Autonomous PID-based code for the SpaceX Dragon docking simulator: https://iss-sim.spacex.com/
Autonomous docking can be activated by pasting the code into the development console of a browser (at your own risk, always skim through code before executing to make sure it's safe). dragon-dock.js is the standard version. dragon_dock_slow.js has added velocity constraints to make it more realistic. Try tweaking the PID parameters to change how the Dragon moves. The default values are conservative and work, but can definetely be tuned. Example of what modified PIDs can do.