Constant M- loci:a)Constant gain and constant phase shift loci of the ...
Answer: d
Explanation: By definition, Constant M loci are Circles of constant phase shift for the closed loop transfer function.
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Constant M- loci:a)Constant gain and constant phase shift loci of the ...
D) Circles of constant phase shift for the closed-loop transfer function
Circles of constant phase shift, also known as constant phase loci, are graphical representations that show the relationship between the magnitude and phase of the closed-loop transfer function as the frequency varies. These circles are useful in analyzing the stability and performance of control systems.
The closed-loop transfer function is the ratio of the output to the input in a control system. It is given by the product of the open-loop transfer function and the feedback transfer function. The open-loop transfer function represents the system without any feedback, while the feedback transfer function represents the effect of the feedback on the system.
The circles of constant phase shift are obtained by plotting the locus of points in the complex plane where the phase of the closed-loop transfer function is constant. The magnitude of the closed-loop transfer function is also constant along these circles.
The phase shift of the closed-loop transfer function is the difference between the phase of the output and the phase of the input. It is a measure of the time delay between the input and output signals. By analyzing the circles of constant phase shift, we can determine the stability and performance of the control system.
The circles of constant phase shift can provide valuable insights into the behavior of the system. For example, if the circles are small and tightly packed, it indicates that the system has good phase margin and is stable. On the other hand, if the circles are large and widely spaced, it indicates that the system has poor phase margin and is likely to be unstable.
In summary, circles of constant phase shift are graphical representations that show the relationship between the magnitude and phase of the closed-loop transfer function as the frequency varies. They are useful in analyzing the stability and performance of control systems. By studying these circles, engineers can gain insights into the behavior of the system and make necessary adjustments to improve its performance.
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