**Output Regulator & the Tracking Problem**

**1. For output regulator problem in performance index the parameter which is set to zero:**

a) Input vector

b) Output vector

c) Control vector

d) State vector

**Answer:** b

**Explanation:** As the problem is to minimize the performance index involving output vector then the output vector must be close to zero.

**2. In tracking problem the parameter reduced is :**

a) Error

b) Output

c) Input

d) State

**Answer:** a

**Explanation:** In tracking problem the main objective is to reduce error and this is the main concern so as to reduce error.

**3. Riccati equation is formed by using:**

a) Output regulator problem

b) Finite state regulator problem

c) Infinite state regulator problem

d) Tracking problem

**Answer:** d

**Explanation:** Riccati equation can be formed using the results of the tracking problem as it is mainly applied in the cases where the errors are reduced to the minimum.

**4. The value of K must further follow the following constraint that the closed loop system must be:**

a) Asymptotically stable

b) Stable

c) Marginally stable

d) Conditionally stable

**Answer:** a

**Explanation:** The value of Ki must further follow the following constraint that the closed loop system must be asymptotically stable and this is due to the fact that the value of k matrix can be varied.

**5. For suboptimal control the value of R is assumed to be:**

a) Positive definite

b) Non-positive definite

c) Negative

d) Complex

**Answer:** b

**Explanation:** For suboptimal control the value of R is not assumed to be positive definite but it can also be assumed to be zero.

**6. Which one of the following compensation is required for improving the transient response of the system?**

a) Phase lead compensation

b) Phase lag compensation

c) Gain compensation

d) Both phase lag compensation and gain compensation

**Answer:** a

**Explanation:** For increasing or improving the transient response derivative controller is used and which is the phase lead compensation.

**7. Pneumatic controller**

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

**Answer:** c

**Explanation:** Pneumatic controllers are fire and explosion proof operation as they require air and gas fuel for its operation.

**8. Hydraulic controller:**

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

**Answer:** b

**Explanation:** Hydraulic controller must have no leakage and also it requires high torque and high speed operation due to high density of the controller.

**9. Electronic Controller:**

a) Flexible operation

b) High torque high speed operation

c) Fire and explosion proof operation

d) No leakage

**Answer:** a

**Explanation:** Flexible in all sense as it does not require heavy components or extra torque or high speed operations.

**10. Which one of the following statement is correct?**

**A plant controlled by a proportional controller. If a time delay element is introduced in the loop its:**

a) Phase margin remains the same

b) Phase margin increases

c) Phase margin decreases

d) Gain margin increases

**Answer:** c

**Explanation:** The introduction of a time delay element decreases both the phase and gain margin.