HW4 solution

# HW4 solution - Homework 4 1 a Settling Time ts 4 6 n 4 6 1...

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Homework 4 1. a) Settling Time: t s 4.6  n  n 4.6 t s 1 Overshoot: M p e  1 2 0.05 e  1 2 0.69. Using  n 1, n 1.45, the desired characteristic equation is s 2 2  n s n 2 0. Substituting 0.69 and n 1.45, it can be obtained that s 2 2 s 2.1025 0 s 1,2 1 1.05 i . The desired poles are s 1,2 1 1.05 i . b) Peak Time: t p n 1 2 n 1 2 n 1.02 The desired characteristic equation is s 2 2  n s n 2 0 s 2 0.408 s 1.0404 0 s 1,2 0.204 i The desired poles are s 1,2 0.204 i c) Rise time: t r 1.8 n n 1.8 t r 1.8 Settling Time: t s 4.6  n 4.6 .56 The desired characteristic equation is s 2 2  n s n 2 0 s 2 2.016

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HW4 solution - Homework 4 1 a Settling Time ts 4 6 n 4 6 1...

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