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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.
Figures 8 and 9 illustrate the gain margin and phase margin for a different amount of feedback β. The feedback factor is chosen smaller than in Figure 6 or 7, moving the condition | β A OL | = 1 to lower frequency. In this example, 1 / β = 77 dB, and at low frequencies A FB ≈ 77 dB as well. Figure 8 shows the gain plot.
Hence the satellites' clocks gain approximately 38,640 nanoseconds a day or 38.6 μs per day due to relativistic effects in total. In order to compensate for this gain, a GPS clock's frequency needs to be slowed by the fraction: 5.307 × 10 −10 – 8.349 × 10 −11 = 4.472 × 10 −10
Classical control theory uses an array of tools to analyze systems and design controllers for such systems. Tools include the root locus, the Nyquist stability criterion, the Bode plot, the gain margin and phase margin.
LQR controllers possess inherent robustness with guaranteed gain and phase margin, [1] and they also are part of the solution to the LQG (linear–quadratic–Gaussian) problem. Like the LQR problem itself, the LQG problem is one of the most fundamental problems in control theory .
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 ...
It turns out that the calculation of the magnitude is not needed to determine if a point in the s-plane is part of the root locus because varies and can take an arbitrary real value. For each point of the root locus a value of can be calculated. This is known as the magnitude condition.
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...