# Control theory related question

1. Mar 19, 2010

### Uridan

1. The problem statement, all variables and given/known data

Assume an under damped transient response graph, the graph will have the form of an envelope. My problem is that I need to find the open loop transfer function of my home build system (for a project) by using the open loop step response (which is an under damped response) to find the open loop transfer function. Another problem is that the response will never reach a set point, i.e when the settling time has been reached the graph will keep oscillating with a constant amplitude and frequency, and the set point is the origin.

For this problem let us assume a general under damped response with a step input from 0 to 5, i.e the rise time will start from 0 and the set point is at 5. Also overshoot etc.. can be taken any reasonable value for this example. (to keep it in general for others to understand)

2. Relevant equations

an under damped response is definitely a second order system or higher so:

The general form of the transfer function of a second order system is

G(s) = a/(s^2+bs+c) = Kwn2/(s2+2zwns+wn2).

How can I find the transfer function G(s)= Y(s)/X(s) of the system with the current open loop response that I have described above?

Note that I am an electronics engineering student and couldn't find the model dynamics of the system (ball flouting in a jet stream of air) since I have no background in fluid mechanics and we all know how complex aerodynamics is :), so I am taking this approach to be able to find the right controller to make this system stable.

3. The attempt at a solution