Match the transfer functions of the second-order systems with the nature of the systems given below.
Consider a unity feedback system with forward transfer function given by
$ G(s)=\frac1{(s+1)(s+2)} $
The steady-state error in the output of the system for a unit-step input is _________(up to 2 decimal places).
The number of roots of the polynomial, $ \style{font-family:'Times New Roman'}{s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200} $ , in the open left half of the complex plane is
The unit step response $ y(t) $ of a unity feedback system with open loop transfer function $ G(s)H(s)\;\frac K{(s+1)^2(s+2)} $ is shown in the figure. The value of $ K $ is _______ (up to 2 decimal places).
The phase cross-over frequency of the transfer function GS=100S+13 in rad/s is
Consider the following asymptotic Bode magnitude plot (ω is in rad/s).
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 ________.
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,
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?
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?
The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $\left(2-j3\right)$. List all the poles and zeroes.
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?
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 _________.
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
The unit step response of a system with the transfer function Gs=1-2s1+s is given by which one of the following waveforms?
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,
For the system governed by the set of equations:
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
The root locus of a unity feedback system is shown in the figure
The closed loop transfer function of the system is
For the given system, it is desired that the system be stable. The minimum value of α for this condition is _______________.
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_____________.
The closed-loop transfer function of a system is TS=4s2+0.4s+4. The steady state error due to unit step input is __________.
The state transition matrix for the system
x1.x2.=1011x1x2+11u
is
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 ______
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
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:
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
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?
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
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
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
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is
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
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
The signal flow graph for a system is given below. The transfer function Y(s)U(s) for this system is
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
The response y(t) to a unit step input is
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
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
The feedback system shown below oscillates at 2 rad/s when
The transfer function of a compensator is given as
Gcs=s+as+b.
Gcs is a lead compensator if
The phase of the above lead compensator is maximum at
The frequency response of a linear system G(jω) is provided in the tubular form below
The gain margin and phase margin of the system are
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
An open loop system represented by the transfer function Gs=s-1s+2s+3 is
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,
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
A two loop position control system is shown below
The gain K of the Tacho-generator influences mainly the
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
For the system 2s+1 the approximate time taken for a step response to reach 98% of its final value is
The frequency response of G(s) = 1 / [s (s + 1) (s + 2) ] plotted in the complex G(jω) plane (for o < ω < ∞) is
The system x = Ax + Bu with A=-1202,B=01 is
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?
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:
The polar plot of an open loop stable system is shown below. The closed loop system is
The first two rows of Routh's tabulation of a third order equation are as follows.
s322s244
This means there are
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
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
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
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
The state transition matrix of the above system is
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
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
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 ?
The asymptotic Bode magnitude plot of a minimum phase transfer function is shown in the figure :
This transfer function has
Figure shows a feedback system where K > 0
The range of K for which the system is stable will be given by
The transfer function of a system is given as
100s2+20s+100
The state space equation of a system is described by
x=Ax+Buy=Cx
where x is state v ector, u is inp ut, y is out put and A=010-2, B=01, C=10.
The transfer function G(s) of this system will be
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
The system shown in the figure is
If x=ReGjω, and y=ImGjω then for ω→0+, the Nyquist plot for Gs=1ss+1s+2 becomes asymptotic to the line
The system 900ss+1s+9 is to be such that its gain-crossover frequency becomes same as its uncompensated phase crossover frequency and provides a 45° phase margin. To achieve this, one may use
If the loop gain K of a negative feedback system having a loop transfer function Ks+3s+82is to be adjusted to induce a sustained oscillation then
The system shown in figure below
can be reduced to the form
with
Consider the feedback system shown below which is subjected to a unit step input. The system is stable and has following parameters kp = 4, ki = 10, ω = 500 and ξ = 0.7.
The steady state value of z is