Root Locus Problem

Root Locus Problem
Problem RLocus6

Assume that you are designing a speed control for an automobile. The system has the following characteristics.

The motor has a time constant of 1.5 sec.
The automobile has a time constant of 4 sec. (When a constant torque is applied to the drive-shaft the speed has a 4 sec. time-constant (first order) response.
The controller has a variable gain, and a time constant of 0.5 sec.
The system is modelled with the block diagram below.

The G(s) for the system is:

G(s) = 10/[(1.5s + 1)(4s + 1)(0.5s + )]

G(s) = [10/(1.5*4*0.5]/[(s + .667)(s + 0.25)(s + 2)]

The goal is to get a precise speed control. Here we will take precise to mean that the speed gets within 2% of the desired steady state value. It is also desired to have the system respond quickly, and quickly will mean a rise time of less than 8 sec.

We will examine this system and we will use a root locus sketch to predict behavior.