# Control Systems II: Design a Phase-Lag Network

## Homework Statement

A unity feedback system of the form:

X(s)-------->Gc(s)---------->G(s)------------>Y(s)
| |
| |
----<------------1---------<----

has a plant:

G(s) = _____5______
s(s2+6s+10)

a) Determine the step response when Gc(s) = 1, and calculate the settling time and steady state for a ramp input r(t)=t, t>0.

b) Design a lag network using the root locus method so that the velocity constant is increased to 10. Determine the settling time (with a 2% criterion) of the compensated system.

## The Attempt at a Solution

I found the transfer function [G(s)/1+Gc(s)G(s)] and drew the root locus plot. I tried to verify it in MATLAB but somehow it thinks the transfer function doesn't have complex roots. Plus the step response plot doesn't act the way it should. The settling time it shows is at 5.84s but it should be somewhere in the high thirties (number obtained from previous student's work).

From there I don't know where to go. I can do second-order systems easily but this third-order stuff is not my cup of tea. I feel like there are not enough constraints and I've read through the entire chapter but this textbook fails to give good examples. The professor just dumped it on us while neglecting to lecture on the subject. Plus he wants me to present a possible solution to the class.

Any help would be greatly appreciated.

Thank you!