To reach -180 degrees at the frequency where the open-loop system's magnitude is 0 dB (the gain crossover frequency, ). The closed-loop system's phase margin is the additional amount of phase lag that is required for the open-loop system's phase įor now, we won't worry about where all this comes from and rather will concentrate on identifying the gain and phase margins That is, a time delay can be represented as a block with magnitude of 1 and phase. The time delay,, can be thought of as an extra block in the forward path of the block diagram that adds phase lag to the system, but has If there is a time delay greater than in the loop (where is the frequency in rad/sec where the magnitude is 0 dB and PM is the phase margin converted to radians), the closed-loop Margin also measures the system's tolerance to time delay. The phase margin is defined as the change in open-loop phase shift required to make the closed-loop system unstable. Systems with greater gain margins can withstand greater changes in system parameters before becoming unstable The gain margin is defined as the change in open-loop gain required to make the closed-loop Where is a variable (constant) gain and is the plant under consideration. Gain margin and phase margin to indicate the margin the system has before it would go unstable.Ĭonsider the following unity feedback system: One aspect, in particular, that a system's frequency response is usedįor determining is a system's "robustness." For example, how close is the system to becoming unstable? Here we use two quantities, Useful information about the system's time response. The manner in which the scaling and shifting of the sinusoidal output changes as a function of frequency provides Recall from the Introduction: System Analysis page that the frequency response of a system consists of evaluating how a sinusoidal input to a system is scaled and shiftedīy the system. Closed-Loop Stability from the Nyquist Diagram.Closed-Loop Performance from Bode Plots.
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