Question

Enter your answer 13 ss 1 2 1.5 3 2 s -1/3 s1 10 2 The following figure shows the first column of a Routh table, How many roots of the corresponding characteristic equation are in left half s-plane?* (5 Points) Enter your answer

Answer 1

Step 1:

Routh–Hurwitz stability criterion:

• It is a mathematical test that gives us idea about stability of a linear time invariant (LTI) control system.
• Thus R-H criterion provides a way to determine if the equations of motion of a linear system have only stable solutions, without solving the system directly.
• Change in number of sign i.e. +ve and -ve values in a R-H tables tells us about the roots which are in right half of s-plane.

Step 2:

In given question it is of fifth order so the given characteristic equation has 5 roots.

Also in given R-H table change in sign is two times i.e.

• 1.5 to -1/3
• -1/3 to 10

So the given characteristic equation has 2 roots in right half of s-plane.

Therefore it have 5 - 2 = 3 roots in left half of plane