Spring 2020 Assignment 9

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20.309: Biological Instrumentation and Measurement

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Signals and systems


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Fill out the table below. Match each system function with its Bode magnitude and phase plot, step response, and pole zero diagram. (Write one letter A-E in each box below.) In the row labeled “Description,” write a descriptive name of each system, such as “low-pass filter” or “overdamped second-order system.”


System function $ \frac{1}{s+1} $ $ \frac{s}{s+1} $ $ \frac{s}{s^2+2s+1} $ $ \frac{s}{s^2+0.1s+1} $ $ \frac{1}{s^2+10s+1} $
Magnitude plot
Phase plot
Step response
Pole/zero plot
Description

Magnitude Plots

Transfer function matching magnitude plots.png

Phase Plots

Transfer function matching phase plots.png

Step Response Plots

Transfer function matching step response plots.png

Pole Zero Plots

Transfer function matching pole zero plots.png

Feedback systems


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  • Find the transfer function H ̂(s)=(V ̂_out (s))/(V ̂_in (s)) of the circuit shown below, assuming L = 1 H and R = 1Ω.
  • Plot the poles and zeros of H ̂(s) on the axes below using x’s for poles and o’s for zeroes.
  • The circuit from Figure 1 is placed in a feedback system, as shown in the block diagram below. The triangle represents an amplifier with gain G that does not depend on frequency. Find the transfer function of the feedback system $ \hat{F}(s)=(\hat{Y}(s))/(\hat{X}(s)). $
  • Plot the poles and zeros of $ \hat{F}(s) $ for G=1,9,and 19. Label the gain value for each point.</math>


LR Low Pass Filter for S20 Assignment 9.png Feedback System Block Diagram for S20 Assignment 9.png

The Frequency Dependence of Osmo-Adaptation in Saccharomyces cerevisiae

Read The Frequency Dependence of Osmo-Adaptation in Saccharomyces cerevisiae and the supporting information.. This paper will be the focus of exam 2. We will discuss the paper and the supporting information on Thursday and Friday.


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Answer the following questions about The Frequency Dependence of Osmo-Adaptation in S. cerevisiae:

  1. What is the primary mechanism by which S. cerevisiae recovers from hyperosmotic shock?
  2. What model did Mettetal, et. al. use for Hog1 activation in response to a hyperosmotic shock?
  3. Mettetal, et. al. found that that the hyperosmotic shock response of wild-type yeast was (choose one): underdamped, critically damped, or overdamped.
  4. The response of the mutant (low Pbs) yeast was (choose one): underdamped, critically damped, or overdamped.
  5. In the plot below, indicate which step response corresponds to the wild-type strain and the mutant strain.
  6. Mettetal yeast model step response.png

    f) Indicate which of the pole zero diagrams below corresponds to the wild-type strain and the mutant strain. g) Indicate which curve in the Bode plots below corresponds to the wild-type strain and the mutant strain. </div>




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Our goal for assignment 10 is to reproduce the bode plot in the paper (Figure 2 B and C), and fit it to a model second-order system. We will only measure the 'wild type' yeast strain, since measuring the mutant would take too much time.

  1. What mathematical model did Mettetal, et. al. use for the yeast response network? Express the model in the following forms: transfer function (TF), poles and zeros (ZPK), single differential equation (SDE), and coupled differential equations (CDE). Express the TF, SDE, and ZPK models in terms of the undamped natural frequency, $ \omega_0 $, damping ratio $ \zeta $, and/or damped natural frequency $ \omega_D $.
  2. Find an expression for the step response and plot it over a range of values of $ \omega_0 $ and $ \zeta $. A hand-drawn plot is fine, but you should probably look into MATLAB's step function.
  3. Plot the frequency response (i.e. make a Bode plot) of the system over a range of $ \omega_0 $ and $ \zeta $ values that includes over damped, critically damped, and under damped.
  4. What are two questions that you have about the paper's methodology or how we're going to implement the experiment in 20.309?




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Turn in all your MATLAB code in pdf format. No need to include functions that you used but did not modify.


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