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 .