Second Order Transfer Function Question regarding Overshoot

[Tom Hardy]

Homework Statement

If I have a closed loop second order transfer function such as:

$$\frac{10-s}{0.3s^2+3.1s+(1+24K_{C})}$$

Can I still use this formula for overshoot (when a step input is applied) ?:
$$\frac{A}{B}=e^{\frac{-\pi \zeta}{\sqrt{1-\zeta^2}}}$$
Where B is the step input size

I don't think you can but I'm not sure, can someone confirm?

 

[NascentOxygen]

There are online tools that can plot step responses, so you can use it to demonstrate the answer.

Here's one that looks good: http://sim.okawa-denshi.jp/en/detatukeisan.htm

 

[donpacino]

Homework Statement

If I have a closed loop second order transfer function such as:

$$\frac{10-s}{0.3s^2+3.1s+(1+24K_{C})}$$

Can I still use this formula for overshoot (when a step input is applied) ?:
$$\frac{A}{B}=e^{\frac{-\pi \zeta}{\sqrt{1-\zeta^2}}}$$
Where B is the step input size

I don't think you can but I'm not sure, can someone confirm?

https://en.wikipedia.org/wiki/Overshoot_(signal)

 

[rude man]

Split your xfr function into two parts: one is a low-pass 2nd order, the other a bandpass 2nd order. For both, there are expressions for overshoot in textbooks etc. Your answer depends on the numerical value of K_C.

You then just add the time responses of the two separated xfr functions.
@nascent, thanks for the link! wow, even does nyquist plot!