Group I gives two possible choices for the impedance Z in the diagram- The circuit elemets in Z satisfy the condition R2C2 - R1C1- The tranfser function V0Vi represents a kind of controller- Match the impedances in Group I with the types of controllers in Group II-Group -IGroup-II1-PID controller2- Lead compensator3- Lag compensator

V_i(R_1C_1s+1)1R_1 = V_0Z ⇒V_0V_i= Z(R_1C_1s+1)R_1 In case of Q,Z=R_2C_2s+1C_2s+1 In case of R, Z=R_2R_2C_2s+1 Considering Q, nbsp; V_0V_i = nbsp; (R_1C ...

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Control Systems

Lag-Lead compensator

Group I gives...

Question

Group I gives two possible choices for the impedance $Z$ in the diagram. The circuit elemets in $Z$ satisfy the condition $R_{2} C_{2} > R_{1} C_{1}$ . The tranfser function $\frac{V_{0}}{V_{i}}$ 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
2. Lead compensator
3. Lag compensator

Q - 1, R - 2

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Q - 1, R - 3

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Q - 2, R - 3

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Q - 3, R - 2

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Solution

The correct option is C $Q - 2, R - 3$
$\frac{V_{i} (R_{1} C_{1} s + 1) 1}{R_{1}} = - \frac{V_{0}}{Z}$
$\Rightarrow \frac{V_{0}}{V_{i}} = - \frac{Z (R_{1} C_{1} s + 1)}{R_{1}}$
In case of Q, $Z = \frac{R_{2} C_{2} s + 1}{C_{2} s + 1}$
In case of R, $Z = \frac{R_{2}}{R_{2} C_{2} s + 1}$
Considering Q,
$\frac{V_{0}}{V_{i}} = - \frac{(R_{1} C_{1} s + 1)}{R_{1}} . \frac{(R_{2} C_{2} s + 1)}{C_{2} s}$
Considering R,
$\frac{V_{0}}{V_{i}} = - \frac{(R_{1} C_{1} s + 1)}{R_{1}} . \frac{R_{2}}{(R_{2} C_{2} s + 1)}$
$∵$ Given that $R_{2} C_{2} > R_{1} C_{1}$
$∴$ Considering R, controller is log compensator.
and Considering Q, Controller is PID controller.

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