Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of \( G(s) \) are given in the table below. The value of the gain \( K_I \; (>0) \) required for a 50° phase margin is __________ (rounded off to two decimal places).
Frequency response data of \( G(s) \):
\(\omega\) (rad/s) Magnitude (dB) Phase (degrees) 0.5 -7 -40 1.0 -10 -80 2.0 -18 -130 10.0 -40 -200
System diagram:
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of \( G(s) \) are given in the table below. The value of the gain \( K_I \; (>0) \) required for a 50° phase margin is __________ (rounded off to two decimal places).
Frequency response data of \( G(s) \):
| \(\omega\) (rad/s) | Magnitude (dB) | Phase (degrees) |
|---|---|---|
| 0.5 | -7 | -40 |
| 1.0 | -10 | -80 |
| 2.0 | -18 | -130 |
| 10.0 | -40 | -200 |
System diagram:
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Correct Answer: 1.11 - 1.13
Solution and Explanation
Top Questions on Current
A single-phase full-controlled thyristor converter bridge is used for regenerative braking of a separately excited DC motor with the following specifications:
- Rated armature voltage = 210 V
- Rated armature current = 10 A
- Rated speed = 1200 rpm
- Armature resistance = 1 Ω
- Input to the converter bridge = 240 V at 50 Hz
Assume that the motor is running at 600 rpm and the armature terminals are suitably reversed for regenerative braking.
If the armature current of the motor is to be maintained at the rated value, the triggering angle of the converter bridge (in degrees) should be ____________ (rounded off to two decimal places).
Motor and converter parameters:
Parameter Value Rated armature voltage 210 V Rated armature current 10 A Rated speed 1200 rpm Armature resistance 1 Ω Input to converter bridge 240 V at 50 Hz The armature of the DC motor is fed from the full-controlled bridge, and the field current is maintained constant.
A difference amplifier is shown in the figure. Assume the op-amp to be ideal. The CMRR (in dB) of the difference amplifier is (rounded off to 2 decimal places).
In the given circuit, the diodes are ideal. The current \( I \) through the diode \( D_1 \) in milliamperes is (rounded off to two decimal places).
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).
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