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QUESTION: 1

The represents of in static diagram will be:

Solution:

From options we can easily solve the problem

Forward paths are:

Individual loop,

∴

QUESTION: 2

the angle of departure of the root locus at s = —1 + j is

Solution:

∴

∴

QUESTION: 3

The open-loop transfer function of a system is . The root locus of the system is

Solution:

QUESTION: 4

The open-loop transfer function of a system is G(s) = Indicate the correct root locus diagram is

Solution:

Breakaway point:

s = —3.4 is a valid breakaway point.

QUESTION: 5

A negative feedback control system has a transfer function G(s)

compensator G_{c}(s) = in order to achieve zero steady state error for a step input. Select 'a' and 'k' so that the overshoot to a step is approximately 5% and the settling time (with a 2% criterion) is approximately 1 second.

Solution:

The characteristics equation is 1 + G_{c}(s) G(s) I-1(s) = 0

compare equation (i) to standard

Now,

QUESTION: 6

The transfer function of a lead compensator is G_{c} s = . The maximum phase shift that can be obtained from this compensator is

Solution:

The standard transfer function of lead compensator is

......(i)

and given transfer function

put s = j ω then,

......(ii)

Compare equation (i) and (ii) we gt,

∴

∴ Maximum phase shift =

∴

QUESTION: 7

Calculate the sensitivity of the closed-loop system shown in figure below with respect to the forward path transfer function at w = 1.3 rad/sec.

Solution:

Here,

and H(s) = 0.50

∴

QUESTION: 8

The magnitude plot of a transfer function is shown in figure below. The transfer function is

Solution:

Initially slope is —6 dB/octave i.e. —20 dB/dec. so there must be a pole at origin. At ω = 2 rad/sec slope change to ω db/dec. so there is a zero at ω = 2

and At 0 = 10 rad/sec, slope change to —20 dB/sec. so there is a pole at ω = 10.

∴ Transfer function =

∴

∴ K = 0

∴ Transfer function =

*Answer can only contain numeric values

QUESTION: 9

The open-loop transfer function of a feedback system is

The gain margin of the system is___

Solution:

∴

∴

*Answer can only contain numeric values

QUESTION: 10

The open-loop transfer function of a feedback system is G (s)H (s) =

The value of gain k for obtaining a gain margin of 3 dB for stable system is_________

Solution:

∴

∴

QUESTION: 11

In the figure given below the phase margin and the gain margin are:

Solution:

QUESTION: 12

A LTI system is characterized by the homogeneous state equation The initial state is

The state transition matrix 4(t) is

Solution:

Given

QUESTION: 13

The state equation in the phase canonical form can be obtained from the transfer function by:

Solution:

The state equation from transfer function by parallel decomposition in the phase canonical form.

QUESTION: 14

Consider the system shown in figure below and investigate whether it is observable or not.

Solution:

and

and

For observability:

So the System is Observable

QUESTION: 15

For a (-)ve feedback second order control system in its step response, the maximum value of the output response in time domain form is given by

**Q. **The damping factor (damping coefficient) of this system is

Solution:

From the conventional approach we have,

Give that C(t)I_{max} = 1.75

∴ M_{p} = Maximum overshoot = 1.75 - 1.00 = 0.75

QUESTION: 16

For a (-)ve feedback second order control system in its step response, the maximum value of the output response in time domain form is given by

**Q. **The open-loop zero frequency gain of this given unity feedback control system equals to

Solution:

** **Closed loop transfer function

(put, H(s) = 1)

= Open loop transfer function

∴ Open loop Gain at zero frequency i.e. s

QUESTION: 17

The block diogram of a feedback system is shown in figure (a).

**Q.** Find the minimum value of G for which the step response of the system would

exhibit an overshoot as shown in figure (b).

Solution:

Closed loop transfer function:

Characteristic equation s^{2} + 3s + G = 0

For minimum valueof G 'ξ’ should be 0.6.

∴

G = 6.25

QUESTION: 18

The block diogram of a feedback system is shown in figure (a).

**Q. ** For G equal to twice this minimum value, find the time period 't' indicated in figure (b).

Solution:

∴

QUESTION: 19

The system shown in figure below has the oscillation of 2.5 rad/sec, and there are no poles in right half of s-plane.

**Q. **Determine the values of **K _{mar}.**

Solution:

Since the system oscillates, it is marginally stable. The characteristic equation of the system becomes.

Now the Routh's Array is

At marginal value of k,

Again, at this value of p,

∴

Given, ω = 2.5 rad /sec, therefore

k + 3 = 6.25

∴ k = 3.25

QUESTION: 20

The system shown in figure below has the oscillation of 2.5 rad/sec, and there are no poles in right half of s-plane.

**Q.** Also find the value of P.

Solution:

From the above solution:

at k = 3.25 then,

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