how to change the rise time of step input in simulink

Hello,

I want to change the rise time of the step input in simulink. I tried the transfer function 1/(s+1) but not satifying my requirement. Can someone suggest me some tricks. Thanks in advace.

Regards,

Swasthik

[Sam Chak]

Hi @Swasthik Baje Shankarakrishna Bhat

Can you specify all the performance requirements?

What did you mean by "tried the transfer function"? What is that transfer function for? For Plant, Actuator, or Compensator, or Prefilter? If possible, please the Plant transfer function.

[Swasthik Baje Shankarakrishna Bhat]

Hi sam,

i just need a step input with variable rise time. Something like this,

Thanks and regards,

Swasthik

Answer 1

[Sam Chak]

Hi @Swasthik Baje Shankarakrishna Bhat

Edit: I created a general one so that you can enter the desired ramp up parameters:

% u = min(1, max(0, "Linear Line function"));
ramp_start = 5;
ramp_end   = 8;
t  = linspace(0, 25, 251);
u  = min(1, max(0, 1/(ramp_end - ramp_start)*(t - ramp_start)));
plot(t, u, 'linewidth', 1.5), grid on, ylim([-1 2])

If you have Fuzzy Logic Toolbox license, then you can use this linsmf() function. Here is a demo for a Double Integrator:

% Plant
Gp = tf(1, [1 0 0])

Gp =
 
   1
  ---
  s^2
 
Continuous-time transfer function.

% PID
kp = 0;
ki = 0;
kd = 0.8165;
Tf = kd;
Gc = pid(kp, ki, kd, Tf)

Gc =
 
               s    
  Kp + Kd * --------
             Tf*s+1 

  with Kp = 0, Kd = 0.817, Tf = 0.817
 
Continuous-time PDF controller in parallel form.

% Closed-loop system
Gcl = feedback(Gc*Gp, 1)

Gcl =
 
           s
  -------------------
  s^3 + 1.225 s^2 + s
 
Continuous-time transfer function.

% Saturated Ramp Response
t  = linspace(0, 25, 251);
u  = linsmf(t, [5 8]);  % rise time is from 5 to 8 sec
lsim(Gcl, u, t), ylim([-1 2]), grid on

[Swasthik Baje Shankarakrishna Bhat]

Hi Sam,

Thanks for your help. But I am getting an error saying "Unrecognized function or variable 'linsmf'."

[Sam Chak]

Hi @Swasthik Baje Shankarakrishna Bhat

I forgot to mention that although linsmf is user-friendly, it requires the Fuzzy Logic Toolbox.

If you don't have Toolbox, then you can try this alternative. It produces the same time-delayed saturated ramp signal.

% Syntax:
% u = min(1, max(0, "Linear Line function"));
t  = linspace(0, 25, 251);
u  = min(1, max(0, 1/3*(t - 5)));
plot(t, u, 'linewidth', 1.5), grid on, ylim([-1 2])

[Swasthik Baje Shankarakrishna Bhat]

Hi Sam,

Sorry to bother you again. Can we have a neative sloped step input with programmable fall time?

Thanks and regards,

Swasthik

Answer 2

[Timo Dietz]

Hello,

what about using a single-sided ramp function: b * (1 - exp(-a*s)) / s^2

The gradient of the rising slope is '1', so after the time 'a' the amplitude 'a' is reached. The factor 'b' should finally allow you to control the steepness of the 'step'.

Does this meet your requirement?

[Swasthik Baje Shankarakrishna Bhat]

Hi Timo,

I am not able follow your explanation, can you elaborate little bit?

Thanks and regards,

Swasthik

[Timo Dietz]

Hello,

I thought you are searching for a solution in the frequency/laplace domain since you mentioned the pT1.

So, with 'H_slope = b/a * (1 - exp(-a*s)) / s^2' you can control the slope (in time domain) via a and b:

syms s;
a = 1.5; % time after which amplitude is reached
b = 2; % amplitude
% frequency domain
H_slope =  b/a * (1 - exp(-a*s)) / s^2;

% time domain
f_slope = ilaplace(H_slope);
fplot(f_slope, [0 2]);
grid on;

[Swasthik Baje Shankarakrishna Bhat]

thanks Timo

Answer 3

[Swasthik Baje Shankarakrishna Bhat]

perfect, Thanks sam. Have a nice day

[Sam Chak]

Hi @Swasthik Baje Shankarakrishna Bhat

It's great to hear that it works. If you find the solution is helpful, please consider accepting ✔ and voting 👍 the Answer. Thanks!

Answer 4

[Paul]

A 1D Lookup Table seems like a good option.