Determining stability of min phase system using GM and PMby HasuChObe Tags: determining, phase, stability 

#1
Jul1709, 06:34 PM

P: 28

Alright, there's something I don't understand. The book says that the gain margin and phase margin must be nonnegative 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.




#2
Jul1809, 07:44 PM

P: 324

Your definition of minimum phase system is not correct:
"[A] system is said to be minimumphase 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). 



#3
Jul1809, 08:31 PM

P: 28





#4
Jul1909, 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? 



#5
Jul2009, 03:38 PM

P: 28

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. 



#6
Jul2109, 03:20 AM

P: 341

Negative gain margin? What is that anyway? You mean less than 1?




#7
Jul2109, 09:39 AM

P: 28




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