Question

Using the following code:

% Ex 6.4 First-order step and impulse response for two time constants
%
clear all; close all;

t = 0:.1:100; % Time vector
subplot(1,2,1);
x = 250*exp(-0.05*t);
plot(t,x,'k');
xlabel('Time (hrs)','FontSize',14); ylabel('P_A (mmHg)','FontSize',14);
title('Impulse Response','FontSize',14);
subplot(1,2,2);
x = 20*(1-exp(-0.05*t));
plot(t,x,'k');
xlabel('Time (hrs)','FontSize',14); ylabel('P_A (mmHg)','FontSize',14);
title('Step Response','FontSize',14);
  

ANSWER:

The response of a 1^st order linear body fluid balance system to step function (L m (t) = 1/s, Eqn. 6.9/p226) and impulse function (L d (t) = 1, Eqn. 6.13/p227) is analyzed by the Laplace TF approach, and then plotted by simple MATLAB routines. First, the Laplace TF is calculated based on the feedforward gain (G) and feedback gain (H); secondly, the output is obtained by multiplying the input and the TF, all written in Laplace variable s, and; thirdly, the output is inversely Laplace transformed from its Laplace-domain representation to time-domain by referring Appendix B. The system’s response to both types of input signals in the time-domain is then found from the inverse Laplace transform of the output in its Laplace-domain.

Assignment #2-1 (10 pts): Find the TF of this 1^st order linear system in s (i.e. its Laplace TF) with its feedforward gain (G) and feedback gain (H). Show your work.

Assignment #2-2 (10 pts): What is the Laplace transform of the step function and impulse function, respectively?

Assignment #2-3 (10 pts): Find the response of this system, in time-domain, to (1) the step function input and (2) the impulse function input. Show your work.

Assignment #2-4 (10 pts): Now plot the two response signals and put a snapshot picture of your results in your lab report with Ex6_4.m. Note: “t” is missing in the codes shown in the textbook (p235) for both the step and impulse responses.

all information provided

Answer 1

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          Please find the answer attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

******** Matlab Code *******

% Ex 6.4 First-order step and impulse response for two time constants
%
clear all; close all;
t = 0:.1:100; % Time vector
subplot(1,2,1);
x = 250*exp(-0.05*t);
plot(t,x,'k');
xlabel('Time (hrs)','FontSize',14); ylabel('P_A (mmHg)','FontSize',14);
title('Impulse Response','FontSize',14);
subplot(1,2,2);
x = 20*(1-exp(-0.05*t));
plot(t,x,'k');
xlabel('Time (hrs)','FontSize',14); ylabel('P_A (mmHg)','FontSize',14);
title('Step Response','FontSize',14);

********* Output ********