(a) Derive the expressions for the rise time $t_{p}$ and peak time $t_{p}$.

Explanation

The rise time tp and peak time tp are two important parameters in control systems. The rise time tp is the time taken by the response to rise from 10% to 90% of its final value, and the peak time tp is the time taken by the response to reach its peak value. The expressions for tp and tp are given by tp = 2.2 / ωn and tp = π / ωn, respectively.

(a) Derive the expressions for the rise time $t_{p}$ and peak time $t_{p}$.

Explanation

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