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Computer science
systems analysis and design
control system analysis and design

Questions and Answers of Control System Analysis And Design

Which one of the following pairs is NOT correctly matched; (input \(=x(t)\) and output \(=y(t))\)(a) Unstable system\(\frac{d y(t)}{d t}-0.1 y(t)=x(t)\)(b) Nonlinear system .... \(\frac{d y(t)}{d
Consider the mechanical system shown below. If the system is set into motion by unit impulse force, the equation of the resulting oscillation will be:(a) \(x(t)=\sin t\)(b) \(x(t)=\sqrt{2} \sin
The open loop DC gain of unity negative feedback system with closed-loop transfer function \(\frac{s+4}{s^{2}+7 s+13}\) is(a) \(\frac{4}{13}\)(b) \(\frac{4}{9}\)(c) 4(d) 13
Choose the correct matching:(P) \(a_{1} \frac{d^{2} y}{d x^{2}}+a_{2} y \frac{d y}{d x}+a_{3} y=a_{4}\)(Q) \(a_{1} \frac{d^{3} y}{d x^{3}}+a_{2} y=a_{3}\)(R) \(a_{1} \frac{d^{2} y}{d x^{2}}+a_{2} x
The transfer function of the system shown below is(a) \(\frac{1}{1+\tau s}\)(b) \(\frac{1}{(1+\tau s)^{2}}\)(c) \(\frac{\tau s}{1+\tau s}\)(d) \(\frac{\tau s}{(1+\tau s)^{2}}\) E,(s) R Cs Amp. gain =
Consider a system shown below:If the system is disturbed so that \(c(0)=1\), then \(c(t)\) for a unit step input will be(a) \(1+t\)(b) \(1-t\)(c) \(1+2 t\)(d) \(1-2 t\) U(s) 2 S C(s)
The impulse response of an initially relaxed linear system is \(e^{-2 t} u(t)\). To produce a response of \(t e^{-2 t} u(t)\), the input must be equal to(a) \(2 e^{-t} u(t)\)(b) \((1 / 2) e^{-2 t}
The unit impulse response of a unity feedback control system is given by;\[c(t)=-t e^{-t}+2 e^{-t},(t \geq 0)\]The open loop transfer function is equal to(a) \(\frac{(s+1)}{(s+2)^{2}}\)(b) \(\frac{2
The system has a transfer function \(\mathrm{P}(\mathrm{s})=\frac{2}{s+2}\). The gain for \(\omega=2 \mathrm{rad} / \mathrm{sec}\) will be(a) 0.707(b) 0.666(c) 0.5(d) 0.25
A linear time-invariant system initially at rest, when subjected to a unit-step input gives a response \(y(t)=t e^{-t} ; t>0\). The transfer function of the system is(a) \(\frac{1}{(s+1)^{2}}\)(b)
Match the following transfer functions and impulse responses: (1) (2) (3) Transfer function S s+1 S (s+1) 1 s(s+1) +1 (P) (Q) (R) Impulse responses h(t) h(t) h(1) A
The output \(y(t)\) of figure shown below with three inputs \(u_{1}, u_{2}\) and \(u_{3}\) using superposition, is(a) \(y(t)=5\left(\cos t-2 \sin 2 t-t^{2}\right)\)(b) \(y(t)=5\left(\cos t+2 \sin 2
The unit step response of a system is\[y(t)=1-\frac{7}{3} e^{-t}+\frac{3}{2} e^{-2 t}-\frac{1}{6} e^{-4 t}\]The transfer function model of the system is(a) \(\frac{(s+8)}{(s+1)(s+2)(s+4)}\)(b)
The figure shown below represents system I and system II. Now, consider following statements in respect of these systems when \(\mathrm{K}_{1}=\mathrm{K}_{2}=100\) nominally.1. System I and system II
A mercury thermometer was kept in ice \(\left(0^{\circ} \mathrm{C}\right)\) for an indefinite period. It was removed and immediately put in boiling water \(\left(100^{\circ} \mathrm{C}\right)\). It
Transform the system of Fig. P2.2 into a unit feedback system. R(s) + 1+s 1 +0.5s 10 3 + + 5 S C(s)
Block diagram model of a position control system is shown in Fig. P2.3:(a) In absence of derivative feedback ( \(\left.K_{t}=0ight)\), determine damping ratio of the system for amplifier gain
The block diagram of a feedback system is shown in Fig. P2.4 (a).(a) Find the closed loop transfer function.(b) Find the minimum value of \(\mathrm{G}\) for which the step response of the system
Consider the system shown in Fig. P 2.5. Determine the value of \(a\) such that the damping ratio is 0.5 . Also obtain the values of the rise time \(t_{r}\) and maximum overshoot
Consider the system shown in Fig. P2.6:(i) In the absence of derivative feedback \((a=0)\) determine the damping factor and natural frequency. Also determine the steady state error resulting from a
For the system shown in Fig. P2.7, determine characteristic equation. Hence find the following when excitation is a unit step ;(a) undamped natural frequency(b) damped frequency of oscillation(c)
The open loop transfer function of a unity feedback system is\[\mathrm{G}(s)=\frac{k}{s(s+2)}\]It is specified that the response of the system to a unit step input should have maximum overshoot of
The open loop transfer function of a unity feedback system is \(\mathrm{G}(s)=\frac{\alpha}{s(1+\beta s)}\). For this system overshoot reduces from 0.6 to 0.2 due to change in \(\alpha\) only. Show
Fig. P2.10 (a). shows a mechanical vibratory system. When \(8.9 \mathrm{~N}\) force is applied to the system, the mass exhibits the dynamics as shown in Fig. P2.10(b). Compute \(m, f\) and \(k\) of
The forward transfer function of a unity feedback type 1, second order system has a pole at \(s=-3\). The gain \(k\) is adjusted for the damping ratio of 0.6 . Compute steady state error if this
The open loop transfer function of unity feedback system is given by\[G(s)=\frac{40}{s(0.2 s+1)}\]Determine steady state error as a function of time for the input given by \(r(t)=(3+4 t) t\).
The closed loop transfer function of a system is given by\[\mathrm{T}(s)=\frac{\mathrm{C}(s)}{\mathrm{R}(s)}=\frac{k(s+z)}{s^{2}+4 s+8}\]where \(k\) and \(z\) are adjustable.(a) If \(r(t)=t\), find
The closed loop transfer function of a position control system is given by\[\frac{\mathrm{C}(s)}{\mathrm{R}(s)}=\mathrm{T}(s)=\frac{k(s+z)(s+4)}{(s+p)\left(s^{2}+6 s+25ight)}\]where \(k, p\) and
Identify order and type of systems shown in Fig. D2.1 (a) and (b). R(s) R(s) + + 10 S K 2 s + 4s + 16 K, S Fig. D2.1 (a) 500 (s + 1) (s+6) S s+2 C(s) C(s)
Determine which of the following second order systems are underdamped, which are critically damped and which are overdamped.(a) \(\mathrm{T}(s)=\frac{9 s^{2}+3 s+10}{s^{2}+5 s+2}\)(b)
Find the constant \(k\) for which the system with transfer function \(T(s)\) has the given second order response property.(a) \(\mathrm{T}(\mathrm{s})=\frac{10}{s^{2}+40 s+k}, \quad \xi=0.7\)(b)
For the system shown in Fig. D2.4, find \(k\) for which damping ratio of overall system is 0.7 . For this value of \(\mathrm{K}\) find undamped natural frequency. k 4 2 s + 12s + 2
For the unity feedback system with the forward transmittance\[\mathrm{G}(s)=\frac{4(s+1)}{(s+2)(s+3)\left(s^{2}+s+10ight)}\]Find system type and if the response reaches steady state, find steady
The Fig. D2.6 shows structure of a feedback control scheme. Determine \(T_{d}\) so that system exhibits critically damped dynamics. Compute its settling time. 1 sta ? 4 s(s+ 1.6)
Fig. D2.7 shows a servo system. Determine(a) Characteristics equation(b) Undamped frequency of oscillation(c) Damping ratio(d) Damping factor(e) Peak overshoot(f) First undershoot(g) Time interval
Compute static error coefficients for a unity feedback system with \(\mathrm{G}(s)=\frac{12}{s(s+6)}\). If input \(r(t)=4+3 t\), find steady state error. For this system if steady state error is to
The open loop transfer function of a unity feedback control system is given by\[\mathrm{G}(s)=\frac{k}{s(s \mathrm{~T}+1)}\](a) By what factor gain \(\mathrm{k}\) should be multiplied so that damping
The dynamics of a servo mechanism is characterised by\[\ddot{y}+4.8 \dot{y}=144 e\]where \(e=c-0.5 y\) is error signal.(a) Sketch block diagram of system(b) Find damping ratio, damped and undamped
Match List-I with List-II and select the correct answer using the codes given below the lists: (Response c(t) A. 0 List I to a unit step input) List II (Location of poles in the s-plane) 1. One at
The open-loop transfer function of a unity feedback control system is given by \(\mathrm{G}(s)=\frac{\mathrm{K}}{s(s+1)}\). If the gain \(\mathrm{K}\) is increased to infinity, then the damping ratio
In the given figure, spring constant is K, viscous friction coefficient is B, mass is M and the system output motion is \(y(t)\) corresponding to input force \(\mathrm{F}(t)\). Which of the following
The system shown in the given figure has a unit step input ;In order that the steady state error is 0.1 , the value of \(\mathrm{K}\) required is:(a) 0.1(b) 0.9(c) 1.0(d) 9.0 R- + K (s + 1) (0.1s +
The system shown in the given figure has a second order response with a damping ratio of 0.6 and a frequency of damped oscillations of \(10 \mathrm{rad} / \mathrm{sec}\). The values of
Match List-I with List-II and select the correct answer using the codes given below the lists: List-I (Location of poles on s-plane) A. B. # X X List-II (Type of response) fum 1. pama 2.
For a unit step input, a system with forward path transfer function \(G(s)=\frac{20}{s^{2}}\) and feedback path transfer function \(\mathrm{H}(s)=(s+5)\), has a steady state output of:(a) 20(b) 5(c)
A linear second-order system with transfer function:\[G(s)=\frac{49}{s^{2}+16 s+49}\]is initially at rest and is subjected to a step input signal. The response of the system will exhibit a peak
The unit impulse response of a linear time-invariant second order system is; \(g(t)=10 e^{-8 t} \sin\) \(6 t(t
Match List-I (Roots in the 's' plane) with List-II (Impulse response) and select the correct answer: List-I A. A single root at the origin (1) h(t) List-II
\([-a \pm j b]\) are the complex conjugate roots of the characteristic equation of a second order system. Its damping coefficient and natural frequency will be respectively:(a)
For a second order system, if both the roots equal then the value of damping ratio will be:(a) less then unity(b) equal to zero(c) equal to unity(d) greater than unity
A series circuit containing R, \(L\) and \(C\) is excited by a step voltage input. The voltage across the capacitance exhibits oscillations. The damping coefficient (ratio) of this circuit is given
If a system is represented by the differential equation ;\[\frac{d^{2} y}{d t^{2}}+\frac{6 d y}{d t}+9 y=0\]then the solution \(\mathrm{y}\) will be of the form:(a) \(k_{1} e^{-t}+k_{2} e^{-9 t}\)(b)
The transfer function of a control system is given as ; \(T(s)=\frac{K}{s^{2}+4 s+K}\). For this system to be critically damped, the value of \(\mathrm{K}\) should be:(a) 1(b) 2(c) 3(d) 4
If the time response of a system is given by the following equation;\[y(t)=5+3 \sin \left(\omega t+\delta_{1}ight)+e^{-3 t} \sin \left(\omega t+\delta_{2}ight)+e^{-5 t}\]Then the steady state part of
The transfer function of a system is \(\frac{10}{1+s}\). When operated as a unity feedback system, the steady state error to a unit step input will be:(a) zero(b) \(1 / 11\)(c) 10(d) infinity
A unity feedback second order control system is characterised by \(\mathrm{G}(s)=\frac{\mathrm{K}}{s(\mathrm{~J} s+\mathrm{B})}\)where \(\mathrm{J}=\) moment of inertia, \(\mathrm{K}=\) system gain,
The open loop transfer function of a unity feedback system is given by \(\frac{\mathrm{K}}{s(s+1)}\). If the value of gain \(\mathrm{K}\) is such that the system is critically damped, the closed loop
For what values of ' \(a\) ' does the system shown in figure has a zero steady state error [i.e., \(\operatorname{Lim}_{t ightarrow \infty} e(t)\) ] for a step input:(a) \(a=0\)(b) \(a=1\)(c) \(a(d)
Match the following transfer functions and impulse responses and choose the correct answer: (1) (2) Transfer function S S+1 S (s+1) (P) (Q) h(t) h(t) Impulse responses
Match the following items from List-I and List-II and choose the correct answer: List-I Root locations of the characteristic equations of second order systems jo s-plane (1) X (2) s-plane X jo (P)
For the system shown in figure with a damping ratio \(\zeta\) of 0.7 and an undamped natural frequency \(\omega_{n}\) of \(4 \mathrm{rad} / \mathrm{sec}\), the values of \(\mathrm{K}\) and \(a\)
Consider the following expressions which indicate the step or impulse response of an initially relaxed control system:1. \(\left(5-4 e^{-2 t}ight) u(t)\)2. \(\left(e^{-2 t}+5ight) u(t)\)3.
Consider the systems with the following open loop transfer functions:1. \(\frac{36}{s(s+3.6)}\)2. \(\frac{100}{s(s+5)}\)3. \(\frac{6.25}{s(s+4)}\)The correct sequence of these systems in increasing
Match List-I with List-II and select the correct answer using the codes given below the lists: List-I (Characteristics equations) A. s + 15s + 26.25 2 B. s + 5s + 6.25 2 C. s+ 20.25 D. s + 4.5s +
A step function voltage is applied to an RLC series circuit having R \(=2 \Omega, \mathrm{L}=1 \mathrm{H}\) and \(\mathrm{C}=1 \mathrm{~F}\). The transient current response of the circuit would
A second order under damped system exhibited a \(15 \%\) maximum overshoot on being excited by a step input \(r(t)=2 u(t)\), and then attained a steady state value of 2 (see figures given). If, at
If the closed loop transfer function \(\mathrm{T}(s)\) of a unity negative feedback system is given by;\[\mathrm{T}(s)=\frac{a_{n-1} s+a_{n}}{s^{n}+a_{1} s^{n-1}+\ldots \ldots . .+a_{n-1}
A unity feedback control system has a forward path transfer function; \(\mathrm{G}(s)=\frac{10(1+4 s)}{s^{2}(1+s)}\), the system is subjected to an input \(r(t)=1+t+\frac{t^{2}}{2}(t \geq 0)\), the
The system shown in figure below is excited by unit step input and is required to exhibit output equal to input in steady state. The design effort is made to ensure that peak over shoot and \(2 \%\)
A continuous system has transfer function with a zero at \(s=-1\), a pole at \(s=-2\) and gain factor \(=2\). The unit step response generated by this system is(a) \(1+e^{-t}\)(b) \(1-e^{-2 t}\)(c)
The unit ramp response of a system having transfer function \(\mathrm{G}(s)=\frac{s+1}{s+2}\), is(a) \(\frac{1}{2}\left(1-e^{-2 t}ight)-t\)(b) \(\frac{1}{4}+\frac{1}{4} e^{-2 t}-\frac{1}{2} t\)(c)
If two identical first order stable low pass filters are cascaded non-interactively, then the unit step response of the composite filter will be(a) critically damped(b) overdamped(c) underdamped(d)
Consider the system shown in figure below. The value of \(K\) that contributes steady state error of \(20 \%\) to a unit step input, is(a) 2(b) 100(c) 20(d) 4 R(S) K s+1 K 4s + 1 Y(s)
When a unit step input is applied, a second order underdamped system exhibits a peak over shoot of \(\mathrm{M}_{p}\) at \(t=t_{p}\). If another step input equal in magnitude to peak overshoot
A third order system is approximated to an equivalent second order system. The rise time of the lower order system will be(a) same as that of original system for any input.(b) smaller than that of
A second order system has poles at \(s=-1 \pm j\). The step response of this system will exhibit peak value at(a) \(4.5 \mathrm{sec}\)(b) \(3.5 \mathrm{sec}\)(c) \(3.14 \mathrm{sec}\)(d) 1 sec.
A closed loop control system shown in figure below, is excited by a unit step function. The error it exhibits in steady state, is(a) -1.0(b) -0.5(c) 0.5(d) 0 R(s) 3/s + 2 s +2 Y(s)
The unit step response of a unity feedback system with open loop transfer function \(G(s)=\frac{K}{(s+1)(s+2)}\) is shown in the figure below. The value of \(K\), is(a) 0.5(b) 2(c) 4(d) 6 y(1) 1 0.75
The system shown in the figure below is excited by unit step input. The system is stable and \(K_{p}=4, K_{i}=10, \omega=500, \xi=0.7\). The steady state value of \(z(t)\), is(a) 1(b) 0.25(c) 0.1(d)
A two loop position control system is shown below.The gain \(\mathrm{K}\) of tachogenerator influences mainly the(a) peak overshoot.(b) natural frequency of oscillation.(c) phase shift of closed loop

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