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computer science
systems analysis design
Questions and Answers of
Systems Analysis Design
In the block-diagram shown in Fig. 1.4 , determine the value of \(k_{1}, k_{2}, k_{3}\), so that the transfer function is as follows:1) \(k_{1}=1, k_{2}=\frac{2}{3}, k_{3}=6\)2) \(k_{1}=\frac{2}{3},
The differential equation of a control system is as follows:Determine the state and output equations of the system in the matrices form.1) \(\frac{d}{d t}\left[\begin{array}{l}x_{1} \\ x_{2} \\
Determine matrix \(\mathbf{A}\) in the state equations \((\dot{\mathbf{X}}=\mathbf{A X}+\mathbf{B} u)\) for the block-diagram of Fig. 1.5 if \(\mathbf{X}=\left[\begin{array}{l}x_{1}(t) \\
Determine the transfer function of a control system with the following state equations:1) \(\frac{m}{s^{2}+b s+k}\)2) \(\frac{k}{b s^{2}+m s+k}\)3) \(\frac{b}{m s^{2}+b s+k}\)4) \(\frac{1}{m s^{2}+b
The state equations of a control system are as follows. Determine the state-transition matrix of the system \((\boldsymbol{\varphi}(t))\).1) \(\left[\begin{array}{cc}(1+t) e^{-2 t} & t e^{-2 t}
Consider the LTI control system below.1) \(e^{-t}+e^{-2 t}\)2) \(e^{-t}+2 e^{-2 t}\)3) \(e^{-t}+1.5 e^{-2 t}\)4) \(1.5 e^{-t}+e^{-2 t}\) X = AX, y=CX Determine the output of the system based on the
Determine the state equations of the control system shown in Fig. 1.6.1) \(\frac{d}{d t}\left[\begin{array}{l}x_{1} \\ x_{2} \\ x_{3}\end{array}ight]=\left[\begin{array}{ccc}-1 & -1 & 0 \\ 0
In the rotational mechanical system shown in Fig. 1.7, determine the transfer function of \(\frac{\theta_{2}(s)}{T(s)}\).1) \(\frac{J_{1} s^{2}+k}{s^{2}\left(J_{1} J_{2}
The equation below shows the characteristic equation of a closed-loop control system. Determine its stability status.1) The system is stable.2) The system has one unstable root.3) The system has
Which one of the transfer functions below has a non-zero primary time response?1) \(\frac{1}{s^{2}+2 s+2}\)2) \(\frac{s}{s^{2}+2 s+2}\)3) \(\frac{s+1}{s^{2}+2 s+2}\)4) \(\frac{s^{2}+2 s+1}{s^{2}+2
Which one of the following choices is correct about a closed-loop control system with the characteristic equation of \(4 s^{3}+2 s^{2}+k s+1=0\) ?1) For \(k=2\), it oscillates with the angular
The open-loop transfer function of a control system with a negative unity feedback is as follows:For what value of \(k\), does the closed-loop system response oscillate?1) -15 2) 15 3) 34 4) 64
Determine the period of oscillations of the closed-loop control system's response illustrated in Fig. 3.1 .1) \(11.2 \mathrm{sec}\)2) \(6.5 \mathrm{sec}\)3) \(2.2 \mathrm{sec}\)4) \(2 \sqrt{10}
The differential equations of a control system are as follows:For what value of " \(a\) " and " \(b\) ", the system is stable?1) \(a b \geq 0\)2) \(a>0, b3) \(a>0, b=0\)4) \(a (x(t) +x(t) 2u(t)
The state equations of a control system are as follows. For what value of " \(k\) ", the system is stable?1) \(k>-2\)2) \(k>-1\)3) \(-24) \((-2,-1.5) \cup(-1, \infty)\) (t) = -k-2 k+1
In the control system shown in Fig. 3.2 , determine the range of " \(p\) ", so that the system is stable.1) \(p>0\)2) \(p>-1\)3) \(-34) \(-3Figure 3.2 1 R(s)- Y(s). s+1 s+p
For a control system with the signal flow graph (SFG), shown in Fig. 3.3 , and the transfer function of \(\frac{C(s)}{R(s)}\), which one of the following choices is correct?1) The system is always
For the control system, shown in Fig. 3.4 , determine the hidden modes of the system.1) \(1, \pm j\)2) 0 3) \(-1,0\)4) 1,0 Figure 3.4 X(s) 2+1 (s+2) Y(s)
For what range of \(k\), the control system, shown in Fig. 3.5 , is stable?1) \(-\frac{4}{3}2) \(-\frac{1}{3}3) \(-\frac{5}{3}4) \(-\frac{2}{3}Figure 3.5 X(s)- k Y(s) S s-1 s2+2s+1
The equation below shows the characteristic equation of a control system. How many unstable poles does it have?1) 1 2) 2 3) 3 4) 0 +s+53 +5s + 12s+ 100
The differential equations of a control system are as follows:For what value of " \(a\) " the system is stable?1) \(a2) \(a>-2\)3) \(-24) \(1 xi(t) = axi(t) +xz(t)+u(t) x2(t) = -2x1(t) +x2(t)
Determine the transfer function of \(\frac{C(s)}{R(s)}\) for the control system, shown in Fig. 3.6 . Is this system internally stable or unstable?1) \(\frac{3}{(s+1)(s+2)}\), stable 2)
In the control system, shown in Fig. 3.7 , the controller is in the form of \(G_{c}(s)=k_{P}+\frac{k_{l}}{s}\). Which one of the choices, illustrated in Fig. 3.8 , graphically shows the stability
For a control system with a negative unity feedback and the following open-loop transfer function, which one of the choices, shown in Fig. 3.9 , graphically shows the stability area of both
Use the defining integral to find the Fourier transform of \(f(t)=A[u(t+1)-u(t-2)]\).
(a) Use the defining integral to find the Fourier transform of the following waveform:\[f(t)=A[u(t+10)-u(t-10)]\](b) Use the MATLAB function fourier to find the same transform.
Use MATLAB and the defining integral to find the Fourier transform of the following waveform:\[f(t)=5 \pi \cos (\pi t / 4)[u(t)-u(t-8)]\]
Use the inversion integral to find the inverse transform of the following function:\[F(\omega)=10 \pi[u(\omega+10)-u(\omega-10)]\]
Use MATLAB and the inversion integral to find the inverse transform of the following function:\[F(\omega)=\cos (\pi \omega / 4)[u(\omega+4)-u(\omega-4)]\]
First find the transforms of the following functions. Then determine what type of characteristics they possess.(a) \(f_{1}(t)=100 e^{-100 t} u(t)\)(b) \(f_{2}(t)=1.25\left[e^{-100 t}-e^{-500 t}ight]
Find the inverse transforms of the following functions:(a) \(F_{1}(\omega)=\frac{10,000}{j \omega(j \omega+100)(j \omega+1000)}\)(b) \(F_{2}(\omega)=\frac{-10 \omega^{2}}{j \omega(j \omega+20)(j
Use MATLAB's fourier function to find the Fourier transforms of the following waveforms:(a) \(f_{1}(t)=3 u(-t)-3\)(b) \(f_{2}(t)=-\operatorname{sgn}(t)-u(-t)\)(c) \(f_{3}(t)=\operatorname{sgn}(t)+1\)
Find the Fourier transforms of the following waveforms:(a) \(f_{1}(t)=\frac{10}{j}\left(e^{i 2 t}-e^{-j 2 t}ight)+10\left(e^{j i t}+e^{-j 2 t}ight)\)(b) \(f_{2}(t)=\frac{10}{t}(\sin 5 t)\)
Find the Fourier transforms of the following waveforms:(a) \(f_{1}(t)=100 \sin [2 \pi(t-10)]\)(b) \(f_{2}(t)=5 e^{j 10 t} \operatorname{sgn}(t)\)
Find the inverse transforms of the following functions:(a) \(F_{1}(\omega)=6 \pi \delta(\omega)+6 \pi \delta(\omega-3)+6 \pi \delta(\omega-4)\)(b) \(F_{2}(\omega)=4 \pi \delta(\omega)-j 6 / \omega+4
Use the duality property to find the inverse transforms of the following functions:(a) \(F_{1}(\omega)=50 \cos (100 \omega)\)(b) \(F_{2}(\omega)=10 u(\omega)-5\)(c) \(F_{3}(\omega)=6 e^{-|2 \omega|}\)
Use the time-shifting property to find the inverse transforms of the following functions:(a) \(F_{1}(\omega)=[6 \pi \delta(\omega) j 6 / \omega] e^{-j 5 \omega}\)(b) \(F_{2}(\omega)=50 e^{-j 4
Given that the Fourier transform of \(f(t)\) is\[F(\omega)=\frac{100,000}{(j \omega+500)(j \omega+1000)}\]Use the integration property to find the waveform\[g(t)=\int_{-\infty}^{t} f(x) d x\]
Use the reversal property to show that\[\mathscr{F}\left\{A e^{-\alpha t \mid} \operatorname{sgn}(t)ight\}=\frac{-2 A j \omega}{\omega^{2}+\alpha^{2}}\]
Use the frequency shifting property to show that\[\mathscr{F}\{\cos (\beta t) u(t)\}=\frac{j \omega}{\beta^{2}-\omega^{2}}+\frac{\pi}{2}[\delta(\omega-\beta)+\delta(\omega+\beta)]\]
The input in Figure P18-17 is \(v_{1}(t)=5 e^{-|t|} \mathrm{V}\). Use Fourier transforms to find \(v_{2}(t)\). V(t) + 0.1 uF + 10 V(1)
The input in Figure P18-18 is \(v_{1}(t)=1 \operatorname{Osgn}(t)\) V. Use Fourier transforms to find \(v_{2}(t)\). V(t) +1 10 www 0.1 F 10 V2(t)
The input in Figure P18-19 is \(v_{1}(t)=10 e^{10 t} u(-t)\) V. Use Fourier transforms to find \(v_{2}(t)\). 1 w + V(t) + 1 F 1 V2(1)
The input in Figure P18-19 is \(v_{1}(t)=2 \operatorname{sgn}(t) \mathrm{V}\). Use Fourier transforms to find \(v_{2}(t)\). V(t) 1 ww + 1 + 1 F: 1 v2(1) 19
(a) The input in Figure P18-21 is \(v_{1}(t)=3 u(-t) \mathrm{V}\). Use Fourier transforms to find \(v_{2}(t)\).(b) Will the OP AMP saturate? 1 0.1 F ww + V(t) 10 w + V2(t) Vcc = 15 V
The input in Figure P18-22 is \(v_{1}(t)=3 e^{-2|t|} u(-t) \mathrm{V}\). Use Fourier transforms to find \(v_{2}(t)\). 0.1 F 2 10 w ww + + V(1) + V(1)
The input in Figure P18-23 is \(i_{1}(t)=10 e^{-5|t|} \mathrm{mA}\). Use Fourier transforms to find \(i_{2}(t)\). i2(t) i(t) 0.1 uF 10 mH 1
The impulse response of a linear system is \(h(t)=5 e^{-3 t}\) \(u(t)\). Find the output for an input \(x(t)=u(-t)\).
The impulse response of a linear system is \(h(t)=e\) \(-2|t|\). Find the output for an input \(x(t)=u(-t)\).
The impulse response of a linear system is \(h(t)=\delta(t\) )\(-5 e^{-2 t} u(t)\). Use MATLAB and Fourier transform techniques to find the output for an input \(x(t)=\operatorname{sgn}(-t)\).
The impulse response of a linear system is \(h(t)\) \(=A\left[\delta(t)-\alpha e^{-\alpha t} u(t)ight]\), with \(\alpha>0\). Let \(A=10\) and \(\alpha=3\) and use MATLAB to plot \(|H(\omega)|\). On
The impulse response of a linear system is \(h(t)=A\) \([\delta(t)-\sin (\beta t) / \pi t]\). Let \(A=5\) and \(\beta=2\) and use MATLAB to plot \(|H(\omega)|\). On the same axes, plot
Use MATLAB's ifourier function to find the system impulse response \(h(t)\) if the frequency response of a linear system is shown in Figure P18-29. 2 H(0) 1 -2 - 0 + +2 3
Find the \(1-\Omega\) energy carried by the signal \(F(\omega)=25 /\left(\omega^{2}ight.\) \(+625)\).
Compute the \(1-\Omega\) energy carried by the signal \(f(t)=\) \(9 e^{4.5^{t}} u(-t)\).
Find the \(1-\Omega\) energy carried by the signal\[F(\omega)=\frac{j \omega A}{\omega^{2}+\alpha^{2}}\]Then, find the percentage of the \(1-\Omega\) energy carried in the frequency band \(|\omega|
The impulse response of a filter is \(h(t)=3 e^{-200}\) \({ }^{t} u(t)\). Find the \(1-\Omega\) energy in the output signal when the input is \(x(t)=4 e^{-20 t} u(t)\). Verify your result using
The impulse response of a filter is \(h(t)=50 e^{-20 t} u(t)\). Find the \(1-\Omega\) energy in the output signal when the input is \(x(t)\) \(=u(t)\).
The current in a \(50-\mathrm{k} \Omega\) resistor is \(i(t)=-5 u(t+1)\) \(+10 u(t)-5 u(t-1) \mathrm{A}\). Find the total energy delivered to the resistor.
The transfer function of an ideal bandpass filter is \((\omega)\) \(=1\) for \(1800 \leq \omega \leq 2200 \mathrm{rad} / \mathrm{s}\). Use MATLAB to find the \(1-\Omega\) energy carried by the output
Given a rectangular pulse as shown in Figure 13-4, with amplitude A, width \(T\), and period \(T_{0}\), we can compute and plot the coefficients in the corresponding Fourier series. If we allow
Theoretically, an impulse has an amplitude spectrum that is constant at all frequencies. In practice, a constant spectrum across an infinite bandwidth cannot be achieved, nor is it really necessary.
The SDLC is just one model for systems development. Find at least one more and describe the differences.
Draw DFDs for each of these scenarios:(a) A customer goes into a bookshop and asks for this book. The member of staff looks for the book in the online stock catalogue and reports that the book is
Draw a physical DFD to model this vet practice scenario. Hallam Vets consists of two vets plus a receptionist. Both vets maintain records of treatment sessions. In addition, they maintain detailed
Draw an entity model to model the following car rental business scenario:● Cars are always rented from one location and are brought back to the same location.● Customers may pay by cash or credit
Draw an entity model to model this university scenario:● A university department employs lecturers and clerical staff.● It offers a three-year degree.● A student has to take 12 modules during
Logicalize the following, if necessary:● Type and copy invoice● Collate customer details● SR1 form – blue● File details from new customer● View patient’s name and address● Photocopy
Logicalize the mail order book company DFD shown in Figure 4.15 (overleaf). Figure 4.15 Book company DFD. Customer order Sales Verify order M1 Book list Sales File valid orders M2 Customer file
Produce a decision table to model the logic in this scenario: A postal delivery company delivers parcels air or rail transport. The price of delivery by air depends upon the weight of the parcel.
Produce a structured English specification for this scenario: A travel agent has account customers and individual customers. Account customers who have spent over £25,000 in the past year get a
Design a report for the Medical Centre showing the appointments for the following week. The report will be used by the receptionists to check patients as they arrive for their appointment, so
Produce a decision table to model the logic in this scenario: A postal delivery company delivers parcels air or rail transport. The price of delivery by air depends upon the weight of the parcel.
Produce a structured English specification for this scenario: A travel agent has account customers and individual customers. Account customers who have spent over £25,000 in the past year get a
Design a report for the Medical Centre showing the appointments for the following week. The report will be used by the receptionists to check patients as they arrive for their appointment, so
Normalize the following data taken from a student assessment form, bearing in mind that students will take a number of modules:- Student Number- Student Name- Student Address- Module Code- Module
Find the \(y\)-parameters of the two-port network in Figure P17-4. V 16 R BI R R3 ww 18+ V2 19
Find the load impedance \(Z\) for the following complex powers.(a) When \(S=2000+j 2500 \mathrm{VA}\) and \(|\mathbf{V}|=1000 \mathrm{~V}\).(b) When \(|S|=15 \mathrm{kVA}, P=12 \mathrm{~kW}, Q>0\),
An inductive load draws an apparent power of \(50 \mathrm{kVA}\) at a power factor of 0.7 from a \(3600-V(\mathrm{rms})\) source. Find the complex power \(S\) and the load impedance \(Z\).
Design an appropriate load that will draw 15 \(\mathrm{A}(\mathrm{rms}), 6 \mathrm{~kW}\), and \(4.5 \mathrm{kVAR}\) from a \(60-\mathrm{Hz}\) source. Would the components be larger or smaller if the
Design an appropriate load that will draw \(28 \mathrm{~A}\) (rms), \(2.2 \mathrm{~kW}\), at \(110 \mathrm{~V}\) (rms) from a \(400-\mathrm{Hz}\) source. Wha1 is its power factor? Prove your design
A load made up of a \(220-\Omega\) resistor in parallel with a \(200-\mathrm{mH}\) inductor is connected across a \(240-\mathrm{V}(\mathrm{rms}), 50-\mathrm{Hz}\) voltage source. Find the complex
An arc welder presents a load made up of a 100- \(\Omega\) resistor in parallel with a \(12-\mu \mathrm{F}\) capacitor in a \(60-\mathrm{Hz}, 110-\mathrm{V}\) (rms) supply.(a) Find the complex power
In Figure P16-11, the load \(Z_{\mathrm{L}}\) is a \(60-\Omega\) resistor in series with a capacitor whose reactance is \(-30 \Omega\). The source voltage is \(440 \mathrm{~V}\) (rms). Find the
Repeat Problem 16-11 when \(Z_{\mathrm{L}}\) is a \(30-\Omega\) resistor in parallel with an impedance of \(30-j 30 \Omega\).Data From Problem 16-11In Figure P16-11, the load \(Z_{\mathrm{L}}\) is a
In Figure P16-13, the load \(Z_{\mathrm{L}}\) is a 1500- \(\Omega\) resistor and the source voltage is \(440 \mathrm{~V}\) (rms). Find the complex power produced by the source. Vs j100 j100 --j25 92
The circuit in Figure P16-14 shows a power line distribution and an intermediate substation and a final user substation. The source \(\mathbf{V}_{S}\) generates and steps up the voltage to \(400
In Figure P16-15, the three load impedances are \(Z\) \({ }_{1}=20+j 15 \Omega, Z_{2}=25-j 10 \Omega\), and \(Z_{3}=75+j 50 \Omega\). UseMATLAB to solve for the three currents
Two loads are connected in parallel across an \(880 \mathrm{~V}(\mathrm{rms})\) line. The first load draws an average power of \(20 \mathrm{~kW}\) at a lagging power factor of 0.87 . The second load
The average power delivered to the load \(Z_{\mathrm{L}}\) in Figure P16-17 is \(46 \mathrm{~kW}\) at a lagging power factor of 0.7. The load voltage is \(2.4 \mathrm{kV}(\mathrm{rms})\) and the line
Repeat Problem 16-17 if the load power factor is a leading 0.92 .Data From Problem 16-17The average power delivered to the load \(Z_{\mathrm{L}}\) in Figure P16-17 is \(46 \mathrm{~kW}\) at a lagging
In Figure P16-20, the voltage across the two loads is \(\mid V_{\mathrm{L}}\) I \(=4.8 \mathrm{kV}\) (rms). The load \(Z_{1}\) draws an average power of \(15 \mathrm{~kW}\) at a lagging power factor
The two loads in Figure P16-20 draw apparent powers of \(\left|S_{1}ight|=50 \mathrm{kVA}\) at a lagging power factor of 0.72 and | \(S_{2} \mid=25 \mathrm{kVA}\) at unity power factor. The voltage
In Figure P16-22, the load voltage is \(\left|V_{L}ight|=4160 \mathrm{~V}\) (rms) at \(60 \mathrm{~Hz}\) and the load \(Z_{\mathrm{L}}\) draws an average power of 12 \(\mathrm{kW}\) at a lagging
In Figure P16-22, the load voltage is \(\left|V_{\mathrm{L}}ight|=\) \(2400 \mathrm{~V}\) (rms) at 60 Hz. The load \(Z_{\mathrm{L}}\) draws an apparent power of \(25 \mathrm{kVA}\) at a lagging power
A load draws \(4 \mathrm{~A}\) (rms) and \(5 \mathrm{~kW}\) at a power factor 0.8 (lagging) from a 60-Hz source. Select an appropriate capacitor to be placed in parallel with the load to raise the
A 60-Hz, 200-hp, 240-V (rms) motor draws 160 \(\mathrm{kW}\) of power with a 0.72 lagging power factor. Compute the complex power drawn by the motor. Then select an appropriate capacitor to improve
In a balanced three-phase circuit the line voltage magnitude is \(V_{\mathrm{L}}=9.8 \mathrm{kV}\) (rms). For a positive phase sequence:(a) Find all of the line and phase voltage phasors using
In a balanced three-phase circuit \(\mathbf{V}_{\text {an }}=500
A balanced Y-connected three-phase source has \(V_{\mathrm{AN}}=\) \(240
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