transfer function from bldc motor step response

hello,
I have managed to obtain a measured step response (speed in revs/sec vs time)of a BLDC motor system (motor, driver circuit) and now need to obtain a transfer function in order to design a controller in matlab. Does anybody know how to work out a systems transfer function from a step response?

I have worked out the mathematical model of the motor using the motor parameters and got a transfer function, but i would like to get one for the whole real system.

Any help much appreciated!

The step response can be directly translated to a time domain transfer function (impulse response). It's connected to s-domain by a laplace transformation.

But what transfer function representation do you want? If it's model expressed in poles and zeros, you are talking about system identification, estimating the model parameters from an empirical time or frequency domain transfer function. The Matlab system identification toolbox offers a convenient way to perform the task.

You can also estimate a time discrete (z-domain) transfer function directly from the impulse response by basic matrix calculus.