damp
Natural frequency and damping ratio
Description
Examples
Input Arguments
Output Arguments
Algorithms
damp
computes the natural frequency, time constant, and damping
ratio of the system poles as defined in the following table:
Continuous Time  Discrete Time with Sample Time Ts  

Pole Location 
$$s$$

$$z$$

Equivalent ContinuousTime Pole 
$$\text{Notapplicable}$$

$$s=\frac{ln(z)}{{T}_{s}}$$

Natural Frequency 
$${\omega}_{n}=\lefts\right$$

$${\omega}_{n}=\lefts\right=\left\frac{ln(z)}{{T}_{s}}\right$$

Damping Ratio 
$$\zeta =cos(\angle s)$$

$$\begin{array}{lll}\zeta \hfill & =cos(\angle s)\hfill & =cos(\angle ln(z))\hfill \end{array}$$

Time Constant 
$$\tau =\frac{1}{{\omega}_{n}\zeta}$$

$$\tau =\frac{1}{{\omega}_{n}\zeta}$$

If the sample time is not specified, then damp
assumes a sample
time value of 1 and calculates zeta
accordingly.