Question

______indicates not only whether a system is stable, but also its degree of stability and how stability may be imposed if necessary.
1. Bode Plot
2. Polar Plot
3. Nyquist Plot
4. Nichols Plot

Answer 1

Correct Answer - Option 3 : Nyquist Plot

Explanation:

Nyquist plot:

1. Nyquist plots are an extension of polar plots for finding the stability of the closed-loop control systems. This is done by varying ω from −∞ to ∞, i.e. Nyquist plots are used to draw the complete frequency response of the open-loop transfer function.
2. In practice, it is not enough that a system is stable. There must also be some margins of stability that describe how stable the system is and its robustness. 
3. There are many ways to express this, but one of the most common is the use of gain and phase margins, inspired by Nyquist’s stability criterion. 
4. An increase in controller gain simply expands the Nyquist plot radially and an increase in the phase of the controller twists the Nyquist plot.
5. Hence from the Nyquist plot, we can easily pick off the amount of gain or phase that can be added without causing the system to become unstable. Hence option (3) is the correct answer.

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Method of drawing Nyquist plot:

• Locate the poles and zeros of the open-loop transfer function G(s)H(s) in the ‘s’ plane.
• Draw the polar plot by varying ω from zero to infinity.
• Draw the mirror image of the above polar plot for values of ω ranging from −∞ to zero.
• The number of infinite radii half circles will be equal to the number of poles at the origin.
• The infinite radius half-circle will start at the point where the mirror image of the polar plot ends. And this infinite radius half-circle will end at the point where the polar plot starts.