# Over damped response transfer function (help pls)

1. Mar 19, 2010

### Uridan

Hi,

Not sure on where to post this tread since it involved some fluid mechanics and Maths/ Control theory.

I have found the response of a ball flouting in a vertical jet stream of air and the result is a highly non linear system. That is, there is different open loop response as the ball goes higher and higher.

As always, there is the choice to select average linear parts within the prerequisite range and I have found 3 linear parts, form 0-5 cm 5- 15cm and 15-25cm, each part gave 3 different open loop response of the system which resulted in this way:

0-5cm = under damped response with small overshoot peak but a very large settling time.
5-15cm= under damped response with average overshoot peak and average settling time.
15-20cm=under damped response with High overshoot peak but very small settling time.

I think you get the picture and physics wise, it makes sens but since I am an electrical student I dont now that much about fluid mechanics.

As shown above each response is an under damped response, thus a graph that oscillated a lot before reaching settling time in the form of an enveloped shape. The problem is that with my system, I can never reach settling time since there are shedding vortex which will not allow the ball to stay at a steady vertical position and will keep oscillating at that particular position.

This means that the under damped response will still have an enveloped shaped form, but it never reaching the steady state position, since it keeps oscillating between the set point (constant amplitude and frequency).

Can anyone tell me how to calculate the transfer function of such under damped response? I have to calculate the order of the system and use z and w notation to find the G(s) (transfer function) of the system. A general example would be great :).

thanks
regards
Uridan