Control system parameters

There are several key parameters in the time response of a control system that we design for: Important parameters we’re interested in:

The yellow line denotes an arbitrary threshold. The time such that it never goes beyond the threshold is called the settling time $T_{s}$ .
- Usually we set this threshold as within 2%.
- $T_{s} = 4 τ = \frac{4}{ζ ω _{n}}$
The time between 10% and 90% of the first rise to the final value is the rise time $T_{r}$ . We can define $t_{r}$ such that $T_{r} \approx \frac{1.8}{ω _{n}}$ .
The peak time $T_{p}$ is the time at which the system attains its maximum value.
The percent overshoot is defined as: $\frac{y ( T _{p} ) - f v}{f v}$ , where $f v$ is the final value of the response as $lim_{t \to \infty}$ .

jszhn