Question regarding Gain/Phase Margins and Bode Plots

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In summary, the conversation discusses the stability of a system with a loop gain of G(s)H(s). It is stated that the open GH loop must be stable for designing via Bode Plots, and that if the gain crossover frequency is less than the phase crossover frequency for the open loop, the closed loop system will be stable. The gain crossover frequency is defined as the frequency at which the gain is unity or 0db. It is also mentioned that the Nyquist plot may not pass through (-1 + j0) if the gain crossover frequency is less than the phase crossover frequency, which indicates stability. However, the reason for this is not clear and further clarification is requested. The use of Sisotool in MATLAB is
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maverick280857
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Hi

While going through http://eprints.iisc.ernet.in/archive/00013500/01/lec_6_web.pdf, I came across the following two statements (on page 3), for a system with loop gain = [itex]G(s)H(s)[/itex]:

1. Open GH loop must be stable for designing via Bode Plots.

2. If for GH, gain crossover < phase crossover for open loop, closed loop will be stable.

The gain crossover frequency is the frequency at which the gain is unity or 0db. If it is less than the phase crossover frequency (at which phase is 180), then as the frequency increases from 0, the gain becomes unity before the phase becomes 180 degrees. So intuitively, the Nyquist plot does not pass through or encircle (-1 + j0). The closed loop system is therefore stable. Is this correct?

I could not understand the reason for (1). Can someone please help?

Thanks.
 
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Anyone?
 
  • #3
Be careful it is for empirical rules!

If you use an open loop unstable plant how can you tell if gain crossover < phase crossover or not where the phase information is flawed by the unstable frequency ?

In reality under some assumptions it is possible to stabilize an open loop unstable system but not with Bode plots. At least try Sisotool in MATLAB
 
  • #4
Thanks trambolin.
 

1. What are gain and phase margins in a control system?

Gain and phase margins are measures of the stability and robustness of a control system. Gain margin is the amount of gain that can be added to the system before it becomes unstable, while phase margin is the amount of phase shift that can be added before the system becomes unstable. They are typically represented graphically on a Bode plot.

2. How do I calculate gain and phase margins from a Bode plot?

Gain margin is calculated as the amount of gain (in decibels) at the frequency where the phase of the system is -180 degrees. Similarly, phase margin is calculated as the amount of phase shift (in degrees) at the frequency where the gain is 0 decibels. These values can also be read directly from the Bode plot.

3. What do gain and phase margins tell us about a control system?

Gain and phase margins provide information about the stability and robustness of a control system. A larger gain margin indicates the system is more stable and can tolerate more gain variations or disturbances. A larger phase margin indicates the system is more robust and can tolerate more phase shifts. A system with low margins may be prone to instability and oscillations.

4. How do I use gain and phase margins to design a stable control system?

To design a stable control system, the gain and phase margins should be greater than a certain threshold, typically 6 decibels for gain margin and 45 degrees for phase margin. If the margins are too low, the system may become unstable. To increase the margins, the controller can be tuned by adjusting the gain and phase of the system using techniques like PID tuning.

5. Can a control system have a positive gain or phase margin?

No, a control system cannot have a positive gain or phase margin. Positive gain margin indicates that the system is unstable, while positive phase margin indicates that the system is not robust and may exhibit overshoot or oscillations. A well-designed control system should have both negative gain and phase margins within a certain range to ensure stability and robustness.

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