Modelling a closed loop system with output disturbance signal using System Identification Toolbox

Hi folks,

I would like to model my plant (a vehicle project at school) that I would like to control with PID controller. To do so, I have made some experiments and collect some output data from closed loop system. In my closed loop system, the reference input is zero and the system tries to make the output signal zero. And for tha test, I gave an output disturbance (or simply initial state).

For the modelling part, I would like to use system Identification toolbox. However, As I add zero as a input signal, the toolbox can not find any plant tansfer function. And as I give, disturbance signal as input, the toolbox treats this signal as ref input and tries to model systems that reaches to disturbance value not zero.

My question is that can I force the toolbox to identify with output disturbance and tries to go to zero at steady state.