Electrical – How to perform System Identification on DC motor

Your approach should work. It's also the simplest way to solve the problem.

You could always work out a position controller that steers directly the motors, but it would be less easy to understand how to tune it. And I understand you have both position and velocity readings, so why not using two loops?

As people's comments to your question highlight, obviously you'd now have a position controller rather than velocity. But it makes sense as it's for a robot.

You need to be careful to a few details:

1. If the two DC motors are working in parallel, you must find a way for the two not to interfere with each other (like forcing load sharing). However you must have faced this problem already in the speed loop.
2. The external loop (position control) is bound to be far slower than the speed loop. If it worked at the same pace, or faster, you'd have the position loop strongly pulling on the speed one without letting it the time to react, and you'd have strong interactions or even instabilities. I suggest that you speed up the internal one (speed) as much as you can, and then tune the external one.
3. The external loop shall here be your 'precise' one. The internal one should just be quick in reaction rather than precise. I'd suggest a P or PD controller for the internal one, and PI or PID for the external one.

Extra tip: as it's for a robot, I'd take into consideration a position reference feed-forward.

You shouldn't be using the PID output as a velocity command in your system, as it will simply become unstable and eventually oscillate between one end limit and the other, or have no response.

Using a linear actuator as you are, you should use the output of the PID as a position command, and have the actuator follow the output that way. By setting the PID min and max limits, the end of travel switches are only safeties if something goes horribly wrong.

Also, if you detect that your PID is at either limit (which it might have to be if the response is very slow), you want to inhibit the integral term for as long as it is at a limit so that you don't suffer from integrator wind-up.

PID's work fine on motor controls, true, but I use them industrially to control temperatures easily on systems with several minutes of lag. Tuning is everything... Remember the basics, Proportional gain will only get you (approximately) half to three quarters way to the setpoint, Integral gain will take you the rest of the way. Derivative tempers the change.

For temperature control loops with a long lag, I find it much easier to ramp the setpoint up slowly to the final setpoint rather than jump it immediately, it allows a tighter tuning of the PID without having it go into oscillation.