**Start Date for Winter Term: **January 7th 2014 (Ends March 15th)

**Location: **PAA A114 (Physics)

**When: **Tuesdays and Thursdays: 1.00 to 2.20 pm

**Office Hours: **

#### Here is the current office hours schedule:

Anh: Monday 11:30 AM – 12:30 PM

#### Cara: Friday 9:30-10:30 AM

#### Office hours will be held in the 4th floor common area.

#### If you cannot make it, feel free to email us and we will do our best to return your questions as soon as possible.

**Graders:** Cara Comfort and Anh Ta

**Class mailing list:** bioen336a_wi14@uw.edu

**Overview of course:**

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.

### Teaching Style

The individual lecture periods are a little long and are also over lunch break – the worst of two worlds. The teaching style for this class will therefore be a little different. If you wish you can bring your lunch with you to class. To break up the time, the class will be made up of segments of lecture and group exercises. Groups should be no more than three people and the exercises may involve problem solving, math problems or simulation on your personal computer. To make up for lost lecture time, online videos will also be posted for to watch as homework. The videos will be a combination of new videos and existing videos from the internet. The first ten minutes or so of every Tuesday will be reserved for a speed quiz which will be graded. There will be the usual mid term and final project at the end of term.

### Brief Syllabus Summary:

Week | Topics |

1 | Introduction to Modeling, Simulation Software, LaTeX (Chap 1, 2) |

2 | Introduction to Feedback Control, Biological Networks (Chap 3, 4) |

3 | The Steady State and Inputs to System (Chap 5, 6) |

4 | Linear Systems, State Space Representation (Chap 7, 8) |

5 | Response of Linear Systems, Laplace Transform (Chap 9, 10) |

6 | Laplace Transforms, Cellular Networks, (Chap 10, 11) |

7 | Frequency Response, Scaled Transfer Functions (Chap 12, 13, 14) |

8 | Stability, Negative Feedback (Chap 15, 16) |

9 | Oscillators, Bistability (Chap 17, 18) |

10 | Nonlinear Systems: Chaos and other Exotic Behavior |

#### A more detail syllabus is given here Syllabus for 336 Bioengineering (v1.4)

### Course Text Book

Control Theory for Bioengineers 0.57 (933)**Other Text Books for Reference:**

Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based Introduction by Semmlow

This is has a reasonable straightforward introduction to linear control systems but the author places much emphasis on electrical systems.

Feedback Systems An Intro for Scientists and Engineers (Astrom and Murray)

This book offer a nice introduction to linear control systems and feedback specifically for scientists and engineers. It comes with examples taken from different areas include some biological. This book is also available for** free** in PDF format.

**Week 1**

- Videos:
- MONIAC
- Actual Moniac in Operation
- Cartoon version of the MONIAC
- Wikipedia Page on the MONIAC
- Antikythera Mechanism
- Nature Video
- Optional Nature Paper
- Electric Models
- Electricity Refresher
- RC Circuits: The Differentiator
- RC Circuits: The Integrator
- Op Amp Circuit Analysis: Non-Inverting Amplifier

**Assignment 1: Go over Chapter 2; Answer questions: 1, 2, 3, 5, 7 in Chapter 1;**

Answer must be handed in using old fashioned paper. Can be handwritten, Word, LaTeX or other word processing software.

**Week 2**

Chapter 3 and 4 in text book

**Assignment 2: Answer questions 1, 2, 3, 4 in Chapter 3; questions 1, 2, 4, 7, 9 in Chapter 4**

**Week 3**

**Assignment 3: Answer questions 1, 3, 4, 5, 6, 7 in Chapter 5; questions 1, 2, 3, 4, 5 in Chapter 6**

**Week 4**

- Simple Example of Evaluating a Transform (8 mins)
- Impulse Function
- Unit Step and Delta Function
- Sinusoidals

**Week 6**

**Midterm Topics:**

- Chapter 1 on Models
- Chapter 3: Intro to negative feedback
- Chapter 4: Biological Networks and Kinetics
- Chapter 5: Steady states
- Chapter 6: System Inputs
- Chapter 7: Linear Systems
- Chapter 8: State Space Representation
- Chapter 9: Response of Linear Systems
- Chapter 10: Laplace Transforms
- Chapter 11: Zero-State Response

**LaTeX Online Tools:**

**Week 7**

**Week 8**

- Paper: A Frequency Domain Approach to Sensitivity Analysis of Biochemical Networks
- PID Controller Demo (For Windows)

**Assignment 8**

**Week 9**

QUIZ: Chapters 16 and 17

- Phase Portrait Viewer from the d’Arbeloff Interactive Math Project – requires Java installed
- Wolfram Phase Portrait Viewer – required Msathematica CDF Installed
- Programmable Interactive Simulator (DField and PPlane) – requires Java (Matlab version also available I believe)

** Final Assignments:**

**Week 10**

More complex systems: Chaos and non linear systems

**Honors Project (To be updated)**

**Grading:**

25% Midterm

25% End of Term Project

20% Quizes

30% Homework