Sun,

Have you found the examples by Kai & Russell to be descriptive of how the controller mimics human actions to control the situations?

Just as a refresher -

The derivative term acts to anticipate a disturbance in the feedback variable, or a change in the command and to send a momentary correction. The derivative term also acts to add damping to the control action if the feedback is approaching the command too quickly. Since the derivative term acts to produce a value based on the rate of change of another variable, it is has a behavior like a high-pass filter.

The proportional term acts to apply a sustained control effort as long as there is a difference (error) between the command and the feedback variable. Since the proportional term acts to produce a control effort that is sustained as long as an error exists, it has a behavior like an all pass (dc amplifier with no frequency dependency) filter.

The integral term acts to apply an increasing or decreasing adjustment as long as the error is non zero. Since the integrator term acts to average the error and attempt to drive it to zero by summing the weighted error, it has a behavior like a (very) low pass filter.

Now, knowing how the terms mimic human behavior to control a generator speed in the presence of a load disturbance, etc., and understanding the relationship between the human behavior and the signal processing jargon of high pass, low pass and all pass filters, you can study a little more.

Bruce