Question

A unity feedback system has the open loop transfer function shown below. Find the imaginary axis crossing of the root locus s=±jω Enter the value of ω to two decimal places. Do not enter ±j

HG(s) = K(s−10)(s−20) / s²+4s+8

Answer 1

The imaginary axis crossing of the root locus occurs at ω = 3.00.

Step-by-step explanation:

To find the imaginary axis crossing, set the real part of the open-loop transfer function equal to zero. In this case, the open-loop transfer function is given by
`\(HG(s) = (K(s-10)(s-20))/(s^2 + 4s + 8)\)`.

Setting the real part to zero gives \(s^2 + 4s + 8 = 0\). Solve for \(s\) to find the roots, and then extract the imaginary part to get the crossing point on the imaginary axis.

The solutions are complex conjugates, and their imaginary parts correspond to the imaginary axis crossing. In this case, ω = 3.00.