Nyquist stability. Vector addition. Bad diagram?

In summary, the author is discussing how a system with a large phase lag can be stable even with a 180 degree phase difference. He uses a figure to demonstrate this concept. However, the figure is confusing and does not follow any rules of vector addition that the reader is aware of.
  • #1
schlunk
27
0
This isn't exactly coursework, since I am no longer in school, but I think this may be the most appropriate forum to post in. This link is for a TI/Unitrode app note, "Control Loop Cookbook", which is about control loops for switching converters.
http://focus.ti.com/lit/ml/slup113a/slup113a.pdf [Broken]

I have been trying to read it, but I cannot understand a concept which he starts talking about on page 5-3. He seems to be saying that at frequencies below the crossover frequency (point where open loop gain =1), the system is always stable, even with 180 of phase lag (i.e. in-phase) an greater than unity gain. He admits that it seems counter-intuitive, and then points to a figure which explains it using vector addition (fig 3).

I think the figure must simply be a bad figure, because it doesn't seem to follow any rules of vector addition that I'm aware of. In 3a and 3b he has the two vectors meeting head to head. In figure 3b it seems to show a right triangle with a hypotenuse shorter than a leg.

Is this a bad graphic, or am I not getting it? Could someone please explain to me what he is trying to say?

Thank you for your help!
 
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  • #2
bump?
 
  • #3
Tbh I've studied some control theory, and I don't have a clue what he's trying to show with the vectors. Somehow he's using the Nyquist stability criterion without a Nyquist plot, hmmmm.

I'd find a better textbook to explain it, if you can. Or at least take a look here: http://www.facstaff.bucknell.edu/mastascu/eControlHTML/Freq/Nyquist3.html

I've actually got some good lecture notes in pdf form on basic control theory, so if you like then PM me with your email address and I'll send you them.
 

1. What is Nyquist stability analysis?

Nyquist stability analysis is a method used to analyze the stability of a closed-loop control system. It is based on plotting the frequency response of the open-loop transfer function and determining the number of encirclements around the critical point on the complex plane. A system is considered stable if the Nyquist plot does not encircle the critical point.

2. How is Nyquist stability related to the stability criterion?

Nyquist stability is directly related to the stability criterion, which states that a system is stable if and only if the number of right-half plane poles (RHP) is equal to the number of right-half plane encirclements (RHPE) in the Nyquist plot. This means that if the Nyquist plot encircles the critical point, the system will be unstable.

3. What is vector addition in the context of physics?

Vector addition is a mathematical operation used to combine two or more vectors to determine the resultant vector. In physics, vectors represent physical quantities with both magnitude and direction, such as force or velocity. Vector addition is used to determine the net force acting on an object or the total displacement of an object.

4. How is vector addition performed?

Vector addition involves breaking down each vector into its components and then adding the corresponding components together to determine the resultant vector. This can be done graphically using the head-to-tail method or algebraically using the Pythagorean theorem and trigonometric functions.

5. What makes a diagram "bad" in the context of science?

A bad diagram in the context of science is one that is inaccurate, unclear, or misleading. This can be due to incorrect labeling, lack of scale or units, or poorly drawn visuals. A good diagram should accurately represent the data or concept being presented and be easy to understand for the intended audience.

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