control system

Suppose I have a the transfer function of a control system in the form of:

T(s)=P(s)/Q(s)

where:
P(s) is the numerator
Q(s) is the denominator and the numerical coefficient of (s) of the factor with the highest power equals 1.

example:

T(s)=(3s+17)/[(s^2)+as+b]

Note:

a and b are constants.

Is there a way or technique I could use to find values for a and b such that the output will be critically damped? or underdamped? or overdamped? given a unit step input?

Hi,

The discriminant from the denominator solution is:
sqrt(a^2-4*b)

When the inside:
a^2-4*b

is equal to zero:
a^2-4*b=0

we have the critically damped case.

When the inside is positive:
a^2-4*b>0

we have the overdamped case.

When the inside is negative:
a^2-4*b<0

we have the underdamped case.

Thank you so much. At the time I was posting this, I was already thinking of the possible (those I know by screen name) users who would give me a reply. To let you know, you're the first on my list.

I asked about this since this is a part of my homework. They discussed this in the lecture but they did not mention about how we are going to do it. They gave examples but I know I would never figure out these things only by looking at them. Thanks again sir. . My homework has a lot harder transfer functions. I'm lucky you had the discussions before for those denominators with imaginary roots.

Thank you sir