1 A) Given G(s) = K/(s)(s5) Determine the phase angle at 0, 5 & frequencies.

Answer:

B) Derive the expressions for resonant peak

Resonant peak (Mr): Maximum value of M (jw) when w is varied from 0 to infinite. The

magnitude of resonant peak gives the information about the relative stability of the system. A

large value of resonant peak implies undesirable transient response.

C) Draw the Bode diagram for the following transfer function and obtain the gain and phase

cross over frequencies: G(S) = 10/ S(1+0.4S) (1+0.1S).

Answer:

2 A) Define polar plot and inverse polar plot.

Answer:

Polar plot is a plot which can be drawn between magnitude and phase. Here, the magnitudes

are represented by normal values only.

The polar form of G(jω) H(jω) is G(jω)H(jω) = |G(jω)H(jω)| ∠G(jω)H(jω)

The inverse polar plot is the mirror image of polar plot with respect to real axis.

The inverse polar plot of G(jω) is a graph of 1/G(jω) as a function of ω.

Ex: if G(jω) =1/jω then 1/G(jω) = jω

B) What is PID controller and write its merits and demerits.

Answer:

Proportional + integral + derivative controller (PID controller). A PID controller is the

combination of proportional control action and derivative control action with an adjustable gain

for each action.

Pd controller improves transient portion, pi controller improve steady state portion combination

of two may be used to improve overall time response of the system.

The proportional integral derivative controller produces an output, which is the combination of

the outputs of proportional, integral and derivative controllers.

C) What is a lag compensator, obtain the transfer function of lag compensator and draw pole-

zero plot?

Answer:

A system which has one zero and one dominating pole (the pole which is closer to origin that

all other poles is known as dominating pole) is known as lag network. The general form of the

transfer function of the lag compensator is

Therefore, the frequency response of the above transfer function will be

D) The open loop T.F. of a system G(s)H(s) = (1+4s)/s2(1+s)(1+2s). Sketch the Nyquist plot

and determine stability of closed loop system.

Answer:

3 A) Derive the transfer function from state space model.

Answer:

We know the state space model of a Linear Time-Invariant (LTI) system is

Apply Laplace Transform on both sides of the state equation.

Apply Laplace Transform on both sides of the output equation.

Substitute, X(s) value in the above equation.

The above equation represents the transfer function of the system. So, we can calculate the

transfer function of the system by using this formula for the system represented in the state

space model.

B) Determine the state controllability and observability of the following system

Answer:

C) Draw the state transition signal flow graph for the following system by parallel

decomposition. G(s) = 6(S+1)/S(S+2)(S+3).

Answer:

D) Given Find the unit step response when,

Answer:

4 A) Draw the state diagram of a state model.

Answer:

The concept of state space analysis of control system is very important to discuss here the

differences between the conventional theory of control system and modern theory of control

system.

B) Consider the matrix ‘A’ and compute eAt. A=

0 1

2 3

.

Answer:

The inverse of a 2×2 matrix is given here.

To find φ(t) we must take the inverse Laplace Transform of every term in the matrix

We now must perform a partial fraction expansion of each term, and solve

C) Find the Gain margin and phase margin of the system if the open loop transfer function is

.

Answer:

D) What is a lead compensator, obtain the transfer function of lead compensator and draw

pole-zero plot?

Answer:

A system which has one pole and one dominating zero (the zero which is closer to the origin

than all over zeros is known as dominating zero.) is known as lead network. The general form

of the transfer function of the load compensator is