Questions & Answers of Control Systems

Question No. 17

The phase cross-over frequency of the transfer function GS=100S+13 in rad/s is

Question No. 40

Consider the following asymptotic Bode magnitude plot (ω is in rad/s).

Which one of the following transfer functions is best represented by the above Bode magnitude plot?

Question No. 42

Loop transfer function of a feedback system is GsHs=s+3s2s-3 Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of GsHs encircles -1+j0

Question No. 43

Given the following polynomial equation

s3+5.5 s2+8.5 s+3=0

the number of roots of the polynomial, which have real parts strictly less than −1, is ________.

Question No. 131

For the network shown in the figure below, the frequency (in rad/s) at which the maximum phase lag occurs is, ___________. 

Question No. 149

The open loop transfer function of a unity feedback control system is given by

Gs=Ks+1s1+Ts1+2s,  K>0,t>0.

The closed loop system will be stable if,

Question No. 159

Consider a linear time invariant system x.=Ax, with initial condition x0 at t=0. Suppose α and β are eigenvectors of (2 x 2) matrix A corresponding to distinct eigenvalues λ1 and λ2 respectively. Then the response xt of the system due to initial condition x0=α is

Question No. 160

A second-order real system has the following properties:
a) the damping ratio ζ=0.5 and undamped natural frequency ωn=10 rad/s,
b) the steady state value of the output, to a unit step input, is 1.02.
The transfer function of the system is

Question No. 162

The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function Gs=Kss-1s-4 is

Question No. 34

A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

Question No. 35

For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function YsX2sX1s=0?

Question No. 62

In the signal flow diagram given in the figure, u1 and u2 are possible inputs whereas y1 and y2 are possible outputs. When would the SISO system derived from this diagram be controllable and observable?

Question No. 63

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at (2-j3). List all the poles and zeroes.

Question No. 64

Find the transfer function YsXs of the system given below.

Question No. 65

The open loop poles of a third order unity feedback system are at 0,-1,-2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at -3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?

Question No. 134

An open loop control system results in a response of e-2tsin 5t+cos 5t for a unit impulse input. The DC gain of the control system is _________.

Question No. 135

Nyquist plot of two functions  G1(s) and G2(s) are shown in figure.

Nyquist plot of the product of G1 (s) and G2(s) is

Question No. 163

The unit step response of a system with the transfer function Gs=1-2s1+s is given by which one of the following waveforms?

Question No. 164

An open loop transfer function G(s) of a system is
Gs=Kss+1s+2
For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

Question No. 165

For the system governed by the set of equations:

dx1/dt = 2x1+x2+u
dx2/dt = -2x1+u
y=3x1


the transfer function Y(s)/U(s) is given by

 

Question No. 27

In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of

Question No. 28

The root locus of a unity feedback system is shown in the figure

The closed loop transfer function of the system is

Question No. 54

For the given system, it is desired that the system be stable. The minimum value of α for this condition is _______________.

Question No. 55

The Bode magnitude plot of the transfer function GS=K1+0.5s1+ass1+s81+bs1+s36 is shown below: Note that -6 dB/octave = -20 dB/decade. The value of abk is_____________.

Question No. 127

The closed-loop transfer function of a system is TS=4s2+0.4s+4. The steady state error due to unit step input is __________.

Question No. 128

The state transition matrix for the system

x1.x2.=1011x1x2+11u

is

Question No. 154

A system with the open loop transfer function

GS=Kss+2s2+2s+2

is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of K is ______

Question No. 155

For the transfer function

GS=5s+4ss+0.25s2+4s+25

The values of the constant gain term and the highest corner frequency of the Bode plot respectively are

Question No. 156

The second order dynamic system

dxdt=PX+Qu

y=RX

has the matrices P, Q and R as follows:

P=-110-3 Q=01 R=01

The system has the following controllability and observability properties:

Question No. 227

The signal flow graph of a system is shown below. U(s) is the input and C(s) is the output.

Assuming, h1=b1 and h0=b0-b1a1, the input-output transfer function, GS=CsUs of the system is given by

Question No. 228

A single-input single-output feedback system has forward transfer function Gs and feedback transfer function Hs. It is given that GsHs<1. Which of the following is true about the stability of the system?

Question No. 254

The block diagram of a system is shown in the figure

If the desired transfer function of the system is

CsRs=ss2+s+1

then G(s) is

Question No. 255

Consider the system described by following state space equations

x1.x2.=01-1-1x1x2+01u;    y=10x1x2

If u is unit step input, then the steady state error of the system is

Question No. 256

The magnitude Bode plot of a network is shown in the figure

The maximum phase angle $\phi_m$ and the corresponding gain Gm respectively, are

Question No. 3

Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is

Question No. 15

The Bode plot of a transfer function G(s) is shown in the figure below.

The gain (20logG(s)) is 32 dB and –8 dB at 1 rad/s and 10 rad/s respectively. The phase is negative for all ω. Then G(s) is

Question No. 28

The open-loop transfer function of a dc motor is given as ω(s)Va(s)=101+10s When connected in feedback as shown below, the approximate value of Ka that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

Question No. 40

The signal flow graph for a system is given below. The transfer function Y(s)U(s) for this system is

Question No. 50

The state variable formulation of a system is given as

x1.x2.=-200-1 x1x2+11u, x10=0, x20=0 and y=10 x1x2

The system is

Question No. 51

The state variable formulation of a system is given as

x1.x2.=-200-1 x1x2+11u, x10=0, x20=0 and y=10 x1x2

The response y(t) to a unit step input is

Question No. 6

A system with transfer function

G(s)=s2+9s+2s+1s+3s+4

is excited by sinωt. The steady-state output of the system is zero at

Question No. 41

The state variable description of an LTI system is given by

x1.x2.x3.= 0a1000a2a300 x1x2x3+001u

y=100x1x2x3

where y is the output and u is the input. The system is controllable for

Question No. 43

The feedback system shown below oscillates at 2 rad/s when

Question No. 54

The transfer function of a compensator is given as

Gcs=s+as+b.

 Gcs is a lead compensator if

Question No. 55

The transfer function of a compensator is given as

Gcs=s+as+b.

The phase of the above lead compensator is maximum at

Question No. 8

The frequency response of a linear system G(jω) is provided in the tubular form below

Gjω 1.3 1.2 1.0 0.8 0.5 0.3 Gjω −130oc −140oc −150oc −160oc −180oc −200oc

The gain margin and phase margin of the system are

Question No. 9

The steady state error of a unity feedback linear system for a unit step input is 0.1. The steady state error of the same system, for a pulse input r(t) having a magnitude of 10 and a duration of one second, as shown in the figure is

Question No. 21

An open loop system represented by the transfer function Gs=s-1s+2s+3 is

Question No. 33

The open loop transfer function Gs of a unity feedback control system is given as

Gs=ks+23s2s+2

From the root locus, it can be inferred that when k tends to positive infinity,

Question No. 41

The response ht of a linear time invariant system to an impulse δt, under initially relaxed condition is ht=e-t+e-2t. The response of this system for a unit step input ut is

Question No. 45

A two loop position control system is shown below

The gain K of the Tacho-generator influences mainly the

Question No. 10

As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately

Question No. 11

For the system 2s+1 the approximate time taken for a step response to reach 98% of its final value is

Question No. 36

The frequency response of G(s) = 1 / [s (s + 1) (s + 2) ] plotted in the complex G(jω) plane (for o < ω < ∞) is

Question No. 37

The system x = Ax + Bu with A=-1202,B=01 is

Question No. 38

The characteristic equation of a closed-loop system is s(s+1)(s+3)+k(s+2)=0, k>0. Which of the following statements is true?

Question No. 2

The measurement system shown in the figure uses three sub-systems in cascade whose gains are specified as G1,G2 and 1G3. The relative small errors associated with each respective subsystem G1,G2 and G3 are ε1,ε2 and ε3. The error associated with the output is:

Question No. 17

The polar plot of an open loop stable system is shown below. The closed loop system is

Question No. 18

The first two rows of Routh's tabulation of a third order equation are as follows.

s322s244

This means there are

Question No. 19

The asymptotic approximation of the log-magnitude vs frequency plot of a system containing only real poles and zeros is shown. Its transfer function is

Question No. 27

The unit-step response of a unity feedback system with open loop transfer function G(s) = K/((s + 1)(s + 2)) is shown in the figure. The value of K is

Question No. 28

The open loop transfer function of a unity feedback system is given by G(s) = (e-0.1s)/s. The gain margin of this system is

Question No. 55

A system is described by the following state and output equations

dx1tdt=-3x1t+x2t+2ut

dx2tdt=-2x2t+ut

yt=x1t

where u(t) is the input and y(t) is the output

The system transfer function is

Question No. 56

A system is described by the following state and output equations

dx1tdt=-3x1t+x2t+2ut

dx2tdt=-2x2t+ut

yt=x1t

where u(t) is the input and y(t) is the output

The state transition matrix of the above system is

Question No. 7

A function y(t) satisfies the following differential equation :

dytdt+yt=δt

where δ(t) is the delta function. Assuming zero initial condition, and denoting the unit step function by u(t), y(t) can be of the form

Question No. 64

The transfer function of a linear time invariant system is given as

Gs=1s2+3s+2

The steady state value of the output of the system for a unit impulse input applied at time instant t = 1 will be

Question No. 65

The transfer functions of two compensators are given below :

C1=10s+1s+10,C2=s+1010s+1

Which one of the following statements is correct ?

Question No. 66

The asymptotic Bode magnitude plot of a minimum phase transfer function is shown in the figure :

This transfer function has

Question No. 67

Figure shows a feedback system where K > 0

The range of K for which the system is stable will be given by

Question No. 68

The transfer function of a system is given as

100s2+20s+100

The system is

Question No. 78

The state space equation of a system is described by

x=Ax+Buy=Cx

where x is state vector, u is input, y is out put and A=010-2, B=01, C=10.

The transfer function G(s) of this system will be

Question No. 79

The state space equation of a system is described by

x=Ax+Buy=Cx

where x is state vector, u is input, y is out put and A=010-2, B=01, C=10.

A unity feedback is provided to the above system G(s) to make it a closed loop system as shown in figure.

For a unit step input r(t), the steady state error in the input will be

Question No. 8

The system shown in the figure is

Question No. 34

If x=ReGjω, and y=ImGjω then for ω0+, the Nyquist plot for Gs=1ss+1s+2 becomes asymptotic to the line