BIOEN 336

Start Date for Winter Term: January 3rd 2012

Location: MOR 220

When: Tuesdays and Thursdays: 12.00 to 1.20 pm

Office Hours: 2pm to 4pm Thursday

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 Thursday will be reserved for a speed quiz which will be graded. There will be the usual mid term and final end of term exam.

Brief Syllabus Summary:

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

A more detail syllabus is given here Syllabus for 336 Bioengineering (v1.2)

Course Materials

Possible 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 and 2

Class Exercises (Now homework)
Notes for Week 1 and 2 - Introduction to Modeling
 

Laplace Transform Review Video:

Week 3

  • Assignment below (also given in first-order document above) – due next Thursday (26th of January)

Consider the following two species biochemical pathway, v_o, k_1, k_2 are parameters, y_1 and y_2 variables:

    \[\xrightarrow{v_o} y_1 \xrightarrow{k_1\ y_1} y_2 \xrightarrow{k_2\ y_2}\]

with ODEs:

    \begin{align*}\frac{dy_1}{dt} &= v_o - k_1 y_1 \\[8pt]\frac{dy_2}{dt} &= k_1 y_1 - k_2 y_2\end{align*}

Derive the free, forced and full Laplace and time-domain solutions for this system for both variables, y_1 and y_2 in response to a step function in v_o.

Week 4

  • The big Assignment <- This was updated on Feb 6 at 12.50pm (Correction to question 7c, input function no longer discontinuous)
Reading material from Astrom and Murray’s book on Feedback systems:
 
Page 34-35 : State Space Models
Chapter  4 (Dynamic Behavior), 5 (Linear Systems),  8 (Transfer Function)
 

 Week 5

No Speed Quiz this week 

 Week 6

No Speed Quiz this week 


 

 

 

 

 

Mid Term Exam on Thursday: 9th of February

A crib sheet in the form of a double sided letter page is permitted in the midterm.

Mid Term Topics

1. Different kinds of modeling approaches, mathematical and non-mathematical
2. Different ways of implement a model and obtaining solutions
3. The purpose of a model, what is a model?
4. Defining the parameters and state variables in a model
5. Electrical models and analog computers
6. Linear and nonlinear models
7. Linearization
8. Review of Laplace transforms to solve ODEs
9. System states: Equilibrium, steady state and transient states
10. Effects of different kinds of perturbations (state variables and parameters)
11. Signal types
12. State space representation
13. Linearization yields the state space model
14. Laplace transform of the state space model
15. Transfer functions
16. Free and forced responses
17. The free response and the transfer function
18. Solution to dx/dt = A x in terms of exponentials and relation to stability 
19. Simple first-order systems
20. Visualization: Phase protraits, nullclines and bifurcation plots 
21. Numerical methods for ODEs and solving nonlinear equations, f(x) = 0 
22. Feedback Control, benefits and costs
23. Frequency Response and Bode plots
24. Phase shifts and onset of instability in feedback systems 

Week 7

The following plot shows the distribution of scores from the midterm exam.
The highest score was about 85%
 
 

  Week 8

No speed quiz this week

Assignments:

Watch the following videos, there will be a speed quiz next Tuesday (28th Feb) :

The Impulse Signal
Introduction to Convolution
Video on computing the convolution for a given function
Also see notes from week 5 on Transfer Function and Convolution

Introduction to Small Signal Analysis of Networks (0.92)

Week 9

Speed quiz this week on convolution

Practice Exercises (v1.15,  includes solutions)

Week 10

An introduction to some of the behaviors exhibited by nonlinear systems

Week 11

Possible project instead of Exam - by a very narrow margin, the exam is the preferred option.

Final Exam: March 15, 2012,1030-1220, MOR 220 

Grading:

25% Midterm
25% Comprehensive Final Exam
20% Speed Quiz
30% Homework

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