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Originally Posted by Ether
That would be static friction and motor controller deadband, not inertia. You can "overcome" friction and deadband, but you never "overcome" inertia: it is always there even when the motor is turning.
If you take a physics class, you'll learn all about inertia and Newton's Second Law 
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And I'm looking forward to it

Unfortunately it's never been offered as a class for me until next year, so I don't have near the understanding I want to have.
For the record, the static friction and deadband was referred to as inertia in previous code I was reading, that's why I had the term in my head. Thank you very much for the information.
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Very good. You're re-mapping the joystick output. There are occasions (as you have discovered) when this can be quite useful. You're encountering the fun of learning useful new stuff.
Just for the record, you don't have to write your own PID to use joystick re-mapping. Just send the re-mapped joystick values to the PID, instead of the raw joystick values.
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Not using a joystick for the PID Controller. Main reason my mentor wanted it is for automated tasks and movements towards a setpoint e.g. Autonomous mode movement, arm presets, etc.
Once again, thanks for the info!