9.1.1 Step 1: Model Identification
    • 3.9.1.1.1 Step Test
    • 3.9.1.1.2 Verify data set
    • 3.9.1.1.3 Fitting FOPDT Parameters for Q1 -> T2
  • 3.9.1.2 Step 2: Controller implementation and testing
    • 3.9.1.2.1 PI Implementation
    • 3.9.1.2.2 PI Controller Tuning
  • 3.9.1.3 Step 3: Controller Testing
• 3.9.2 Exercise 2
  • 3.9.2.1 Step 1: Determining the Inner Controller
  • 3.9.2.2 Step 2: Step Testing the Inner Controller
  • 3.9.2.3 Step 3: Implement the Outer Controller
  • 3.9.2.4 Step 4: Test the Cascade Control Configuration

Chapter 4.0 Process Analytics

• 4.0.1 Learning Goals
  • 4.0.1.1 Process Historians
  • 4.0.1.2 State-Space Models
  • 4.0.1.3 State Estimation
• Markdown Figures
  • ./figures/state_estimation_1.png
  • ./figures/state_estimation_2.png
• Figure files used
  • figures/state_estimation_2.png
  • figures/state_estimation_1.png

4.1 Data/Process/Operational Historian

• 4.1.1 Introduction
  • 4.1.1.1 Terminology
  • 4.1.1.2 Major Vendors of Data Historians
  • 4.1.1.3 Example: OSIsoft PI System
  • 4.1.1.4 Process Analytics
• 4.1.2 The tclab Data Historian
  • 4.1.2.1 Data Logging
    • 4.1.2.1.1 Creating a log
    • 4.1.2.1.2 Accessing Data using .columns and .fields
    • 4.1.2.1.3 Accessing Data by Name logdict
    • 4.1.2.1.4 Accessing Data using pandas
    • 4.1.2.1.5 Specifying additional sources
  • 4.1.2.2 Persistence
    • 4.1.2.2.1 Saving to a file
• 4.1.3 Plotter
• Markdown Figures
  • http://www.automatedresults.com/images/arpidiagram.png
• Markdown Links
  • Historian
  • Plotter
  • SQLite

4.2 State Estimation

• 4.2.1 Output Feedback Control
• 4.2.2 The Trouble with Output Feedback
• 4.2.3 Heater/Sensor Model
• 4.2.4 Converting to a State-Space Model
• 4.2.5 Model Predictions
• 4.2.6 The Trouble with Model Predictions
  • 4.2.6.1 Issue 1: Heater temperature is markedly different from the sensor temperature.
  • 4.2.6.2 Issue 2: The model may not be an accurate predictor of temperatures.
• 4.2.7 Incorporating Measurements
  • 4.2.7.1 Fun with Eigenvalues
  • 4.2.7.2 Model Prediction / Measurement Correction
• 4.2.8 State Estimation and Closed-Loop Relay Control
• Markdown Figures
  • figures/FeedbackControlDiagram2.png
• Figure files used
  • figures/FeedbackControlDiagram2.png

4.3 Lab Assignment 5: State Estimation

- [4.3.1 Step 1. Estimate model parameters](https://jckantor.github.io/cbe30338-2021/04.03-Lab-Assigment-State-Estimation.html#4.3.1-Step-1.-Estimate-model-parameters)
- [4.3.2 Step 2. Create state-space model](https://jckantor.github.io/cbe30338-2021/04.03-Lab-Assigment-State-Estimation.html#4.3.2-Step-2.-Create-state-space-model)
- [4.3.3 Step 3. Implement a state estimator](https://jckantor.github.io/cbe30338-2021/04.03-Lab-Assigment-State-Estimation.html#4.3.3-Step-3.-Implement-a-state-estimator)
- [4.3.4 Step 4. Implement relay control for the heater temperatures T1H and T2H](https://jckantor.github.io/cbe30338-2021/04.03-Lab-Assigment-State-Estimation.html#4.3.4-Step-4.-Implement-relay-control-for-the-heater-temperatures-T1H-and-T2H)

4.4 Anomaly Detection

4.4 Estimation and Anamoly Detection

• 4.4.1 State-Space Model
  • 4.4.1.1 Prediction and Correction
• 4.4.2 Testing
• 4.4.3 Choosing L
• 4.4.4 Eigenvalues
• Markdown Figures
  • figures/FeedbackControlDiagram2.png
• Figure files used
  • figures/FeedbackControlDiagram2.png

4.6 Lab Assignment 6: Anomaly Detection

• 4.6.1 Part 1. Determing the Observer Gains $L$
  • 4.6.1.1 State Space Model
  • 4.6.1.2 Observer
  • 4.6.1.3 Testing the Observer
  • 4.6.1.4 Eigenvalues and Eigenvectors
  • 4.6.1.5 Placing the eigenvalues of $A-LC$
  • 4.6.1.6 Exercise 1.
• 4.6.2 Part 2. Estimating Disturbances
  • 4.6.2.1 Testing Disturbance Estimator
  • 4.6.2.2 Exercise 2.

4.7 Observer Synthesis using Linear Matrix Inequalities

• 4.7.1 References
• 4.7.2 Model Parameters
• 4.7.3 Lyapunov Design
• 4.7.4 CVXPY
• 4.7.5 $\cal{H}_2$ Optimal State Estimation
• 4.7.6 $\cal{H}_{\infty}$ Optimal State Estimation
• Markdown Links
  • Linear matrix inequalities in system and control theory.
  • "Lmi properties and applications in systems, stability, and control theory."

4.8 Application of Luenberger Observers to Environmental Modeling of Rivers

• 4.8.1 Model
• 4.8.2 State Space Model
• Markdown Links
  • https://www.mdpi.com/2297-8747/25/3/44

Chapter 5.0 Optimization

5.1 Linear Production Model

• 5.1.1 Example: Production Plan for a Single Product Plant
  • 5.1.1.1 Mathematical Model
  • 5.1.1.2 Exercises
• 5.1.2 Production Plan: Product Y
  • 5.1.2.1 Exercises
• 5.1.3 Production Plan: Mixed Product Strategy
• 5.1.4 Solution using CVXPY
• 5.1.5 Solution using scipy.optimize.linprog
• 5.1.6 What are the active constraints?
• 5.1.7 What is the incremental value of labor?
  • 5.1.7.1 Exercise
• 5.1.8 Theory of Constraints
• Markdown Figures
  • LP_ProductX.png
  • LP_ProductY.png
  • LP_ProductXY.png
• Markdown Links
  • Pyomo
  • glpk
  • CVXPY
  • scipy.optimize library
• Figure files used
  • figures/LP_ProductXY.png
  • figures/LP_ProductX.png
  • figures/LP_ProductY.png
  • figures/LPprob01.png

5.2 Linear Blending Problems

- [5.2.1 Learning Goals](https://jckantor.github.io/cbe30338-2021/05.02-Linear-Blending-Problem.html#5.2.1-Learning-Goals)

• 5.2.1 Problem Statement (Jenchura, 2017))
• 5.2.2 Solving optimization problems with CVXPY
  • 5.2.2.1 Step 1. Coding Problem Data as a Python Dictionary
  • 5.2.2.2 Step 2. Identifying index sets
  • 5.2.2.3 Step 3. Create decision variables
  • 5.2.2.4 Step 4. Objective Function
  • 5.2.2.5 Step 5. Constraints
    • 5.2.2.5.1 Volume Constraint
    • 5.2.2.5.2 Product Composition Constraint
  • 5.2.2.6 Step 6. Create CVXPY Problem object
  • 5.2.2.7 Step 7. Display solution
• 5.2.3 Parametric Studies
  • 5.2.3.1 Consolidating
  • 5.2.3.2 Optimal blend as a function of product specification

5.3 Homework Assignment 4

• 5.3.1 Exercise 1. Getting Started
  • 5.3.1.1 Solution
• 5.3.2 Exercise 2. Incorporating Constraints
• 5.3.3 Exercise 3. Sensitivity Analysis

5.4 Gasoline Blending

• 5.4.1 Gasoline Product Specifications
• 5.4.2 Stream Specifications
• 5.4.3 Blending Model
• 5.4.4 Display Results
  • 5.4.4.1 Results for each Stream
  • 5.4.4.2 Results for each Product
• 5.4.5 Exercise 1.
• 5.4.6 Exercise 2.
• 5.4.7 Exercise 3.
• Tags: exercise

5.5 Linear Programming

• 5.5.1 Matrix/Vector format
• 5.5.2 Example 19.3: Refinery Blending Problem

5.6 Design of a Cold Weather Fuel

• 5.6.1 Data
• 5.6.2 Denatured Alcohol
• 5.6.3 Cold Weather Product Requirements
• 5.6.4 Optimization Model
• 5.6.5 Display Composition
• Markdown Figures
  • ./figures/alcohol_stove.jpeg
• Markdown Links
  • manufacturer's product
• Figure files used
  • figures/alcohol_stove.jpeg

5.98 Linear Production Model in Pyomo

• 5.98.1 Installation
  • 5.98.1.1 Anaconda
  • 5.98.1.2 Google Colab
• 5.98.2 Algebraic Modeling Languages
• 5.98.3 Key Concepts in Pyomo
• 5.98.4 Example: Linear Production Model with Constraints
  • 5.98.4.1 Step 1. Import Pyomo.
  • 5.98.4.2 Step 2. Create the model object.
  • 5.98.4.3 Step 3. Add the Decision Variables, Objective, and Constraints to the model object.
  • 5.98.4.4 Step 4. Create a solver object and solve.
  • 5.98.4.5 Step 5. Display the solution.
• 5.98.5 Python Lists, Sets, Dictionaries, and Iterators
  • 5.98.5.1 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

5.99 Pyomo Examples

• 5.99.1 Pyomo Model
• 5.99.2 Example: Nonlinear Optimization of Series Reaction in a Continuous Stirred Tank Reactor
• 5.99.3 Example 19.3: Linear Programming Refinery
• 5.99.4 Example: Making Change
• 5.99.5 Example: Linear Production Model with Constraints with Duals

Chapter 6.0 Predictive Control

6.1 Static Operability

- [6.1.1 State Space Model](https://jckantor.github.io/cbe30338-2021/06.01-Static-Operability.html#6.1.1-State-Space-Model)

• 6.1.1 Steady State Operability
• 6.1.2 Steady State Model
  • 6.1.2.1 Steady-State input constraints
  • 6.1.2.2 Steady-State output constraints
  • 6.1.2.3 Steady-State setpoint targets or ranges
• 6.1.3 CVXPY Solution
  • 6.1.3.1 Imports
  • 6.1.3.2 Model Parameters
  • 6.1.3.3 CVXPY Model
• 6.1.4 Lab Assigment 7
  • 6.1.4.1 Exercise 1.

6.2 Simulation and Open-Loop Optimal Control

• 6.2.1 Heater Model
  • 6.2.1.1 Model
  • 6.2.1.2 Parameter Values
• 6.2.2 The Control Problem
  • 6.2.2.1 Reference Tractory
  • 6.2.2.2 Guessing a Solution
• 6.2.3 Simulation
• 6.2.4 Feedforward Optimal Control
• 6.2.5 Lab Assignment 8
  • 6.2.5.1 Exercise 1
  • 6.2.5.2 Exercise 2
  • 6.2.5.3 Exercise 3

6.3 Predictive Control

- [6.3.1 Model](https://jckantor.github.io/cbe30338-2021/06.03-Predictive-Control.html#6.3.1-Model)

• 6.3.1 Feedforward Optimal Control
• 6.3.2 Assumptions for Predictive Control
• 6.3.3 TCLab Event Loop
• 6.3.4 What we need our predictive controller to do ...

6.4 Implementing Predictive Control

• 6.4.1 Model
• 6.4.2 Control Objective
• 6.4.3 Assumptions Need to Use Optimization for Real-Time Feedback
• 6.4.4 Bare Bones Event Loop
  • 6.4.4.1 Relay Control
  • 6.4.4.2 Observer
• 6.4.5 Feedforward Optimization
  • 6.4.5.1 A Predictive Controller
• 6.4.6 Testing the Predictive Controller
• 6.4.7 Lab Assignment 9
  • 6.4.7.1 Exercise 1. Improving the Predictive Controller
  • 6.4.7.2 Exercise 2. Predictive control of the four state model.
  • 6.4.7.3 Exercise 3. Putting it all together.
  • 6.4.7.4 Exercise 4. Do something nice for yourself.

6.5 Quiz Review for Chapters 5 and 6

• 6.5.1 Material covered
• 6.5.2 Learning Goals
• 6.5.3 Exercises

Chapter 7.0 Discrete Event Systems

7.1 Introduction to Simpy

• 7.1.1 Creating a simulation environment
• 7.1.2 Creating simulation processes
• 7.1.3 Events
• 7.1.4 Ready to Roomba
• 7.1.5 Chemotaxis
• Markdown Links
  • Simpy

7.2 Agent Based Models

• 7.2.1 Simpy: What we have learned so far
• 7.2.2 3.3.2 Example: A room full of Roombas
• 7.2.3 One Roomba
• 7.2.4 Processing the data log with Pandas
  • 7.2.4.1 Convert nested list to a Pandas Dataframe
  • 7.2.4.2 Aggregating data with pivot tables
• 7.2.5 Adding the full complement of Roombas
  • 7.2.5.1 Gantt Charts
• 7.2.6 Charging stations as shared resources
• 7.2.7 How many charging stations are required?
• 7.2.8 Adding a reporter process
• Markdown Figures
  • roomba

7.3 Chemotaxis

• 7.3.1 Simulation with Simpy
• Markdown Links
  • Chemotaxis
  • See, for example.
  • Brown and Berg (1974)
  • a

7.4 Batch Chemical Process

• 7.4.1 Problem Statement
• 7.4.2 Analysis
• 7.4.3 Simpy Shared Resources
• 7.4.4 Generating Customer Orders
• 7.4.5 Order Processor
• 7.4.6 Analysis
• 7.4.7 Completed Model
• 7.4.8 Tuning the process
• Markdown Figures
  • Batch Process
• Markdown Links
  • Resources
  • Containers
  • Stores
• Figure files used
  • figures/BatchProcess.png

7.5 Simulating Queuing Systems

• 7.5.1 Examples of Queues
  • 7.5.1.1 Service Lines
• 7.5.2 Concepts
  • 7.5.2.1 Nomenclature
  • 7.5.2.2 Service Disciplines (of many possibilities))
• 7.5.3 Poisson Process
  • 7.5.3.1 Poisson distribution
  • 7.5.3.2 Waiting time between events
• 7.5.4 Simulating a Poisson Process in SimPy
• 7.5.5 Kendall notation for queues
• 7.5.6 Example: Simulation of an Order Processing Queue
• 7.5.7 Batch Processing Example (NEEDS REWORK))
• 7.5.8 Processing the Simulation Log
• Markdown Figures
  • mathworks queue
  • Aircraft queue
  • Call Center
  • Batch Process
• Markdown Links
  • Tesla China - Shanghai Gigafactory production line
  • Store
• Figure files used
  • figures/BatchProcess.png

Chapter 8.0 Projects

Appendix A. A.0 Appendices

A.1 Animation in Jupyter Notebooks

• A.1.1 Summary
• A.1.2 Prerequisites
• A.1.3 Step-by-Step Approach to Animation with Matplotlib
  • A.1.3.1 Step 1. Create the background frame.
  • A.1.3.2 Step 2. Define a function to draw each frame
  • A.1.3.3 Step 3. Create the Animation Object
  • A.1.3.4 Step 4. Render the Animation
• A.1.4 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