16. PD Math and Reparametrization
C3 L2 L10 L PD Math And Reparameterization V2
To simplify, we can summarize the behavior of delta (damping ratio) and omega (natural frequency) as below.
A big value (close to 1) of damping ratio (delta) yields to a faster decay. A smaller value (close to 0) constitutes, instead, a slower decay.
A big value of natural frequency (omega) causes high frequency oscillations. Smaller values of omega, instead, reduce the oscillations' amplitude.
The behavior of the PD controller's equation is a sinusoidal oscillation, whose amplitude is modified by a decaying exponential.