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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.
The notion of gain and phase margin is based upon the gain expression for a negative feedback amplifier given by = +, where A FB is the gain of the amplifier with feedback (the closed-loop gain), β is the feedback factor, and A OL is the gain without feedback (the open-loop gain). The gain A OL is a complex function of frequency, with both ...
Randomly varying channel gains such as fading are taken into account by adding some margin depending on the anticipated severity of its effects. The amount of margin required can be reduced by the use of mitigating techniques such as antenna diversity or multiple-input and multiple-output (MIMO). A simple link budget equation looks like this:
By selecting a point along the root locus that coincides with a desired damping ratio and natural frequency, a gain K can be calculated and implemented in the controller. More elaborate techniques of controller design using the root locus are available in most control textbooks: for instance, lag, lead , PI, PD and PID controllers can be ...
Usually system performance is described as robustness to instability (phase and gain margins), rejection to input and output noise disturbances and reference tracking.In the QFT design methodology these requirements on the system are represented as frequency constraints, conditions that the compensated system loop (controller and plant) could not break.
The geometry of these hyperplanes can be treated by using the gain graph with the same vertex set and an edge ij with gain g (in the direction from i to j) for each hyperplane with equation x j = x i + g. These hyperplanes are studied via the lift matroid of the gain graph (Zaslavsky 2003). Suppose the gain group has an action on a set Q.
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The loop gain is calculated by imagining the feedback loop is broken at some point, and calculating the net gain if a signal is applied. In the diagram shown, the loop gain is the product of the gains of the amplifier and the feedback network, −Aβ. The minus sign is because the feedback signal is subtracted from the input.