An open loop system represented by the transfer function \(G\left
A. Stable and of the minimum phase type
B. Stable and of the non-minimum phase type
C. Unstable and the minimum phase type
D. Unstable and of the non-minimum phase type
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
Concept:
Minimum phase system: It is a system in which poles and zeros will not lie on the right side of the s-plane. In particular, zeros will not lie on the right side of the s-plane.
For a minimum phase system,
\(\mathop {\lim }\limits_{\omega \to \infty } \angle G\left( s \right)H\left( s \right) = \left( {P - Z} \right)\left( { - 90^\circ } \right)\)
Where P & Z are finite no. of poles and zeros of G(s)H(s)
Non-minimum phase system: It is a system in which some of the poles and zeros may lie on the right side of the s-plane. In particular, zeros lie on the right side of the s-plane.
Stable system: A system is said to be stable if all the poles lie on the left side of the s-plane.
Application:
\(G\left( s \right) = \frac{{\left( {s - 1} \right)}}{{\left( {s + 2} \right)\left( {s + 3} \right)}}\)
As one zero lies in the right side of the s-plane, it is a non-minimum phase transfer function.
As there no poles on the right side of the s-plane, it is a stable system.