1
GATE ECE 2008
+2
-0.6
Group I gives two possible choices for the impedance Z in the diagram. The circuit elements in Z satisfy the condition $${R_2}{C_2} > {R_1}{C_{1.}}$$ The transfer $${\textstyle{{{V_0}} \over {{V_1}}}}$$ function represents a kind of controller. Match the impedances in Group I with the types of controllers in Group II. Group - I

Group - II
1. PID controller
3. Lag compensator

A
Q - 1, R - 2
B
Q - 1, R - 3
C
Q - 2, R - 3
D
Q - 3, R - 2
2
GATE ECE 2007
+2
-0.6
The open-loop transfer function of a plant is given as $$G(s) = {1 \over {{s^2} - 1}}.$$ If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is
A
$${{10\left( {s - 1} \right)} \over {s + 2}}$$
B
$${{10\left( {s + 4} \right)} \over {s + 2}}$$
C
$${{10\left( {s + 2} \right)} \over {s + 10}}$$
D
$${{2\left( {s + 2} \right)} \over {s + 10}}$$
3
GATE ECE 2007
+2
-0.6
A control system with a PD controller is shown in the figure. If the velocity error constant $${K_v} = 1000$$ and the damping ratio $$\zeta = 0.5,$$ then the values of $${K_P}$$ and $${K_D}$$ are
A
$${K_P} = 100,{K_D} = 0.09$$
B
$${K_P} = 100,{K_D} = 0.9$$
C
$${K_P} = 10,{K_D} = 0.09$$
D
$${K_P} = 10,{K_D} = 0.9$$
4
GATE ECE 2005
+2
-0.6
A double integrator plant, $$G(s) = {K \over {{s^2}}},H(s) = 1$$ is to be compensated to achieve the damping ratio $$\zeta = 0.5$$ and an undamped natural frequency, $${\omega _n} = 5$$ rad/sec. Which one of the following compensator $${G_c}(s)$$ will be suitable?
A
$${{s + 3} \over {s + 9.9}}$$
B
$${{s + 9.9} \over {s + 3}}$$
C
$${{s - 6} \over {s + 8.33}}$$
D
$${{s + 6} \over s}$$
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