01․ The transfer function for tachometer E(S)/θ(S) is

Tachometer is a speed transducer. They are used as feedback elements in control system applications.
DC tachometer is a small DC generator whose input is mechanical speed and output is electrical voltage, voltage is proportional to speed.
Voltage E ∝ Speed (ω = dθ/dt)
E = K dθ/dt or E = Kω
By taking Laplace transforms,
E(S) = KS θ(S) or E(S) = Kω(S)
Transfer function E(S)/θ(S) = KS
E(S)/ω(S) = K

02․ Transient state analysis deals with -------------

Transient state analysis:
It deals with the nature of response of the system when subjected to an input.
Steady state analysis:
It deals with the estimation of magnitude of steady state error between output and input.

03․ Open loop transfer function,

This denotes a zero at s = 2 and a pole at s = - 2. So there exists a pole and a zero one at left half of s plane and other at right half of s plane. They denote symmetrical mirror images, so the given open loop transfer function denotes an all pass filter.

04․ When compared to a 1

^{st}order LPF, a 2^{nd}order LPF has2

^{nd}order low pass filter have higher cut off frequency than 1^{st}order low pass filter.05․ The step response of the system described by the differential equation will be

Applying Laplace Transform,
Applying Inverse Laplace Transform,
Y(t) = (1/6) × (1-e

^{-6t})06․ The impulse response of the system described by the differential equation will be

Applying Laplace Transform,
Applying Inverse Laplace Transform,
Y(t) = 1/3.

07․ The impulse response of the system described by the differential equation
will be

Take Laplace transform above differential equation.

08․ The type of a control system is obtained from -------------- transfer function?

The type of the system is obtained from open loop transfer function. The number of open loop poles occurring at origin determines the type of the control system.

09․ What is the type of closed loop system for the plant transfer function G(s) = k/s²(1+Ts) and with unity feedback?

Every transfer function representing a control system has certain type and order. The steady state analysis depends on the type of the control system. The type of the system is obtained from open loop transfer function. The number of open loop poles occurring at origin determines the type of the control system.
Therefore, for given transfer function type is 2.

10․ Which of the following statement is/are true statements?

Every transfer function representing a control system has certain type and order. The transient state analysis depends on the order of the control system. The order of system is obtained from closed loop transfer function. The highest power of the characteristic equation (1 + G(s)H(s) )determines the order of the control system.
The steady state analysis depends on the type of the control system. The type of the system is obtained from open loop transfer function. The number of open loop poles occurring at origin determines the type of the control system.

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