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Welcome to the University of Michigan Chemical Engineering Process Dynamics and Controls Open Textbook.
This electronic textbook is a student-contributed open-source text covering the materials used at Michigan in our senior level controls course.

Follow this link to find more information about this course.

Iif you would like to suggest changes to these pages, please email .

Click here for the 2007 version and here for the 2006 version of the text.


Recorded video lectures by Prof. Peter Woolf, and lecture materials for the course, are freely available online.


These lectures are available here.

Chemical Process Dynamics and Controls Text


Process Control Introduction


  1. Introduction to Controls: Background and design methodology
  2. Introduction to DCS: Control system hardware
  3. Current Significance: Process controls and you
  4. Failures in Process Control: Bhopal, Three Mile Island
  5. Process Controls in Everyday Life: Applying process control thinking to everyday situations.

Modeling Basics

  1. Verbal modeling: process description, control specifications, and connections
  2. Degrees of Freedom: importance, calculation procedure, and examples
  3. Incidence graphs: interpretations, consistency, and inconsistency
  4. Excel modeling: logical models, optimization with solver for nonlinear regression, sampling random numbers
  5. Noise modeling: more detailed information on noise modeling: white, pink, and brown noise, pops and crackles
  6. Numerical ODE solving in Excel: Euler’s method, Runge Kutta, Dead time in ODE solving
  7. Solving ODEs with Mathematica: How to find numerical and analytical solutions to ODEs with Mathematica
  8. Fitting ODE parameters to data using Excel: Using regression to fit complex models in Excel
  9. Helpful Mathematica Syntax: Hints on how to use Mathematica to model chemical processes

Sensors and Actuators

  1. Control Systems: Measurement devices
  2. Temperature sensors
  3. Pressure sensors
  4. Level sensors
  5. Flow sensors
  6. Composition sensors
  7. pH and viscosity sensors
  8. Miscellaneous sensors
  9. Valves: types, kinds, and selection
  10. Valves: modeling dynamics

More information on sensors and actuators at ECOSSE

Piping and Instrumentation Diagrams

  1. P&ID general information
  2. P&ID standard notation
  3. P&ID standard structures, location of features
  4. P&ID standard pitfalls
  5. Safety features in P&ID
  6. Regulatory Agencies and Compliance

Logical Modeling

  1. Boolean models: truth tables and state transition diagrams
  2. Logical control programs: IF.. THEN.., WHILE..

Modeling Case Studies

  1. Surge tank model
  2. Heated surge tank see also ECOSSE
  3. Bacterial chemostat
  4. ODE & Excel CSTR model w/ heat exchange
  5. ODE & Excel model of a simple distillation column
  6. ODE & Excel model of a heat exchanger
  7. ODE & Excel model of an adiabatic PFR
  8. Cruise control for an electric vehicle
  9. Blood Glucose Control in Diabetic Patients

More information on chemical process modeling in general at ECOSSE example 1 and ECOSSE example 2

Chemical Process Controls

Mathematics for Control Systems

  1. Dirac delta (impulse) function (10/09)
  2. First-order differential equations (12/14/09)
  3. Second-order differential equations (10/13)
  4. Taylor Series
  5. Laplace Transforms


  1. Optimization
  2. Linear Optimization
  3. Non-linear Optimization

PID control

  1. Constructing Block Diagrams: Visualizing control measurements
  2. P, I, D, PI, PD, and PID control see also ECOSSE
  3. PID tuning via classical methods See also ECOSSE
  4. PID tuning via Frequency Response w/ Bode Plots
  5. PID tuning via optimization
  6. PID downsides and solutions See also ECOSSE

Dynamical Systems Analysis

  1. Finding fixed points in ODEs and Boolean models
  2. Linearizing ODEs
  3. Eigenvalues and Eigenvectors
  4. Using eigenvalues and eigenvectors to find stability and solve ODEs
  5. Phase plane analysis: attractors, spirals, limit cycles
  6. Root locus plots: effect of tuning
  7. Routh stability: ranges of parameter values that are stable

Control Architectures

  1. Feedback control: What is it? When useful? When not? Common usage.
  2. Feed forward control: What is it? When useful? When not? Common usage. see also ECOSSE
  3. Cascade control: What is it? When useful? When not? Common usage.
  4. Ratio control: What is it? When useful? When not? Common usage.
  5. Summary: Summary on Control Architectures' philosophies, advantages, and disadvantages.
  6. Common control loops / model for liquid pressure and liquid level see also ECOSSE
  7. Common control loops / model for temperature control
  8. Common control architectures / model for reactors

MIMO Control

  1. Determining if a system can be decoupled
  2. MIMO control using RGA see also ECOSSE
  3. MIMO using model predictive control
  4. Neural Networks for automatic model construction
  5. Understanding MIMO Control Through Two Tanks Interaction

Statistical Analysis for Chemical Process Control

Statistics and Probability Background

  1. Basic statistics: mean, median, average, standard deviation, z-scores, and p-value
  2. SPC: Basic Control Charts: Theory and Construction, Sample Size, X-Bar, R charts, S charts
  3. Six Sigma: What is it and what does it mean?
  4. Bayes Rule, conditional probability, independence
  5. Bayesian network theory
  6. Learning and analyzing Bayesian networks with Genie
  7. Occasionally dishonest casino?: Markov chains and hidden Markov models
  8. Continuous Distributions: normal and exponential
  9. Discrete Distributions: hypergeometric, binomial, and poisson
  10. Multinomial distributions
  11. Comparisons of two means
  12. Factor analysis and ANOVA
  13. Correlation and mutual information
  14. Random sampling from a stationary Gaussian process

Design of Experiments

  1. Design of experiments via Taguchi methods: orthogonal arrays
  2. Design of experiments via factorial designs
  3. Design of experiments via random design
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