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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.
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.
An easier method, but less general, is to use Bode plots developed by Hendrik Bode to determine the gain margin and phase margin. Design to ensure stability often involves frequency compensation to control the location of the poles of the amplifier. Electronic feedback loops are used to control the output of electronic devices, such as ...
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]
Within economics, margin is a concept used to describe the current level of consumption or production of a good or service. [1] Margin also encompasses various concepts within economics, denoted as marginal concepts , which are used to explain the specific change in the quantity of goods and services produced and consumed.
Margin loan rates for small investors generally range from as low as 6 percent to more than 13 percent, depending on the broker. Since these rates are usually tied to the federal funds rate, the ...
Average physical product (APP), marginal physical product (MPP) In economics and in particular neoclassical economics, the marginal product or marginal physical productivity of an input (factor of production) is the change in output resulting from employing one more unit of a particular input (for instance, the change in output when a firm's labor is increased from five to six units), assuming ...