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)a_1\frac{dy}{dt} + a_0y = F(t)\tag{1}

A first order differential equation in Equation (1) may be written as:

τdydt+y=kF(t)\tau\frac{dy}{dt}+y = kF(t)\tag{2}

Question 2: If a step input

F(t)={0,if t < 0A,if t > 0F(t) =

\begin{cases}

0, & \text{if $t$ < 0} \\
A, & \text{if $t$ > 0}

\end{cases}\tag{3}

of the system has an output response of a

y(t)=kA(1âˆ′eâˆ′tد„)y(t) = kA( 1âˆ’ e^\frac{âˆ’t}{د„}) \tag{4}

then the system can be modeled as first differential equation where

ymax=kAy_{max} = kA\tag{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?

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1 Answer

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Your output response y(t) = k A (1-e^{-t/\tau})y(t) = k A (1-e^{-t/\tau}) for t > 0t > 0 satisfies the first-order differential equation y’ = -y/tau + (k/\tau) F(t)y’ = -y/tau + (k/\tau) F(t).

wait i will edit my question.

– Paul Jabines

2 days ago