# Control system stability with respect to gain margin and phase margin

I have learn from control system that for a stable system gain margin and phase margin both must be positive. That is the truth.

But I have a doubt about this simple third order type 2 open loop transfer function whose phase margin is positive but gain margin is NEGATIVE. But both Nyquist stability criterion and Routh Hurwitz's criterion are showing that the close loop system will be stable.

How is it possible? Am I doing something wrong?

The system is as follows :

$\dfrac{K*(s+3)*(s+2)}{(s^2)*(s+1)}$ and value of K is "1".

I will be very thankful if someone clears my doubt. I have checked the system using MATLAB also.

• The open loop system MUST be stable but without knowing how you "close the loop" this question is unanswerable. – Andy aka Jan 9 '16 at 17:20
• gain margin and phase margin are nice hints for first order systems, but Nyquist criterion is the ultimate weapon you should always use. – Vladimir Cravero Jan 9 '16 at 17:22
• That is what I have been observed by examining the system. – Saprativ Saha Jan 10 '16 at 3:54