Question:
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of \( G(s) \) has a constant slope of \( -20 \, \text{dB/decade} \) at least till \( 100 \, \text{rad/sec} \) with the gain crossover frequency being \( 10 \, \text{rad/sec} \). The asymptotic Bode phase plot remains constant at \( -90^\circ \) at least till \( \omega = 10 \, \text{rad/sec} \). The steady-state error of the closed-loop system for a unit ramp input is (rounded off to 2 decimal places).
\includegraphics[width=0.5\linewidth]{58.png}
Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of \( G(s) \) has a constant slope of \( -20 \, \text{dB/decade} \) at least till \( 100 \, \text{rad/sec} \) with the gain crossover frequency being \( 10 \, \text{rad/sec} \). The asymptotic Bode phase plot remains constant at \( -90^\circ \) at least till \( \omega = 10 \, \text{rad/sec} \). The steady-state error of the closed-loop system for a unit ramp input is (rounded off to 2 decimal places).
\includegraphics[width=0.5\linewidth]{58.png}
\includegraphics[width=0.5\linewidth]{58.png}
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For steady-state error, identify the system type and calculate the velocity error constant \( K_v \) for a ramp input.
Updated On: Jan 23, 2025
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Solution and Explanation
Step 1: Steady-state error formula.
For a unit ramp input, the steady-state error is:
\[
e_{ss} = \frac{1}{K_v},
\]
where \( K_v \) is the velocity error constant.
Step 2: Calculate \( K_v \).
Substitute the given slope and crossover frequency:
\[
e_{ss} = 0.09 \, \text{to} \, 0.11.
\]
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