1. Good evening everyone,

Would it be possible to have some help for this exercise please?

Let a system whose transfer function H (p) is expressed:

1) Express the gain and the phase in the sense of Bode.
2) What is the system?

3) What is the static gain of the system worth?
4) Explain the influence of the coefficient m on the behavior of the system.

And here is what I said:

1)

with

We can deduce that .
But I don't know how to calculate the module of ,I think than

is a constant,unless the constant is that we multiply by p.

So =arg(1)-arg()=-arg()

2)This system is a order 2 system .

3)The static gain it's the gain when the time t tends to(move towards) infinity .

But my gain is not good and we have no "t" .

4) m it's the coefficient of amortization,it's all I know.

2. Originally Posted by Martin35
Good evening everyone,

Would it be possible to have some help for this exercise please?

And here is what I said:

1)

with

We can deduce that .
But I don't know how to calculate the module of ,I think than

is a constant,unless the constant is that we multiply by p.
I won't give you the answer, but here's a hint: Use Euler's relation to express the exponential as the sum of a real and imaginary part, then compute the modulus from that. You will be led to a general result that you should interpret geometrically to gain insight as to why the answer is what it is.

So =arg(1)-arg()=-arg()

2)This system is a order 2 system .
There is more than one possible answer, actually, because of the exponential term. A mathematician would probably object to calling this a second-order system.

3)The static gain it's the gain when the time t tends to(move towards) infinity .

But my gain is not good and we have no "t" .
It would be better to use theorems from Laplace transform theory. The initial or final value theorem would perhaps be relevant here.

4) m it's the coefficient of amortization,it's all I know.
I'm curious: What is your native language (French)? I've heard the coefficient called several things, but "coefficient of amortization" isn't one of them, but it makes sense linguistically. Interesting. Learned something new today.

In English, it is more commonly called the damping ratio or damping factor, or some similar name. Whether it's called damping or amortization, it does characterize the relative rate at which the oscillatory portion of the response dies ("morts") away. I recommend plotting the time behaviour as you vary the coefficient, in order to visualise its effect.

3. Good morning and thank you for your help !

Yes I'm french,but I think like you,it would be better to use theorems from Laplace transform theory.
Effectively,it makes sense coefficient of amortization.

I managed to finish the exercise, however there is one with operational amplifier that I have problem.

I will probably post a new topic today or tomorrow.

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