Question 1

Q.1. What is synchro?

Accepted Answer

A synchro is an electromechanical transducer that converts angular shaft position into a set of AC voltages, used in pairs (transmitter-receiver) for remote position sensing and error detection in servo systems.

Question 2

Q.2. Write the Laplace transform of :

Accepted Answer

Using the Laplace transform property L{t^n e^{-at}U(t)} = n!/(s+a)^(n+1) with n = 2 and a = 3 gives X(s) = 2/(s+3)^3.

Question 3

Q.3. Find the order and type of the unity feedback system whose transfer func…

Accepted Answer

The system is of order 7 (highest power of s in the denominator) and Type 4 (number of poles at the origin, from the s^4 factor).

Question 4

Q.4. Classify the control system on the basis of damping ratio.

Accepted Answer

Based on damping ratio ζ, systems are classified as undamped (ζ = 0), underdamped (0 < ζ < 1), critically damped (ζ = 1), and overdamped (ζ > 1).

Question 5

Q.5. List any two applications of Root Locus.

Accepted Answer

Root locus is used to determine the range of gain K for closed-loop stability, and to select K/design compensators for desired transient response (damping ratio, settling time).

Question 6

Q.6. Draw the polar plot for function :

Accepted Answer

For G(s) = 1/[s^3(s+1)], the polar plot starts at infinite magnitude with phase -270° at ω→0 and ends at the origin with phase -360° as ω→∞, spiraling through the third and second quadrants.

Question 7

Q.7. What is feed forward control configuration?

Accepted Answer

Feed-forward control configuration adds a disturbance/reference-driven signal directly to the controller output path in anticipation of a known disturbance, without waiting for feedback error, thereby improving response speed and reducing steady-state error.

Question 8

Q.8. Explain Nyquist stability criterion.

Accepted Answer

The Nyquist criterion states that the number of closed-loop right-half-plane poles Z equals N + P, where N is the number of clockwise encirclements of the (-1, j0) point by the G(jω)H(jω) plot and P is the number of open-loop right-half-plane poles; the system is stable if Z = 0.

Question 9

Q.9. Draw electrical lag network and its pole zero plot.

Accepted Answer

An electrical lag network is an RC circuit (series R1 with parallel R2-C across the output) whose transfer function has a pole closer to the origin than its zero, producing phase lag; its pole-zero plot shows the zero to the right of the pole on the negative real axis.

Question 10

Q.10. What is all pass system? Also write its application.

Accepted Answer

An all-pass system has a magnitude response equal to unity (constant) at all frequencies but a frequency-dependent phase shift, achieved by pole-zero pairs symmetric about the jω-axis; used for phase/delay equalization without altering amplitude.

Question 11

Q.1. Derive the transfer function of electrical network as shown in Figure 1 …

Accepted Answer

Using the Laplace-domain impedance method on the L-C-R-R ladder network, the transfer function works out to Vo(s)/Vi(s) = R^2Cs / [LCs^2R + (L+R^2C)s + R], obtained via two-node analysis of the ladder circuit.

Question 12

Q.2. What is the closed loop transfer function of system with positive feedba…

Accepted Answer

For positive feedback, the closed-loop transfer function is C/R = G/(1-GH); since the denominator can approach zero (when GH→1), positive feedback tends to reduce the effective damping/increase gain sensitivity and can destabilize a system that would otherwise be stable under negative feedback.

Question 13

Q.3. State the difference between pneumatic actuator and pneumatic valve.

Accepted Answer

A pneumatic actuator is the complete final control element that converts air pressure into mechanical (linear/rotary) motion to position a load, whereas a pneumatic valve is the control element that regulates/directs the air-flow signal which drives the actuator; the actuator produces motion, the valve controls the fluid.

Question 14

Q.4. The step response of second order underdamped system is given by :

Accepted Answer

Matching C(t) to the standard underdamped step response gives ωn = √29 rad/s and ζ = 2/√29 ≈ 0.371; rise time tr ≈ 0.449 s and peak time tp ≈ 0.628 s.

Question 15

Q.5. The unit feedback control system transfer function is given by following…

Accepted Answer

For G(s)H(s) = K/[s(s²+2s+5)], the phase crossover frequency is ωpc = √5 rad/s; requiring a 6 dB gain margin gives K ≈ 5.02, and the corresponding phase margin at that K works out to approximately 20°.

Question 16

Q.6. Obtain STM (State Transition Matrix) for the state model whose matrix A …

Accepted Answer

For A = [[0,1],[-2,-3]], eigenvalues are -1 and -2; using the Laplace method φ(t) = L⁻¹[(sI-A)⁻¹] gives STM φ(t) with entries built from e^(-t) and e^(-2t) terms.

Question 17

Q.7. What is the need of compensation in control system? Compare lag-lead and…

Accepted Answer

Compensation is added to reshape a system's frequency/root-locus response to meet performance specs (steady-state accuracy, transient response, stability margins) that the uncompensated plant cannot satisfy on its own; lag-lead and lead-lag networks are two orderings of combining phase-lag and phase-lead stages to achieve both accuracy and speed simultaneously.

Question 18

Q.1. Obtain the overall transfer function C/R from the signal flow graph as s…

Accepted Answer

Using Mason's Gain Formula on the signal flow graph of Figure 2 (two forward paths through the diamond lattice and two feedback loops via ±H1), the overall transfer function reduces to C/R = (G2G4G6 + G3G5G1)/(1 + G2G9H1 + G3G1H1 + ... ) after evaluating all loop gains and non-touching combinations.

Question 19

Q.2. The open loop transfer function of a unity feedback control system is :

Accepted Answer

For G(s)=K/[s(1+sT)], damping ratio ζ is inversely proportional to √K, so raising ζ from 0.3 to 0.69 requires multiplying K by (0.3/0.69)² ≈ 0.189, i.e. the gain must be reduced to about 18.9% of its original value.

Question 20

Q.3. A unit feedback system is described by :

Accepted Answer

For G(s)H(s) = 10/[s(1+0.2s)(1+0.01s)], the Bode plot gives gain crossover frequency ≈ 6.9 rad/s, phase crossover frequency = √(1/0.002) ≈ 22.4 rad/s, gain margin ≈ 12.2 dB, phase margin ≈ 42°, and the closed-loop system is stable.

Question 21

Q.4. Given the unity feedback system, make an accurate plot of the root locus…

Accepted Answer

For G(s)=K²(s²-2s+2)/[(s+1)(s+2)], the root locus has 2 poles (-1,-2), 2 zeros (1±j1); breakaway/entry points occur on the real axis between the poles, the loci cross the jω-axis at specific points found via the Routh array, and the angle of arrival at the complex zero is computed from the angle condition.

Question 22

Q.5. Write short notes on the following : (a) Optimal control (b) Non-linear …

Accepted Answer

Optimal control designs the input that minimizes a defined performance index (e.g., quadratic cost, LQR) subject to system dynamics and constraints; non-linear control deals with systems violating superposition/homogeneity, using techniques like feedback linearization, sliding mode, and Lyapunov-based design instead of standard linear tools.

Control System