Try linmod command instead of using it in system identification toolbox

You might compare the fourth figure with a step response to a second order linear system.

Then you could obtain the natural frequency and the damping coefficient, from the maximum overshoot and the peak time, and consequently you can build its transfer function.

I seem the system has an overshoot about 60% and peak time occurs around 7.5 seconds, then:

Mp - (peak output - steady state)/step size = 0.6

Mp = exp(-pi*zeta/sqrt(1-zeta^2))

where zeta is the damping coefficient, then zeta = 0,160493047 (more or less)

Tp - peak time = 7.5

Tp = pi/[wn*(1-zeta^2)^(1/2)]

where wn is the natural frequency, then wn = 0,424380274 (more or less)

And the corresponding second order transfer function:

wn^2/(s^2 + 2*zeta*wn*s + wn^2)

You could approximate it by:

0.18/(s^2 + 0.137*s + 0.18)

You must remember that this expression is only a linear approximation

Hi,

Instead of linearizing your system from PID tuner, define you linarization input/output points in the simulink model (search for linio in MATLAB help) and  then linearize your simulink system for the defined input and output points using the command (search for linearize in MATLAB help). Then check if the linearized model is stable or not and see whether or not you can stabilize the linearized model using PI controller. You may have to design different controller.

By the way, after linearizing your system, if the order of the linearized model was high, you can reduce the order of the linearized model (I recommend Hankel singular value based model order reduction: search for reduce in MATLAB help) . The reduced order model can help you in the controller design stage.

Regards,

An alternative, with respect to the given above, is to use Ziegler-Nichols rules for tuning continuous PID controllers or Takagi-Sugeno rules for discrete-time PID controllers. Also, in the simscape model I do not see the friction model (viscous, Coulomb, etc.) and yielding dead-zone in the response. 

Motors with angular position as output are semi-stable (marginally stable), hence the ramp output. Instead of taking the position as the output, add a tachometer/speed measuring device and use the rotational speed as the output.