This video describes how to make an ideal PID controller more robust when controlling real systems that don’t behave like ideal linear models.
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Noise is generated by sensors and is present in every system. The derivative in an ideal PID controller amplifies high-frequency noise. Even if that noise is relatively low amplitude, the derivative will sense it and possibly amplify it enough to impact the controller. To protect against high-frequency noise impacting the system, you can modify the derivative path with a low pass filter to reduce the noise before it causes any problems.
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