ACT3701
Assessment 3
Due 2025
, ACT3701
Assessment 3 – Question 1 Solution
Problem Statement:
Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system
that has the following characteristic equations. Determine the number of roots of each
equation that are in the right-half-plane and on the jω-axis.
(a) s3 + 25s2 + 10s + 450 = 0
(b) 2s4 + 10s3 + 5.5s2 + 10 = 0
Part (a): s3 + 25s2 + 10s + 450 = 0
Step 1: Construct the Routh Array
We start by placing the coefficients in the first two rows:
s3 1 10
s2 25 450
Now compute the third row:
(25)(10) − (1)(450) −200
Element at s1 = = = −8
25 25
s3 1 10
s2 25 450
s1 −8 0
s0 450
1
Assessment 3
Due 2025
, ACT3701
Assessment 3 – Question 1 Solution
Problem Statement:
Using the Routh-Hurwitz criterion, determine the stability of the closed-loop system
that has the following characteristic equations. Determine the number of roots of each
equation that are in the right-half-plane and on the jω-axis.
(a) s3 + 25s2 + 10s + 450 = 0
(b) 2s4 + 10s3 + 5.5s2 + 10 = 0
Part (a): s3 + 25s2 + 10s + 450 = 0
Step 1: Construct the Routh Array
We start by placing the coefficients in the first two rows:
s3 1 10
s2 25 450
Now compute the third row:
(25)(10) − (1)(450) −200
Element at s1 = = = −8
25 25
s3 1 10
s2 25 450
s1 −8 0
s0 450
1
