How to simulate my system

Hello, I am trying to evaluate the performance of a PID controller on the following system in the picture. Essentially, I have a simple model for the amplifier and the motor. I also have a model of the load based on rigid body dynamics. I have data for the encoder position and the image position for a step so I used the system identification toolbox to come up with a transfer function for plant 2. Essentially, i want to model the image response because the encoder is located early in the system where the stucture is rigid. The issue that I'm having is how do I combine the identified model with my rigid body model... I initially thought that I could model the motor and amplifier theoretically to identify a plant and then used my measured data to identify plant 2 and then multiply their transfer functions, but I realize that my identified model will contain some of the structure inertia. I am not feeding back on the image.

So what I have to work with is I have the controller voltages, amplifier currents, motor positions, and image positions all for step inputs that I have from an experiment that I've performed.

I guess I'm getting myself all wrapped in a knot in my head and I just want to figure out how to successfully combine the early part of the system with my identified model for the more flexible part.