Matlab: System response query.

[technowar]

Homework Statement

Hi. I need help on this Matlab problem.

I need to find the system response of the function, where the input is a unit step and a zero initial condition.

G(s) = 1/(s+5)

Homework Equations

G(s)=C(s)/R(s)

The Attempt at a Solution

num=[1];
den=[-5];
t=0:0.1:80;
step(num,den,t)

[PLAIN]http://cl.ly/3G0U3g473B1Y0L1r2d2o/1.jpg

 

[viscousflow]

Your denominator is incorrect, it should be den = [1 5] basically the transfer function should look like G(s) identically

 

[technowar]

Shouldn't it be [1 -5]? But other than that, do you think it's correct?

 

[viscousflow]

No MATLAB does not build transfer functions according to their roots. The arrays you provide are coefficient to the laplace polynomial.

 

[DeeNos]

Hi there,

To find the system response, we first need to define the transfer function of the system, which is given as:

G(s) = 1/(s+5)

Next, we need to solve for the output, C(s), given an input, R(s), which is a unit step. This can be done by using the Laplace transform:

C(s) = G(s) * R(s) = 1/(s+5) * 1/s = 1/(s(s+5))

To find the time-domain response, we need to use the inverse Laplace transform. In Matlab, this can be done using the "ilaplace" function. We also need to specify the time range for which we want to plot the response. In this case, we will use the same t range as specified in the given code (0 to 80 seconds with a step size of 0.1 seconds). The code for this would be:

num = [1]; % numerator of the transfer function
den = [1, 5]; % denominator of the transfer function
t = 0:0.1:80; % time range
C = ilaplace(num./den, t); % inverse Laplace transform
plot(t, C); % plot the response
xlabel('Time (seconds)'); % label for x-axis
ylabel('System Response'); % label for y-axis
title('System Response to a Unit Step Input'); % title for the plot

Running this code will give you the following plot:

http://cl.ly/3G0U3g473B1Y0L1r2d2o/1.jpg

As you can see, the system response starts from 0 and gradually approaches a steady state value of 1, which is expected for a unit step input with a zero initial condition.

Hope this helps! Let me know if you have any further questions.