Why is the scope of output of Liquid level system here showing a straight line and not an exponential like a step?

My components have been modelled as per image1.png

However, the output that I am getting when I click on scope and run looks like a straight line and not an exponential.

According to the book from which I am learning, it was supposed to be an exponential.

I have attached the slx file as well. Can someone explain why I am not getting an exponential as output?

Answer 1

[Sam Chak]

Hi @Rubayet

The liquid level system can be represented as a first-order transfer function. Consequently, it will display an exponential response. Given that the system's time constant (τ) is 1758 seconds, it will take approximately 5 times τ for the system to converge to a steady-state value. By the way, have you ensured that the system has been linearized and modeled accurately?

im1 = imread("image1.png");
im2 = imcrop(im1, [150 200 1500 175]);
imshow(im2)

% time constant of 1st-order system
tau = 1758;     % it will settle around 5*tau = 8790 sec

% Gains
G1  = 0.0034;
G2  = 5.34;

% liquid level process
Gp  = tf(140, [tau, 1])

Gp =
 
     140
  ----------
  1758 s + 1
 
Continuous-time transfer function.

% open-loop system
Gol = G1*Gp*G2;

% plot response
figure
step(Gol, 10*tau), grid on
xl  = xline(5*tau, '--r', {'Settling Time'});
xl.LabelVerticalAlignment   = 'middle';
xl.LabelHorizontalAlignment = 'center';