# Scaled Step Response & Scaled Ramp Response of Transfer Function

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Ibrahim Erdem Uzuncayir el 4 de En. de 2023
Comentada: Ibrahim Erdem Uzuncayir el 4 de En. de 2023
Hi,Everyone I am new here this will be my first question I don't know I am asking properly. Anyway I try to get step response of some transfer function but step function should be 1.5u(t) and also I should get ramp response of transfer function that ramp function should be 1.5r(t) as well. I couldn't find how can I do this.If anyone could help me I will be happy!
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Bora Eryilmaz el 4 de En. de 2023
Editada: Bora Eryilmaz el 4 de En. de 2023
Since responses of linear time-invariant (LTI) systems have the same shape for various amplitudes of a given input signal and are just scaled linearly with the magnitude of the input signal, you can just multiply the system transfer function with the magnitue, a, of the step input to find the step response for a*u(t):
G = tf(1, [1 .5 1]);
scale = 1.5;
step(scale*G) % Step response for 1.5*u(t)
title('Step Response for 1.5*u(t)')
The ramp response is the same as the step response of the original system augmented by 1/s. In other words, the ramp response is the integral of the step response and 1/s corresponds to integration in s-domain:
s = tf('s');
step(scale*G/s, 25)
title('Ramp Response for 1.5*r(t)')
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Ibrahim Erdem Uzuncayir el 4 de En. de 2023
Thanks! I knew it was something easy but couldn't find thanks again

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### Más respuestas (1)

Mathieu NOE el 4 de En. de 2023
hello
for linear time invariant systems , you can simply multiply the normalized output of step and impulse by your input amplitude
see example below :
s = tf('s');
G = 1/(s+1);
[yi,ti] = impulse(G); % Impulse reponse (for input amplitude = 1)
[ys,ts] = step(G); % Step Response (for input amplitude = 1)
[yr,tr] = step(G / s); % Ramp response (for input amplitude = 1)
figure
subplot(311), plot(ti,1.5*yi); % Impulse reponse (for input amplitude = 1.5)
subplot(312), plot(ts,1.5*ys); % Step Response (for input amplitude = 1.5)
subplot(313), plot(tr,1.5*yr); % Ramp response (for input amplitude = 1.5)
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Ibrahim Erdem Uzuncayir el 4 de En. de 2023
Thanks ! It helped me and I solved it.

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