Question:
Which of the following is the best method for determining the stability and transient response?
Which of the following is the best method for determining the stability and transient response?
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Use \textbf{Root Locus} for time-domain analysis (like stability and transient response), and \textbf{Bode/Nyquist plots} for frequency-domain analysis.
Updated On: Jun 24, 2025
- Root locus
- Bode plot
- Nyquist plot
- Polar plots
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The Correct Option is A
Solution and Explanation
The root locus method is one of the most effective graphical techniques used in control systems to study how the roots of the characteristic equation (i.e., the poles of the closed-loop transfer function) change with variation in system gain.
This technique is particularly useful for evaluating:
- Stability of the system — by observing whether the poles lie in the left half of the $s$-plane.
- Transient response — because the location of poles determines damping ratio, natural frequency, and hence the rise time, overshoot, and settling time.
Why not the others?
- Bode plots are mainly used for analyzing the frequency response and gain/phase margins.
- Nyquist plots also assess stability in frequency domain, but don’t provide insight into transient behavior.
- Polar plots show magnitude and phase but are not typically used for analyzing transient response or detailed stability margins.
Hence, Root Locus is the best tool for analyzing both stability and transient response characteristics.
This technique is particularly useful for evaluating:
- Stability of the system — by observing whether the poles lie in the left half of the $s$-plane.
- Transient response — because the location of poles determines damping ratio, natural frequency, and hence the rise time, overshoot, and settling time.
Why not the others?
- Bode plots are mainly used for analyzing the frequency response and gain/phase margins.
- Nyquist plots also assess stability in frequency domain, but don’t provide insight into transient behavior.
- Polar plots show magnitude and phase but are not typically used for analyzing transient response or detailed stability margins.
Hence, Root Locus is the best tool for analyzing both stability and transient response characteristics.
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