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Non-minimum phase systems and Bode plot
Consider the bode plot for the system shown below:
What can be said about this system:
- The magnitude plot has a slope of -40 dB/decade. Its predominantly a second order system with double pole at origin.
- It has a non-minimum phase characteristic with negative phase margin.
Now can we say that the system is BIBO unstable. One of my undergrad student pointed out this to me. He said that its an unstable system because it seemed to have a double pole at origin. Infact another student approximated this bode plot with following transfer function:
s = tf('s');
g = 507*(s+7)/(s^2*(s^2+601*s+600));bode(g);
However, we need to keep following points in mind:
- Non-minimum phase systems are not always unstable system.
- Negative phase margin does not always imply instability.
- For non-minimum phase systems with stable poles, we can't apply the approximations that hold for a standard second order system.
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3 comments:
Hi Swagat,
How are you? How is your Research work at Ulster University.
What is the original transfer function that you are referring here.
Non-minimum phase system is always an unstable system in open loop.
Srinivas
Srinu: Nice to hear you after a long time.
Here the transfer function is not given. One has to find a suitable transfer function that describe the behaviour shown in the bode plot.
The conclusion is one can not always say that non-minimum phase systems are unstable (in open loop ofcourse!). Infact one has to be careful while using bode information to judge stability of a non-minimum phase systems.
Remember that if a zero lies on the right hand side of s-plane, then it is a non-minimum phase system. But this system is not unstable. Stability is determined by the poles of a transfer function only. However an unstable system is always a non-minimum phase system.
Yes, I am wrong. Non-minimum phase systems can not be controlled in closed-loop.
As you said, poles decide stability of a system.
BTW, how is work going on at Ulster.
Srinivas
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