Question

A closed-loop system's transfer function is given in the form: T(S) = $3 + 732 - 21s + 10 S6 + 55 – 6s+ - 52 - S + 6 How many poles does the system have on the right-half side, RHS of the s-plane, on the left-half side, LHS of the es-plane, and on the jw-axis. O poles on the RHS, O poles on the LHS, and 6 poles on the jw-axis. 1 pole on the RHS, 1 pole on the LHS, and 4 poles on the jw-axis. 2 poles on the RHS, 2 poles on the LHS, and 2 poles on the jw-axis. O2 poles on the RHS, O poles on the LHS, and 4 poles on the jw-axis.

Answer 1

by solving characteristic equation,

s^6 + s^5 - 6s^4 - s^2 - s + 6 = 0

we get a root of equation is,

s = -3

s = -1

s = 1

s = 2

s = i (imaginary)

s = -i (imaginary)

so we say like the 2 poles on RHS , 2 poles on LHS and 2 poles on the jw axis.

so option 3 is correct.