**Cascade Compensation in Frequency Domain**

**1. A phase lead compensation leads to:**

a) Increase in overshoot

b) Reduction in bandwidth of closed loop system

c) Reduction in rise time of closed loop system

d) Reduction in gain margin

**Answer:** c

**Explanation:** Phase lead compensation and this is similar to the high pass filter results in increase in bandwidth reduction in settling time and thus, speed of response is improved.

**2. PD controller is used to compensate system. Compared to the uncompensated system, the compensated system has:**

a) A higher type number

b) Reduced damping

c) Higher noise amplification

d) Large transient overshoot

**Answer:** c

**Explanation:** Proportional Derivative controller is used to increase the bandwidth and also increases the signal to noise ratio by reducing the noise and increasing the signal.

**3. P+D controller:**

a) Introduces offset

b) Increases bandwidth

c) Increases margin of stability

d) Reduces velocity constant

**Answer:** c

**Explanation:** Proportional Derivative controller is the controller increases margin of stability and also used to increase he bandwidth and also increases the signal to noise ratio.

**4. Proportional controller:**

a) Introduces offset

b) Increases bandwidth

c) Increases margin of stability

d) Reduces velocity constant

**Answer:** a

**Explanation:** Proportional controller is the controller that is block used to control the gain of the control system and introduces offset error and there is no effect on the damping factor.

**5. The transfer function of a lead controller is 1+20s/1+5s. The high frequency magnitude of the lead controller to dB is ___________**

a) 1

b) 2

c) 3

d) 4

**Answer:** d

**Explanation:** G(s) = Tp (1+Tds)/s^2

It is type-2 function.

The type-2 function has a finite steady state error for unit-parabolic input.

**6. Controllers play the following role in control system:**

a) They amplify the signals going to the actuator

b) They act on the error signal coming out of the summing junction and output a suitable to the actuator

c) They try to reduce steady state error optimizes overshoot.

d) All of the mentioned

**Answer:** a

**Explanation:** Controller amplify the signals going to the actuator and they are of many types as proportional, integral, derivative some combinational controller as combination of two controllers and combination of all the controllers.

**7. The transfer function of the compensator is s+4/s+16. The maximum phase lead frequency and the corresponding phase is :**

a) 6 rad/sec, 36.87°

b) 8 rad/sec, 36.87°

c) 6 rad/sec, -36.87°

d) 8 rad/sec, -36.87°

**Answer:** b

**Explanation:** Phase lead frequency is calculated when magnitude of transfer function is 1 and this is the phase cross over frequency and the phase is calculated by using the tanget formula with the transfer function.

**8. Response to error is very fast for integral controller.**

a) True

b) False

**Answer:** b

**Explanation:** Integral controller is used to reduce or eliminate the error of the control system and for derivative controller the damping factor is increased and speed of response also increases.

**9. Consider the following statements:**

**1. Integral controller improves steady state response**

**2. By use of proportional controller, maximum peak overshoot decreases**

**3. Type and order of system reduces by one for derivative controller**

**4. Integral controller makes the system less stable in transient state due to oscillations**

**Select the correct answer using the codes given below:**

a) 1,3 and 4

b) 1,2 and 3

c) 2.3 and 4

d) 1,2 and 4

**Answer:** a

**Explanation:** Integral controller improves steady state response and derivative controller improves the transient response, type and order of system reduces by one for derivative controller.

**10. Rate mode controller is also known as ______________ controller mode.**

a) Anticpatory

b) Delay

c) Integral

d) Derivative

**Answer:** a

**Explanation:** Anticipatory controller mode is also known as the rate mode controller that is used to anticipate the future value with the use of the state.