Which of the following analysis is more convenient to see the effect of additional zero and pole in the system on the phase margin and the gain margin?
Which of the following analysis is more convenient to see the effect of additional zero and pole in the system on the phase margin and the gain margin? Correct Answer Root locus
Concept:
Root locus:
- It is a technique to analyze the movement of poles in the complex plane for a variable-gain closed-loop transfer function.
- A closed-loop system can be modeled in this way by determining an optimal value for the gain, K.
- This method is very much useful because it shows graphically the extremes of the circuit and helps to define regions of stability for gain in the range between K＝0 and K = ∞.
- Root-locus calculations also allow us to find the gain and phase margins and the damping ratio in a graphical or analytical fashion.
- The gain margin will be given by the point where the root locus crosses the imaginary axis in the complex plane.
- The phase margin is associated with the place where the root locus has a magnitude of one, and the damping ratio is equivalent to the cosine of the angle of the poles.
Important Points
The addition of poles to the transfer function has the effect of shifting the root locus to the right, making the system less stable. And less stable means the phase margin and gain margin are also less.
The addition of zeros to the transfer function has the effect of shifting the root locus to the left, making the system more stable. And more stable means the phase margin and gain margin are also high.
Hence, the Root locus may not be used for finding the exact phase margin and gain margin values.
But it is a more convenient method to analyze just the effect of the additional pole and zero on phase margin and the gain margin.
