Register to reply

Determining stability of min phase system using GM and PM

by HasuChObe
Tags: determining, phase, stability
Share this thread:
HasuChObe
#1
Jul17-09, 06:34 PM
P: 32
Alright, there's something I don't understand. The book says that the gain margin and phase margin must be non-negative for a minimum phase system to be stable. But the definition of a minimum phase system is one without right half plane poles or zeroes. Doesn't that inherently make it stable? Looking for a good explanation.
Phys.Org News Partner Engineering news on Phys.org
Tiny UAVs and hummingbirds are put to test
Britain to trial driverless cars from 2015
NIST corrosion lab tests suggest need for underground gas tank retrofits
es1
#2
Jul18-09, 07:44 PM
P: 324
Your definition of minimum phase system is not correct:

"[A] system is said to be minimum-phase if the system and its inverse are causal and stable."

http://en.wikipedia.org/wiki/Minimum_phase

So the definition is more restrictive than just stable. The definition also doesn't care how you get the stability.

Also, I am not 100% sure about this but I think phase margin and gain margin only apply to systems with feedback. However there is nothing in the definition of a minimum phase system that requires feedback (i.e. the system could be an open amplifier).
HasuChObe
#3
Jul18-09, 08:31 PM
P: 32
Quote Quote by es1 View Post
Your definition of minimum phase system is not correct:

"[A] system is said to be minimum-phase if the system and its inverse are causal and stable."

http://en.wikipedia.org/wiki/Minimum_phase

So the definition is more restrictive than just stable. The definition also doesn't care how you get the stability.

Also, I am not 100% sure about this but I think phase margin and gain margin only apply to systems with feedback. However there is nothing in the definition of a minimum phase system that requires feedback (i.e. the system could be an open amplifier).
Okay, maybe not the definition, but one of the properties as a result of what you just said. But that still doesn't answer the question. Even in your definition, it says the system is stable. How is there instability resulting from gain margins and phase margins in my stable system?

es1
#4
Jul19-09, 11:55 PM
P: 324
Determining stability of min phase system using GM and PM

I guess I don't understand the question.
Here is what I thought you were asking:

System with such and such gain and phase margin = stable
Minimum phase system = stable

As both systems are stable, what makes them different?
HasuChObe
#5
Jul20-09, 03:38 PM
P: 32
Quote Quote by es1 View Post
I guess I don't understand the question.
Here is what I thought you were asking:

System with such and such gain and phase margin = stable
Minimum phase system = stable

As both systems are stable, what makes them different?
Alright, I figured out what the answer was. But my original question was this.

The book states that, given that a system is minimum phase, if the gain margin or phase margin are negative, the system is unstable. My issue was that a minimum phase system is already stable. Turns out, the book was referring to the open loop transfer function of the system, which makes a lot more sense. If the closed loop transfer function was minimum phase, the system would definitely already be stable. The open loop transfer function being minimum phase does not guarantee stability of the closed loop transfer function.

The stability for a closed loop system can be found using the open loop transfer function with the nyquist stability theorem which is where gain and phase margin come into play.
trambolin
#6
Jul21-09, 03:20 AM
P: 341
Negative gain margin? What is that anyway? You mean less than 1?
HasuChObe
#7
Jul21-09, 09:39 AM
P: 32
Quote Quote by trambolin View Post
Negative gain margin? What is that anyway? You mean less than 1?
Gain margin is how much gain (in decibels) you can add to the open loop transfer function of a feedback system before it becomes unstable. Essentially, if the transfer function of the open loop is minimum phase, you want the magnitude of the open loop transfer function to be less than 1 (which, in decibels, results in a negative dB value) when the phase is 180. This criteria relates to the Nyquist stability theorem. So if the gain at 180 degrees phase has a negative dB value, the gain margin would be positive. This indicates how much gain in dB you can add before your system becomes unstable. If the magnitude is greater than 1, and your open loop transfer function is minimum phase, your system is going to be unstable. The gain in dB at 180 degrees will be some positive number which means the gain margin would be a negative value.


Register to reply

Related Discussions
Stability of the Origin of an Almost Linear System Differential Equations 0
Stability of the Solar System Astronomy & Astrophysics 5
Asymptotic stability of a system ( ordinary DE) Calculus & Beyond Homework 3
Determining total amplitude of out of phase waves Introductory Physics Homework 2