# Difference between revisions of "Spring 2020 Assignment 9"

20.309: Biological Instrumentation and Measurement

## Signals and systems 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

Phase Plots

Step Response Plots

Pole Zero Plots

## Feedback systems 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.[/itex]

## 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. Answer the following questions about The Frequency Dependence of Osmo-Adaptation in S. cerevisiae: What is the primary mechanism by which S. cerevisiae recovers from hyperosmotic shock? What mathematical model did Mettetal, et. al. use for Hog1 activation in response to a hyperosmotic shock? 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 $\omega_D$. What model did Mettetal, et. al. use for 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. 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. Mettetal, et. al. found that that the hyperosmotic shock response of wild-type yeast was (choose one): underdamped, critically damped, or overdamped. The response of the mutant (low Pbs) yeast was (choose one): underdamped, critically damped, or overdamped. Which of the step responses below corresponds to Mettetal's model for the wild-type strain and the mutant strain (neglecting the nonlinear element). Which of the Bode plots below corresponds to Mettetal's model for the wild-type strain and the mutant strain. Which of the pole zero diagrams below corresponds to Mettetal's model for the wild-type strain and the mutant strain. What are two questions that you have about the paper's methodology?

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