A controller $D(s)$ of the form $(1+K_D s)$ is to be designed for the plant $G(s) = \frac{1000\sqrt{2}}{s(s+10)^2}$ as shown in the figure. The value of $K_D$ that yields a a phase margin of $45^\circ$ at the gain cross-over frequency of $10 \text{ rad/sec}$ is ________ (round off to one decimal place).

GATE 2025 Electrical Engineering Q65 — Electrical Engineering

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Electrical Engineering · Control Systems - Frequency Response Analysis

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Drill mode: Phase Margin · 1/8

Figure from the original GATE 2025 paper. (IIT Roorkee archive)

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Recurring concept

Control Systems - Frequency Response Analysis has appeared in GATE Electrical Engineering 2 times across 2 years (2024, 2025).

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Control SystemsPhase MarginGain Crossover FrequencyController Design