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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.
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 ...
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. [2]
This is a technique used as a stability criterion in the field of classical control theory developed by Walter R. Evans which can determine stability of the system. The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot).
Two optimal control design methods have been widely used in industrial applications, as it has been shown they can guarantee closed-loop stability. These are Model Predictive Control (MPC) and linear-quadratic-Gaussian control (LQG). The first can more explicitly take into account constraints on the signals in the system, which is an important ...
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.
In a two-pole case, the result is peaking in the frequency response of the feedback amplifier near its corner frequency and ringing and overshoot in its step response. In the case of more than two poles, the feedback amplifier can become unstable and oscillate. See the discussion of gain margin and phase margin. For a complete discussion, see ...