Most systems can be modeled using first order system just like a temperature control system of an in

Layla-Rose Ellison

Layla-Rose Ellison

Answered question

2022-02-15

Most systems can be modeled using first order system just like a temperature control system of an incubator.
Question 1: How can we know that a certain system can be modeled using first order differential equation?
a1dydt+a0y=F(t)    (1)
A first order differential equation in Equation (1) may be written as:
τdydt+y=kF(t)    (2)
Question 2: If a step input
F(t)={0   if t<0A   if t>0    (3)
of the system has an output response of a
y(t)=kA(1etτ    (4)
then the system can be modeled as first differential equation where
ymax=kA    (5)
Is this correct?
Given a step input and the graph of the step response of the system. Am i correct if I say that if the output of the system behaves similar to equation (4), then I can model the system using first differential equation?

Answer & Explanation

Elodie Williamson

Elodie Williamson

Beginner2022-02-16Added 7 answers

Your output response y(t)=kA(1e1τ) for t>0 satisfies the first-order differential equation
y=yτ+(kτ)F(t).

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