The phase cross-over frequency of the transfer function $G\left(S\right)=\frac{100}{{\left(S+1\right)}^{3}}$ in rad/s is
Consider the following asymptotic Bode magnitude plot (ω is in rad/s).
Given the following polynomial equation
${s}^{3}+5.5{s}^{2}+8.5s+3=0$
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
$G\left(s\right)=\frac{K\left(s+1\right)}{s\left(1+Ts\right)\left(1+2s\right)},K0,t0.$
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?
For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function ${\overline{)\frac{Y\left(s\right)}{{X}_{2}\left(s\right)}}}_{{X}_{1}\left(s\right)=0}$?
In the signal flow diagram given in the figure, ${u}_{1}$ and ${u}_{2}$ are possible inputs whereas ${y}_{1}$ and ${y}_{2}$ 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 (2-j3). List all the poles and zeroes.
Find the transfer function $\frac{Y\left(s\right)}{X\left(s\right)}$ of the system given below.
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 ${e}^{-2t}\left(\mathrm{sin}5t+\mathrm{cos}5t\right)$ for a unit impulse input. The DC gain of the control system is _________.
Nyquist plot of two functions ${G}_{1}$(s) and ${G}_{2}$(s) are shown in figure.
Nyquist plot of the product of ${G}_{1}$ (s) and ${G}_{2}$(s) is
The unit step response of a system with the transfer function $G\left(s\right)=\frac{1-2s}{1+s}$ is given by which one of the following waveforms?
An open loop transfer function G(s) of a system is $G\left(s\right)=\frac{K}{s\left(s+1\right)\left(s+2\right)}$ 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:
the transfer function Y(s)/U(s) is given by
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 $\alpha $ for this condition is _______________.
The Bode magnitude plot of the transfer function $G\left(S\right)=\frac{K\left(1+0.5s\right)\left(1+as\right)}{s\left(1+{\displaystyle \frac{s}{8}}\right)\left(1+bs\right)\left(1+{\displaystyle \frac{s}{36}}\right)}$ is shown below: Note that -6 dB/octave = -20 dB/decade. The value of $\frac{a}{bk}$ is_____________.
The closed-loop transfer function of a system is $\mathrm{T}\left(\mathrm{S}\right)=\frac{4}{\left({\mathrm{s}}^{2}+0.4\mathrm{s}+4\right)}$. The steady state error due to unit step input is __________.
The state transition matrix for the system
$\left[\begin{array}{c}\stackrel{.}{{x}_{1}}\\ \stackrel{.}{{x}_{2}}\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]+\left[\begin{array}{c}1\\ 1\end{array}\right]u$
is
A system with the open loop transfer function
$G\left(S\right)=\frac{K}{s\left(s+2\right)\left({s}^{2}+2s+2\right)}$
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
$G\left(S\right)=\frac{5\left(s+4\right)}{s\left(s+0.25\right)\left({s}^{2}+4s+25\right)}$
The values of the constant gain term and the highest corner frequency of the Bode plot respectively are
The second order dynamic system
$\frac{dx}{dt}=PX+Qu$
$y=RX$
has the matrices P, Q and R as follows:
$P=\left[\begin{array}{cc}-1& 1\\ 0& -3\end{array}\right]Q=\left[\begin{array}{c}0\\ 1\end{array}\right]R=\left[\begin{array}{cc}0& 1\end{array}\right]$
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, h_{1}=b_{1} and h_{0}=b_{0}-b_{1}a_{1}, the input-output transfer function, $G\left(S\right)=\frac{C\left(s\right)}{U\left(s\right)}$ of the system is given by
A single-input single-output feedback system has forward transfer function $G\left(s\right)$ and feedback transfer function $H\left(s\right)$. It is given that $\left|G\left(s\right)H\left(s\right)\right|<1.$ 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
$\frac{C\left(s\right)}{R\left(s\right)}=\frac{s}{{s}^{2}+s+1}$
then G(s) is
Consider the system described by following state space equations
$\left[\frac{{\displaystyle \stackrel{.}{{x}_{1}}}}{\stackrel{.}{{x}_{2}}}\right]=\left[\begin{array}{cc}0& 1\\ -1& -1\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]+\left[\begin{array}{c}0\\ 1\end{array}\right]u;y=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]$
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 G_{m} 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 $(20log\left|G\left(s\right)\right|)$ 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 $\frac{\omega \left(s\right)}{{V}_{a}\left(s\right)}=\frac{10}{1+10s}$ When connected in feedback as shown below, the approximate value of K_{a} 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 $\frac{Y\left(s\right)}{U\left(s\right)}$ for this system is
The state variable formulation of a system is given as
$\left[\begin{array}{c}\stackrel{.}{{x}_{1}}\\ \stackrel{.}{{x}_{2}}\end{array}\right]=\left[\begin{array}{cc}-2& 0\\ 0& -1\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]+\left[\begin{array}{c}1\\ 1\end{array}\right]u,{x}_{1}\left(0\right)=0,{x}_{2}\left(0\right)=0andy=\left[\begin{array}{cc}1& 0\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]$
The system is
The response y(t) to a unit step input is
A system with transfer function
G(s)=$\frac{\left({s}^{2}+9\right)\left(s+2\right)}{\left(s+1\right)\left(s+3\right)\left(s+4\right)}$
is excited by $\mathrm{sin}\left(\omega t\right)$. The steady-state output of the system is zero at
The state variable description of an LTI system is given by
$\left(\begin{array}{c}\stackrel{.}{{x}_{1}}\\ \stackrel{.}{{x}_{2}}\\ \stackrel{.}{{x}_{3}}\end{array}\right)=\left(\begin{array}{ccc}0& {a}_{1}& 0\\ 0& 0& {a}_{2}\\ {a}_{3}& 0& 0\end{array}\right)\left(\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\end{array}\right)+\left(\begin{array}{c}0\\ 0\\ 1\end{array}\right)u$
$y=\left(\begin{array}{ccc}1& 0& 0\end{array}\right)\left(\begin{array}{c}{x}_{1}\\ {x}_{2}\\ {x}_{3}\end{array}\right)$
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
${G}_{c}\left(s\right)=\frac{s+a}{s+b}$.
${G}_{c}\left(s\right)$ 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 $G\left(s\right)=\frac{\left(s-1\right)}{\left(s+2\right)\left(s+3\right)}$ is
The open loop transfer function $G\left(s\right)$ of a unity feedback control system is given as
$G\left(s\right)=\frac{k\left(s+{\displaystyle \frac{2}{3}}\right)}{{s}^{2}\left(s+2\right)}$
From the root locus, it can be inferred that when k tends to positive infinity,
The response $h\left(t\right)$ of a linear time invariant system to an impulse $\delta \left(t\right)$, under initially relaxed condition is $h\left(t\right)={e}^{-t}+{e}^{-2t}$. The response of this system for a unit step input $u\left(t\right)$ 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 $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$\left(s+1\right)$}\right.\phantom{\rule{0ex}{0ex}}$ 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 $A=\left[\begin{array}{cc}-1& 2\\ 0& 2\end{array}\right],B=\left[\begin{array}{c}0\\ 1\end{array}\right]$ 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 G_{1},G_{2} and $\frac{1}{{G}_{3}}$. The relative small errors associated with each respective subsystem G_{1},G_{2} and G_{3} are ε_{1},ε_{2} and ε_{3}. 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.
$\begin{array}{ccc}{\mathrm{s}}^{3}& 2& 2\\ {\mathrm{s}}^{2}& 4& 4\end{array}$
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
$\frac{d{x}_{1}\left(t\right)}{dt}=-3{x}_{1}\left(t\right)+{x}_{2}\left(t\right)+2u\left(t\right)$
$\frac{d{x}_{2}\left(t\right)}{dt}=-2{x}_{2}\left(t\right)+u\left(t\right)$
$y\left(t\right)={x}_{1}\left(t\right)$
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 :
$\frac{dy\left(t\right)}{dt}+y\left(t\right)=\delta \left(t\right)$
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
$G\left(s\right)=\frac{1}{{s}^{2}+3s+2}$
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 :
${C}_{1}=\frac{10\left(s+1\right)}{\left(s+10\right)},{C}_{2}=\frac{s+10}{10\left(s+1\right)}$
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
$\frac{100}{{s}^{2}+20s+100}$
The state space equation of a system is described by
$\mathrm{x}=\mathrm{Ax}+\mathrm{Bu}\phantom{\rule{0ex}{0ex}}\mathrm{y}=\mathrm{Cx}$
where x is state v ector, u is inp ut, y is out put and $\mathrm{A}=\left[\begin{array}{cc}0& 1\\ 0& -2\end{array}\right],\mathrm{B}=\left[\begin{array}{c}0\\ 1\end{array}\right],\mathrm{C}=\left[\begin{array}{cc}1& 0\end{array}\right]$.
The transfer function G(s) of this system will be
where x is state vector, u is input,