oscillate

Error in my integrator that I might overshoot a little bit, then I might come down and oscillate. But at some point, the pink string, which is the integrator component, brings the actual position of the weight up to R. Now R and Y are the same thing, and there's zero error. We said earlier that because there is zero error, the spring or proportional component is doing nothing; the pink string is.

Introduction to PID Control

Try something more viscous, like water. If I pour water in here, I have increased the D component of this controller. You see how much more damped out it is? You see how this thing does not bounce around or oscillate as much? There is now a lot more force; it's much harder for that weight to move through the fluid quickly. But what's interesting is, look at this: as we.

Introduction to PID Control

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

No external loads are acting on the system - the purpose of the model is to understand how the system behaves in free vibration, or in other words how it will oscillate when it's displaced, and then released.

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

An important property that can be calculated from a mass-spring model is the system's natural frequency, the frequency at which it will oscillate naturally when in free vibration.

Understanding Vibration and Resonance