- #1

jegues

- 1,097

- 3

## Homework Statement

A Nyquist (polar) plot of a

*standard*second-order system is shown below (drawn to scale).

Suppose a unit-step function is applied as the input to this system. Determine the peak percentage overshoot expected in the system output.

## Homework Equations

## The Attempt at a Solution

My idea was to trace backwards from the ω→+∞ at the origin until I reach a vector from the origin to a point on the curve with magnitude one. This ω will correspond to a gain cross over frequency and provide me with the phase margin.

I could then link this value of the phase margin back to zeta through the following equation,

[tex]\text{P.M.} = \gamma = tan^{-1}\left( \frac{2\zeta}{\sqrt{-2\zeta^{2}+\sqrt{1+4\zeta^{2}}}}\right)}[/tex]

The first point I could find that would give me a vector of magnitude one resides at (0.6, -0.8) yielding a phase margin of 126.87°. Unfortunately this PM yields a negative value for zeta.

Any idea where I went wrong or an easier way to solve the problem?