Course: BIOEN 336: Bioengineering Systems and Control

Credits: 3

Instructor: Herbert Sauro

Texts and Supplemental Materials:  Course Text Book – Control Theory for Biologists 1.21 (1507) has been developed by Dr. Sauro and is available to students enrolled in the course in pdf form.  Other Text Books for Reference:  Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based Introduction by Semmlow and Feedback Systems An Intro for Scientists and Engineers by Astrom and Murray.  Teaching videos have also been created by Dr. Sauro and are available at http://sys-bio.org/tutorials-and-books/

UW Catalog Description: Reviews linear and nonlinear systems analysis and control system design and biological and medical applications.

Instructor Overview: The course gives an introduction to linear and non-linear systems analysis and control systems with biological and medical applications. The class starts with an introduction to modeling with examples taken from physiological, (bio)chemical, fluidic and electrical systems. The course then continues with a more general study of linear and non-linear systems using ordinary differential equations that includes for example a study of numerical methods, software applications, transfer functions, feedback control, transient and steady state responses, phase portraits, system linearization and chaotic systems. The course is motivated with examples taken from biochemical control, synthetic biology and physiological systems.

Prerequisites by Course: BIOEN 327; either MATH 136, MATH 308, or AMATH 352

Required or Elective: Required

Course Schedule:  Two 80-min. lecture periods per week (TR).

Computer Use:  Requires word-processing software for preparing homework assignments and the final report, and on-line access to communicate via email and download materials from the course web site.  Access to electronic journal databases, such as PubMed, will be provided through the University of Washington on-line network while on campus or via the healthlinks.washington.edu remote server or the BIOEN student terminal server when a student is off-campus.  Use of simulation software including Matlab and specialized tools such as Jarnac.

Course Grading:

  • 30%     Assignments (4 assignments total; a detailed description of each assignment will be posted on the course website)
  • 20%     Speed Quiz (4 speed quizzes in total)
  • 25%     Mid Term Exam
  • 25%     Final Comprehensive Exam

Course Outcomes and Assessment:  This course presents, through bi-weekly class meetings an opportunity for students to explore a variety of analytical and numerical methods to solve bioengineering problems and the techniques used to address them.  As such, this course addresses certain ABET outcome criteria at a variety of levels.

Specific Outcomes: By the end of this course, students should be able to:

  1. Recast a range of biological problems (involving biochemistry, fluid mechanics, mechanics, electricity and physiology) into linear or nonlinear quantitative ordinary differential equation models.
  2. Choose and apply appropriate analytical and numerical tools to solve ordinary differential equation models of biological problems.
  3. Understand, predict and interpret the biological significance of linear and nonlinear control systems.
  4. Identify systems models that fit experimental data. (Performs systems identification and parameter estimation.)

Outcomes Addressed by this Course:

A. An ability to apply knowledge of mathematics, science, and engineering.

  • Linearize a non-linear model and derive its frequency response.

E. An ability to identify, formulate, and solve engineering problems.

  • Formulate a system with negative feedback and analyze the system to understand the effect of negative feedback on the system.

L. An understanding of biology and physiology.

  • Identify parts of a gene regulatory network.

M.  The capability to apply advanced mathematics (including differential equations and statistics), science, and engineering to solve the problems at the interface of engineering and biology.

  • Determine the stability criterion for a genetic circuit with positive feedback using Laplace transforms.

Relationship of Course to Program Educational Objectives:

The course provides students with an introduction to linear and non-linear systems analysis and control systems with biological and medical applications. Students are introduced to modeling approaches using examples taken from physiological, (bio)chemical, fluidic and electrical systems. This variety helps motivate and engage the students, laying the foundation for potential future studies and/or employment in a related area.  The course then continues with a more general study of linear and non-linear systems using ordinary differential equations that includes for example a study of numerical methods, software applications, transfer functions, feedback control, transient and steady state responses, phase portraits, system linearization and chaotic systems. In teaching these concepts, this course incorporates examples taken from biochemical control, synthetic biology and physiological systems.  As such, students learn the terminology and procedures from a wide variety of science and engineering disciplines which will be useful in their future endeavors.  Thus, BIOEN 336 contributes to providing students with the tools necessary to reach the following Program Educational Objectives:

  1. Earn advanced degrees and/or obtain employment in bioengineering-related fields, such as medicine, device development, or biotechnology.
  2. Advance their careers by obtaining appropriate educational and professional qualifications.
  3. Contribute to responsible development of new technical knowledge.

Topics Covered:

  1. Modeling
  2. Electrical, fluid, mechanical and chemical models
  3. Numerical methods
  4. Laplace transforms
  5. Linearization
  6. Solutions to differential equations
  7. Signals
  8. Frequency response
  9. Negative feedback including instability
  10. PID Controller
  11. Understanding systems in terms of component parts
  12. Positive feedback and instability

Course Schedule:

Week Topics
1 Introduction to Systems Theory
2 Model Behavior and Examples
3 The Mathematics of Continuous/Deterministic Systems
4 Computer Modeling and Visualization Techniques
5 Introduction to Feedback Control
6 PID Control and Reverse Engineering Techniques
7 Fundamental Aspects of Control in Biochemical Systems
8 Linear, Branched, Feedback, Feed forward and Amplifier Systems
9 Oscillators, Bistability and Other Emergent Behaviors
10 Nonlinear Systems: Chaos and other Exotic Behavior

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