First order unit step response

In summary, the speaker is mostly understanding how a certain concept works and finds it intuitive. However, they are confused by a step in the proof process, specifically a δ(t) term in a statement on the second page of a PDF. They are unsure where this term comes from and question if it evaluates to 0 or (r/k + c2). The speaker acknowledges that this may not be the appropriate forum for their question.
  • #1
charlie.elvers
2
0
I think I mostly understand how this works, and it makes intuitive sense. However, I'm a little bit confused by one step in the proving of this.

On the second page of the attached PDF, there is this statement:

x' + kx = (r/k + c2)δ(t) ... (followed by the cases of t<0 and t>0

What comes after δ(t) is easy for me to follow, but I don't know where this δ(t) term comes from. Does this term evaluate to 0? If so, how? I would think it'd evaluate to (r/k + c2) because the (r/k + c2) is independent of t

Thanks.
 

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  • #2
Sorry folks. I just read the forum rules, and I think this is probably the wrong forum for such a thread.
 

Related to First order unit step response

1. What is a first order unit step response?

A first order unit step response is a type of response seen in a system when a unit step input is applied. It is characterized by a single exponential function that models the system's output.

2. How is the first order unit step response calculated?

The first order unit step response is calculated using the transfer function of the system. This involves solving the differential equation that represents the system and finding the inverse Laplace transform of the resulting expression.

3. What is the significance of the first order unit step response?

The first order unit step response provides important information about the behavior and stability of a system. It can help in predicting how a system will respond to different inputs and how it will behave over time.

4. How does the time constant affect the first order unit step response?

The time constant, represented by the symbol τ, is a measure of the speed of response of a system. A larger time constant results in a slower response, while a smaller time constant results in a faster response. Therefore, the value of the time constant affects the shape and duration of the first order unit step response.

5. Can the first order unit step response be used to analyze all systems?

No, the first order unit step response is only applicable to systems that exhibit first order dynamics. Systems with higher order dynamics will have more complex responses that cannot be modeled by a single exponential function.

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