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Phase margin and gain margin are two measures of stability for a feedback control system. They indicate how much the gain or the phase of the system can vary before it becomes unstable. Phase margin is the difference (expressed as a positive number) between 180° and the phase shift where the magnitude of the loop transfer function is 0 dB.
It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
Figure 5: Bode gain plot to find phase margin; scales are logarithmic, so labeled separations are multiplicative factors. For example, f 0 dB = βA 0 × f 1. Next, the choice of pole ratio τ 1 /τ 2 is related to the phase margin of the feedback amplifier. [9] The procedure outlined in the Bode plot article is followed. Figure 5 is the Bode ...
Bode's ideal control loop frequency response has the fractional integrator shape and provides the iso-damping property around the gain crossover frequency. This is due to the fact that the phase margin and the maximum overshoot are defined by one parameter only (the fractional power of s {\displaystyle s} ), and are independent of open-loop gain.
Hendrik Wade Bode (/ ˈ b oʊ d i / BOH-dee, Dutch:; [1] December 24, 1905 – June 21, 1982) [1] was an American engineer, researcher, inventor, author and scientist, of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research.
Tools include the root locus, the Nyquist stability criterion, the Bode plot, the gain margin and phase margin. More advanced tools include Bode integrals to assess performance limitations and trade-offs, and describing functions to analyze nonlinearities in the frequency domain. [4]
The result is a phase margin of ≈ 45°, depending on the proximity of still higher poles. [ b ] This margin is sufficient to prevent oscillation in the most commonly used feedback configurations. In addition, dominant-pole compensation allows control of overshoot and ringing in the amplifier step response , which can be a more demanding ...
Magnitude response of a low pass filter with 6 dB per octave or 20 dB per decade roll-off. Measuring the frequency response typically involves exciting the system with an input signal and measuring the resulting output signal, calculating the frequency spectra of the two signals (for example, using the fast Fourier transform for discrete signals), and comparing the spectra to isolate the ...