What is the easiest way to model a PID actuator? I am particularly interested on the Integral part. Thank you!

The integral part introduces another state variable. MuJoCo has 3-rd order actuators designed to model things like pneumatic cylinders and biological muscles. You could adapt it to represent the integral term. Then you need a second actuator for the PD term. Alternatively, you could implement this on your end as a feedback controller, and use simple force actuators in MuJoCo.

I am not sure whether I should create a new thread (sorry if that is the case) but I have the same question. For example I want to simulate this baxter robot which has PID controller for joints, and I need to use same model. https://github.com/RethinkRobotics/...m_hardware/config/baxter_sim_controllers.yaml I think I understand second part of the answer (using force actuators and implement controller), but first part I am not sure. Is it possible to simulate exact same controller in MuJoCo, if yes what are steps I need to take? Thank you.

If you are not sufficiently familiar with MuJoCo's actuation model, it may be easier for you to simulate a PID controller in your code, and then provide the resulting forces to MuJoCo as control signals for a torque actuator.