How do I determine the transfer function of a plant?

Question

I sitting here with a system which I have to determine the transfer function. The unit receives a velocity and position, and move towards that position with the given velocity. What kind of test would one perform for determining the transfer function...

I know MATLAB provides a method. The problem though I am a bit confused on what kind of test it should perform, and how I should use Matlab to determining the transfer function?

The unit which is being used is a Flir PTU D48E

Answer 1

For real processes the standard way to determine the transfer function of the plant is to implement system identification methods using experimental data of the plant. This procedure would yield the state space representation of the system (A,B, C, D matrices):
$\dot{x} = Ax + Bu$
$y = Cx + Du$

Then using the tf command one can derive the transfer function of the plant.

Another way of deriving the transfer function is by using reverse Bode plots.

Links on the methods are provided below:

http://www.mathworks.com/products/sysid/?refresh=true

http://www.mathworks.com/help/control/ref/tf.html

http://vimeo.com/64611091

Answer 2

As I understand, you want to have a transfer function based on your the plant you have. This should be seen as a system identification problem. You need to select a model, which normally can be linear, and try to find the model's parameters. MATLAB has tools for that.