damping

Said earlier, at steady state, the derivative is doing nothing. The velocity is zero; error dot is zero. So the derivative component isn't playing that much of a role in this situation. To compare and contrast, let me oscillate this a few times; you can see that when we increase the damping ratio, or the D component of the PID controller, there's a lot less oscillation.

Introduction to PID Control

that again, we saw the derivative component is sort of related to adding damping to your system. So there's a couple ways you can think about this: you can think about the PID controller as basically a present, past, future kind of system, or you can think of it as adding a spring, mass, and damper to your system. So there's a lot of nice parallel analogies, but again, I think the rigorous way to look at it is

Introduction to PID Control

We'll also neglect the effects of gravity, and for now we'll assume that there's no damping, meaning that no energy is lost from the system as it vibrates, by friction or other means.

Understanding Vibration and Resonance

Since we've assumed there's no damping, the mass will continue to oscillate like this indefinitely.

Understanding Vibration and Resonance

This loss of energy is called damping, and it occurs in all real mechanical systems. There are several different mechanisms that can contribute to the overall damping of a system.

Understanding Vibration and Resonance

circumstances of our lives. However, Sartre referred to this as "bad faith," a form of lying to ourselves and denying our basic freedom—a short-term attempt at damping the anxiety of being that in turn causes the potential loss of our true self and true sense of the world. Even choosing to not choose is still a choice. There is no escaping the requirement of choice; choice can only be minimized to choosing or not choosing, and this is perhaps the fundamental existential choice: to choose or not to choose.

Why We Experience An Existential Crisis - The Philosophy of Jean-Paul Sartre