Discuss the characteristics of open-loop and closed-loop systems. Further, describe the block diagram of the speed control system of an automobile with a human driver.

Explain the principle of servomechanism.

2. Write the differential equations for the mechanical system shown in Figure 1. Also obtain the electrical analogous circuit based on force ­current analogy.

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3. Use Mason's gain formula for determining the overall transfer function of the system shown in Figure 2.

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Define synchros. Explain its principle of working. Also mention its application.

Derive an expression for the transfer function of a field controlled d.c. servomotor.

5. A unity feedback system is characterized by an open-loop transfer function

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Determine the gain k so that the system will have a damping ratio of 0·5. For this value of k determine the settling time, peak overshoot and time to peak overshoot for a unit step input.

Discuss the different static error coefficients. How are these coefficients related to steady-state error?

Write and explain the defining equation of PI and PID modes of feedback control. Also derive their corresponding transfer functions.

7. A unity negative feedback control system has an open-loop transfer function consisting of two poles, two zeros and a variable gain k. The zeros are located at and and the poles at 0·1 and 1.

Using Routh stability criterion, determine the range of values of k for which the closed-loop system has 1 and 2 poles in the right-half of s-plane.

8. Write short notes on any four of the following:

Gain Margin and Phase Margin

Concept of State Variable

Diagonalisation

Application of Nyquist

Pneumatic Controller