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computer science
digital control system analysis and design
Questions and Answers of
Digital Control System Analysis And Design
(a) Design a PI controller for Problem 8.6-4(b).(b) Design a PD controller for Problem 8.6-4(c).(c) Use the results of parts (a) and (b) to repeat Problem 8.6-4(d).Problem 8.6-4(b) (c) (d) (b) Design
To minimize the noise, the controller should have,a) Small gain at high frequenciesb) Small gain at low frequenciesc) Large gain at low frequenciesd) Large gain at high frequencies
In a lead compensator design, the requirement on pole is,a) \(p>\zeta \omega_{n}\)b) \(p-\zeta \omega_{n}\)d) \(p
Control system is a study(a) To control the failure of a system(b) To control the operation of a function(c) To control the actual output to match with desired output(d) To control the input
Open loop control system is the one that(a) Depend on output(b) Depend on input(c) Does not depend on input(d) Does not depend on output
Closed loop control system is the one that(a) Depend on output(b) Provides feedback(c) Provides stability(d) All of the above
Positive feedback system(a) Makes the system unstable(b) Makes the system stable(c) Makes the output positive(d) None of the above
Controller is defined as(a) A device that activates the plant(b) A device that activates the actuator(c) A device that controls the sensor(d) All of the above
Actuator is defined as(a) A device that activates the plant(b) A device that activates the controller(c) A device that activates the sensor(d) All of the above
A Plant or Process is defined as(a) A system that controls the activator(b) A system that controls the sensor(c) A system that activates the controller(d) A system to be controlled
A sensor is defined as(a) A device to measure the output from plant(b) A device to give feedback to controller(c) A device to function as sensing element in the system(d) All of the above
Transfer function is defined as(a) Ratio of input to output(b) Ratio of output to input(c) Sum of output and input(d) Difference between output and input
G/(1+GH) is the transfer function for(a) Open loop system(b) Positive feedback system(c) Negative feedback system(d) None of the above
G/(1-GH) is the transfer function for(a) Open loop system(b) Positive feedback system(c) Negative feedback system(d) None of the above
The transfer function of a dynamic system requires(a) The initial conditions to be zero(b) The initial conditions to be not zero(c) The initial conditions to be infinity(d) None of the above
[Z(s)] matrix is obtained from A. S2[M] + S2[C] + S2[K] B. S[M] + S2[C] + S3[K] C. [M]+ S[C] + S2[K] D. S2[M] + S[C] + [K]
Transfer function G(s) can be obtained from A. [Z(s)] B. [Z(s)]–1C. [Z(s)] [Z(s)] D. none of the above
Rule based method is applicable when, A. the mass matrix is dynamically uncoupled B. the mass matrix is diagonal C. the stiffness and damping matrix are symmetric D. all of the above
Poles are defined as A. the roots of the characteristic equation B. the square root of characteristic equation C. the roots of numerator equation of transfer function D. the square root of numerator
Zeros are defined as, A. square root of characteristic equation B. square root of numerator equation C. roots of numerator equation D. roots of denominator equation
At Poles, the output y(s) is equal to A. zero B. infinity C. one D. none of the above
At Zeros, the output y(s) is equal to A. zero B. infinity C. one D. none of the above
If G1 and G2 are in series, the equivalent transfer function is equal to(a) G1/G2(b) G1+G2(c) G1-G2(d) G1*G2
When you move the summing point from behind to ahead, the input ‘R2’ becomes(a) R2+G(b) R2/G(c) R2-G(d) R2*G
When you move the Pick-off point from ahead to behind, the Pick-off value is(a) Divided by G(b) Multiplied by G(c) All of the above(d) None of the above
In SFG (signal flow Graph), the Nodes represent(a) Input(b) Output(c) Junction point in a path(d) All of the above
In SFG, the lines (Branches) represent,(a) The total transfer function(b) The transfer function of a block(c) The loop transfer function(d) The path transfer function
The path transfer function is equal to(a) Sum of all transfer function in a path(b) Ratio of all transfer function in a path(c) Product of all transfer function in a path(d) None of the above
Mason’s formula is a function of(a) Path transfer function(b) Loop transfer function(c) Determinant function(d) All of the above
For single path,(a) Δ1=1(b) All the loop touches the path(c) T(s)=P1Δ1/Δ(d) All of the above
For two paths,(a) T(s)= (P1+P2) ( Δ1+Δ2)/ Δ(b) T(s)= (P1Δ1+P2Δ2)/ Δ(c) T(s)= (P1-P2) ( Δ1-Δ2)/ Δ(d) T(s)= (P1Δ1+P2Δ2)/ Δ
The loop are identified as touching, if(a) They are adjacent(b) They across(c) They overlap(d) All of the above
The error is given asa) \(\mathrm{E}=\mathrm{R}-\mathrm{Y}\)b) \(\mathrm{E}=\mathrm{R}(1-\mathrm{T})\)c) \(\mathrm{E}=\mathrm{R}-\mathrm{R}(\mathrm{Y} / \mathrm{R})\)d) All of the above
To minimize the disturbance, the controller should have,a) Large gain at high frequenciesb) Small gain at high frequenciesc) Large gain at low frequenciesd) Small gain at low frequencies
A marginally stable system in general considered as,A. Stable systemB. Unstable systemC. Neutral systemD. None of the above
For \(T=K P /(1+K P)\), the poles of a closed loop system at \(\mathrm{K}=0\) are equal toa) Open loop polesb) Open loop zerosc) Roots of the characteristic equationd) All of the above
The path or loci exist in a region wherea) \(K>0\)b) \(K=0\)c) \(K
\(K>0\) in a region if the sum of poles and zeros to the right of an arbitrary point in this region isa) Zerob) Oddc) Evend) None of the above
The value of \(K\) is zero ata) A zerob) On the horizontal axis of Root Locusc) On the vertical axis of Root Locusd) A pole
At a given zero, the value of ' \(K\) ' isa) Zerob) Infinityc) Positived) Negative
if there is no path or loci in a region, thena) \(K=0\)b) \(K=\infty\)c) \(K>0\)d) \(K
If a loci travels to a zero at infinity, it needsa) Cross-over pointsb) Break-away pointc) Asymptotesd) Break-in point
Angle of departure is required for a locia) To begin the travel from a real poleb) To begin the travel from a complex polec) To end the travel at complex poled) To end the travel at real pole
Cross-over points for a loci are the points wherea) The system is marginally stableb) The loci intersects the vertical axisc) They represent the roots of the auxiliary polynomiald) All of the above
PID controllers are used to improvea) Stabilityb) Steady state errorc) Industrial process controld) All of the above
Bode plot is,a) A logarithmic plotb) A polar plotc) A linear plotd) None of the above
Nyquist plot isa) A logarithmic plotb) A polar plotc) A linear plotd) None of the above
If \(T=\frac{1}{3+j 4}\), the magnitude \(|T|\) isa) \(1 / 5\)b) \(1 / 7\)c) \(1 / 25\)d) 25
The angle, \(\angle T\) isa) \(37^{\circ}\)b) \(-37^{\circ}\)c) \(-53^{\circ}\)d) \(53^{\circ}\)
If \(T=4, \angle T\) isa) \(90^{\circ}\)b) \(0^{\circ}\)c) \(76^{\circ}\)d) \(0.07^{\circ}\)
If \(T=j 4, \angle T\) isa) \(90^{\circ}\)b) \(0^{\circ}\)c) \(76^{\circ}\)d) \(0.07^{\circ}\)
Bandwidth frequency is the frequency ata) Magnitude \(=-3 d B\)b) Magnitude \(=-(1 / 2)\) (octave)c) \(|T|=0.71\)d) All of the above
If \(|T|=-1 d B @ \omega=5\) and \(-5 d B @ \omega=6\), the bandwidth frequency is,a) 11b) \(5 / 6\)c) 5.5d) \(6 / 5\)
Phase margin is the phase angle evaluated ata) Crossover frequencyb) Magnitude is zero \(d B\)c) Magnitude \(=1\)d) All of the above
Gain margin is the magnitude in \(d B\) evaluated ata) Frequency at \(\phi=-180^{\circ}\)b) Frequency at \(\phi=90^{\circ}\)c) Frequency at \(\phi=-90^{\circ}\)d) Frequency at \(\phi=180^{\circ}\)
the design parameter in the design of compensator are,a) \(\alpha\)b) \(\tau\)c) \(\alpha\) and \(\tau\)d) None of the above
In a lead compensator, if \(p=\) pole and \(z=\) zero,a) \(\alpha=p / z\)b) \(\alpha=z / p\)c) \(\alpha=p z\)d) \(\alpha=p+z\)
In a lag compensatora) \(\alpha=p / z\)b) \(\alpha=z / p\)c) \(\alpha=p z\)d) \(\alpha=p+z\)
In a lead compensator design,a) \(\tau=z p\)b) \(\tau=1 / z\)c) \(\tau=1 / p\)d) \(\tau=p z\)
In a Lag compensator design,a) \(\tau=1 / p z\)b) \(\tau=1 / z\)c) \(\tau=1 / p\)d) \(\tau=p z\)
Sensitivity of a system T.F. (T) with respect to Plant T.F. (G) is given bya) \(S_{G}^{T}=\left(\frac{\partial T}{\partial G}\right)\left(\frac{T}{G}\right)\)b) \(S_{G}^{T}=\left(\frac{\partial
Sensitivity of \(\mathrm{T}(\mathrm{s})\) with respect to a parameter \((\alpha)\) in \(\mathrm{G}(\mathrm{s})\) is given bya) \(S_{\alpha}^{T}=\frac{\partial T / T}{\partial \alpha / \alpha}\)b)
The steady state error is the value of error function, \(\mathrm{e}(\mathrm{t})\) evaluated ata) \(t=0\)b) \(t=\infty\)c) \(s=\infty\)d) All of the above
Gain setting is defined asa) The effect of change in gain on error functionb) The effect of change in gain on steady state errorc) The effect of error on gaind) The effect of gain on sensitivity
If \(E(s)=\frac{(s+4)(s+5)}{s\left(s^{2}+3 s+2\right)}\); the steady state error is,a) 10b) 0c) 0.1d) \(\infty\)
If \(E(s)=\left(\frac{1}{s^{3}}\right)\left(\frac{s^{3}+2 s^{2}}{s^{3}+4 s^{2}+5 s+1}\right)\); the steady state error is,a) 0.5b) \(\infty\)c) 0d) 2
If \(E(s)=\frac{s^{2}+3 s+4}{s^{3}+4 s^{2}+(5+2 K) s}\) and \(e_{s s}=0.05\), the value of \({ }^{\prime} K^{\prime}\) is,a) 375b) 3.75c) 37.5d) 0.375
\(T=\frac{9 S}{S^{2}+10 S}\) representsa) First order systemb) Second order systemc) Third order systemd) All of the above
Find value theorem is useful to find,a) Steady state errorb) Steady state responsec) The final value of outputd) All of the above
If \(E(s)=\frac{8 s^{2}+5 s}{9 s^{3}+4 s^{2}}\), the steady state error isa) \(8 / 9\)b) \(9 / 8\)c) \(5 / 4\)d) \(4 / 5\)
If \(\mathrm{T}_{\mathrm{s}}=\mathrm{K} / \zeta \omega_{\mathrm{n}}\) the value of \(\mathrm{K}\) for settling time within \(2 \%\) of final value isa) 4.6b) 3.9c) 3.0d) 2.3
For the above problem, the value of \(\mathrm{K}\) for settling time within \(5 \%\) of final value is,a) 4.6b) 3.9c) 3.0d) 2.3
For step input, the steady state error is zero fora) Type-1 systemb) Type-2 systemc) Type-3 systemd) All of the above
For ramp input, the steady state error is NOT zero fora) Type-1 systemb) Type-2 systemc) Type-3 systemd) All of the above
For quadratic input, the steady state error, \(e_{s s}=\frac{A}{K_{a}}\) fora) Type-1 systemb) Type-2 systemc) Type-3 systemd) All of the above
The error function is defined fora) \(E(s)=R(s)-Y(s)\)b) \(E(s)=R(s)[1-T(s)]\)c) \(E(s)=-R(s)\left[\frac{Y(s)-R(s)}{R(s)}\right]\)d) All of the above
If percent overshoot and settling time are given, we can finda) Damping ratiob) Natural frequencyc) Peak time and Peak valued) All of the above
The characteristic equation is,A. The number of controller transfer functionB. The denominator of controller transfer functionC. The numerator of total(system) transfer functionD. The denominator of
The roots of characteristic equation are called asA. ZerosB. PolesC. Complex zerosD. None of the above
For stability, the roots of characteristic equation should be on,A. Left half plane of S-PlotB. Right half plane of S-PlotC. On the Real Axis of S-PlotD. On the vertical Axis of S-Plot
For stability, the coefficients of \(s\) in the characteristic equation should beA. All positiveB. All negativeC. At least one positive and one negativeD. Equal number of positive and negative
For stability, the Routh array should beA. All values in the first column be positiveB. All values in the second column be positiveC. At least one negative value in the first columnD. None of the
On the given Routh array, the value \(b_{1}\) is,A. -12B. 6C. 0D. 3 $3 1 8 0 $2 2 4 0 S $1 5 b C1 b
Regarding first two rows on Routh array,A. One row is with odd powers and the other with even powersB. The coefficients of " \(s\) " are used to complete these two rowsC. First row begins with
The value of \(\mathrm{c}_{1}\) on the Routh array is,A. 4B. 0C. 8D. -16
Auxiliary polynomial is used for stability ifA. One of the elements on the first column of Routh array is zeroB. One of the columns on the Routh array is zeroC. One of the rows on the Routh array has
Auxiliary polynomial,A. Is the row preceding the row of zeros.B. Is an even order polynomial.C. Has symmetric rootsD. All of the above
If the roots are on vertical axis, the system isA. StableB. UnstableC. Marginally stableD. None of the above
Pre-filter in general is addeda) to eliminate a poleb) to eliminate a zeroc) to add a zerod) to add a pole
for a PI compensator, the prefilter is,а) \(G_{p}=\frac{\left(K_{I} / K_{p}\right)}{\left(s+{ }^{K_{I}} /
Prefilter for a system with \(T(s)=\frac{s+12}{s^{2}+7 s+12}\) is,a) \(G_{p}=12 /(s+12)\)b) \(G_{p}=7 /(s+12)\)c) \(G_{p}=1 /(s+12)\)d) \(G_{p}=4 /(s+12)\)
The velocity error constant for \(L(s)\) is,a) \(K_{v}=[L(s)]_{s=0}\)b) \(K_{v}=s[L(s)]_{s=0}\)c) \(K_{v}=s^{2}[L(s)]_{s=0}\)d) \(K_{v}=\frac{1}{s}[L(s)]\)
A fourth order system with state variables reduces to(a) 2 second order system(b) 1 third order and 1 first order system(c) 4 first order system(d) None of the above
The size of \([A]\) matrix in the state equation of a third order system is,(a) \(3 \times 3\)(b) \(3 \times 1\)(c) \(1 \times 1\)(d) \(1 \times 3\)
The size of \([C]\) matrix in the output equation of a third order system is,(a) \(3 \times 3\)(b) \(3 \times 1\)(c) \(1 \times 1\)(d) \(1 \times 3\)
If the \(T . F\). of a system is given, the state equation can be obtained from(a) Denominator polynomial(b) Input function in time domain(c) Numerator polynomial(d) Output function in time domain
The output equation can be obtained from(a) Denominator polynomial(b) Input function in time domain(c) Numerator polynomial(d) Output function in time domain
The Routh array for stability requires(a) characteristic equation(b) \(|Z(s)|=0\)(c) \(S[I]-[A]=0\)(d) All of the above
A system is controllable if(a) \(\left[P_{o}\right]=0\)(b) \(\left[P_{C}\right]=0\)(c) \(\left[P_{0}\right] eq 0\)(d) \(\left[P_{C}\right] eq 0\)
A system is observable if,(a) \(\left[P_{o}\right]=0\)(b) \(\left[P_{C}\right]=0\)(c) \(\left[P_{0}\right] eq 0\)(d) \(\left[P_{C}\right] eq 0\)
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