82 + Interview Questions in Digital Control Systems in Control Systems Page 2 InterviewSolution

51.	If X(z) =(z+z^-3)/(z+z^-1), then x(n) series has:(a) Alternate 0s(b) Alternate 1s(c) Alternate 2s(d) Alternate -1sI have been asked this question in an interview.Origin of the question is Difference Equations in section Digital Control Systems of Control Systems
Answer» The CORRECT choice is (a) Alternate 0s Easy explanation: Using the long division METHOD divide from DENOMINATOR. So, x(n) series has alternate ZEROS n =1,3,5……

Discussion

52.	The ROC of z-transform of the discrete time sequence x(n) = is:(a) 1/3>\|z\|1/2(c) \|z\|\|z\|
Answer» CORRECT choice is (a) 1/3>\|z\|<1/2 Easiest explanation: One PART of the EQUATION is the RIGHT sided signal and other part is the left sided signal hence the ROC of the system will be 1/3>\|z\|<1/2.

Discussion

53.	An LTI system having transfer function s^2+1/s^2+2s+1 and input x(t) =sin(t+1) is in steady state.The output is sampled at ws rad/s to obtain the final output {y (k)}. Which of the following is true?(a) Y is zero for all sampling frequencies ws(b) Y is non zero for all sampling frequencies ws(c) Y is non zero for ws>2 but zero for ws2 but non zero for ws
Answer» The CORRECT OPTION is (a) Y is zero for all sampling frequencies ws To explain I would SAY: X (t) =sin (t+1) w = 1 rad/s X(s) = e^s/s^2+1 Y(s) = e^s/s^2+2s+1 Y (∞) =0.

Discussion

54.	Assertion (A): The discrete time system described by y[n] =2x[n] +4x[n-1] is unstableReason (R): It has an impulse response with a finite number of non-zero samples(a) Both A and R are true and R is correct explanation of A(b) Both A and R are true but R is not correct explanationof A(c) A is true but R is false(d) A is false but R is trueThe question was asked in class test.I'd like to ask this question from The Z-Transfer Function in chapter Digital Control Systems of Control Systems
Answer» The CORRECT answer is (d) A is false but R is true The explanation is: For the system to be stable the value of the transfer FUNCTION in the discrete time domain must be SUMMABLE and H[n] calculated is summable HENCE the system is stable.

Discussion

55.	Consider the following statements:(a) The effect of feedback is to reduce the system error(b) Feedback increases the gain of the system in one frequency range but decreases in the other(c) Feedback can cause a system originally stable to become unstable(d) Both a and cThe question was asked in a job interview.This question is from Stability Analysis topic in section Digital Control Systems of Control Systems
Answer» Correct ANSWER is (d) Both a and c The best I can explain: Feedback reduces ERROR and can CAUSE STABLE system to become UNSTABLE and also can make unstable system stable.

Discussion

56.	Difference equation is used in :(a) Discrete time analysis(b) Continuous time analysis(c) Digital analysis(d) None of the mentionedI have been asked this question during an interview for a job.This key question is from Difference Equations in division Digital Control Systems of Control Systems
Answer» The CORRECT choice is (a) Discrete time ANALYSIS Easiest explanation: Difference equation are SIMILAR to the differentiation in the continuous SYSTEMS and they have same function in discrete time systems and is used in discrete time analysis.

Discussion

57.	Difference equation model results in:(a) Sampled-data systems(b) Numerical analysis of continuous time systems(c) Continuous time feedback systems(d) Both a and bI had been asked this question during an interview.The question is from Difference Equations in portion Digital Control Systems of Control Systems
Answer» Right OPTION is (d) Both a and b For explanation I WOULD say: EQUATION in discrete time systems can be difference equation which are SIMILAR to the differentiation in the continuous time systems and difference equation results in sampled data system and numerical analysis of continuous system.

Discussion

58.	Sampled data technique is appropriate as:(a) For long distance data transmission(b) Pulses are transferred by little loss of accuracy(c) More than one channel of information is sequentially sampled and transmitted.(d) All of the mentionedI got this question during an interview for a job.The query is from Signal Reconstruction in section Digital Control Systems of Control Systems
Answer» Right answer is (d) All of the mentioned To ELABORATE: Sampled data technique refers to the data which is sampled and is APPROPRIATE as for long DISTANCE COMMUNICATION, for ACCURATE transmission and multi channel transmission.

Discussion

59.	The characteristic equation of a system is 2s^5+s^4+4s^3+2s^2+2s+1=0 . Which one of the following is correct?(a) Stable(b) Marginally stable(c) Unstable(d) OscillatoryThe question was posed to me during an online interview.My question is based upon Compensation Techniques topic in section Digital Control Systems of Control Systems
Answer» Correct OPTION is (c) Unstable To explain: The solution is OBTAINED by using the Routh-Hurwitz table in which with the conventional method the number of sign CHANGES are SEEN in the FIRST row of the table and number of sign changes is equal to the number of the roots on the right half of s plane.

Discussion

60.	The region of convergence of a causal finite duration discrete-time signal is(a) The entire z-plane except z = 0(b) The entire z-plane except z = ∞(c) The entire z-plane(d) A strip in z-plane enclosing jω–axisI have been asked this question in quiz.My question is based upon The Z-transform Analysis of Sampled-Data Control Systems topic in division Digital Control Systems of Control Systems
Answer» Correct option is (a) The ENTIRE z-plane except z = 0 Best EXPLANATION: For DISCRETE time signal for any CAUSAL SYSTEM the region of convergence is always entire z-plane but except z =0.

Discussion

61.	Assertion (A): The z-transform of the output of the sampler is given by the series.Reason (R): The relationship is the result of the application of z = e^-sT, where T stands for the time gap between the samples.(a) Both A and R are true and R is correct explanation of A(b) Both A and R are true but R is not correct explanationof A(c) A is true but R is false(d) A is false but R is trueThe question was posed to me in homework.I would like to ask this question from The Z-Transfer Function in section Digital Control Systems of Control Systems
Answer» The correct choice is (c) A is true but R is false For explanation: T is termed as the time of the sampling instant and z TRANSFORM is ALWAYS DEFINED for the instant of the sampling event and this can be as desired by the USER.

Discussion

62.	A sequence x (n) with the z-transform X (z) = Z^4 + Z^2 – 2z + 2 – 3Z^-4 is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be:(a) -6(b) Zero(c) 2(d) -4I have been asked this question in unit test.Origin of the question is The Z-Transform in section Digital Control Systems of Control Systems
Answer» Correct CHOICE is (B) Zero The best I can explain: H (z) = 2z^-3 Then TAKING the inverse Laplace transform of the equation of Y (z) at n=4 y(n) =0.

Discussion

63.	If the region of convergence of x1[n]+x2[n] is 1/>\|z\|\|z\|\|z\|\|z\|\|z\|
Answer» Right OPTION is (d) 1/3>\|z\|<2/3 For EXPLANATION I would SAY: Region of Convergence is the region for which the values of the roots in z transform are lying in the function and ROC remains the same for ADDITION and subtraction in z-domain.

Discussion

64.	Two sequences x1 (n) and x2 (n) are related by x2 (n) = x1 (- n). In the z- domain, their ROC’s are(a) The same(b) Reciprocal of each other(c) Negative of each other(d) Complements of each otherThe question was asked by my college professor while I was bunking the class.The question is from The Z-Transform topic in section Digital Control Systems of Control Systems
Answer» The correct OPTION is (B) Reciprocal of each other To explain: x1(N) is the signal in the discrete domain and X1(z) is the signal in the z domain, ROC Rx z Reciprocals x2(n) = x1(-n) X1(1/z), RoC 1/ R

Discussion

65.	A signal m(t) with bandwidth 500 Hz is first multiplied by a signal g(t). The resulting signal is passed through an ideal low pass filter with bandwidth 1 kHz. The output of the low pass filter would be :(a) Impulse(b) m(t)(c) 0(d) m(t)del(t)The question was posed to me in homework.I'm obligated to ask this question of Spectrum Analysis of Sampling Process topic in chapter Digital Control Systems of Control Systems
Answer» CORRECT answer is (c) 0 The EXPLANATION is: m (t) G (t)->M (f)*G (f) After low pass filtering with FC =1 kHz, hence the output is zero.

Discussion

66.	Which of the following may result in instability problem?(a) Large error(b) High selectivity(c) High gain(d) NoiseI had been asked this question in my homework.The query is from Compensation Techniques topic in portion Digital Control Systems of Control Systems
Answer» Correct CHOICE is (c) HIGH gain Explanation: High gain results in instability problem and this is DUE to the low DAMPING factor and damping factor is inversely proportional to the gain of the system.

Discussion

67.	The characteristic equation of a control system is given by s^6+2s^5+8s^4+12s^3+20s^2+16s+16=0 . The number of the roots of the equation which lie on the imaginary axis of s-plane:(a) 0(b) 2(c) 4(d) 6The question was posed to me by my school teacher while I was bunking the class.The doubt is from Stability Analysis in section Digital Control Systems of Control Systems
Answer» Correct answer is (c) 4 For explanation I would say: The stability analysis is done USING Routh-Hurwitz CRITERION and hence the NUMBER of roots on the RIGHT is CALCULATED.

Discussion

68.	Assertion (A): Feedback control system offer more accurate control over open-loop systems.Reason (R): The feedback path establishes a link for input and output comparison and subsequent error correction.(a) Both A and R are true and R is correct explanation of A(b) Both A and R are true and R is not correct Explanation of A(c) A is True and R is false(d) A is False and R is trueThe question was posed to me in a national level competition.This interesting question is from Stability Analysis in portion Digital Control Systems of Control Systems
Answer» The correct option is (a) Both A and R are true and R is correct explanation of A The explanation: Feedback CONTROL system OFFERS more accuracy and also reduces the gainof the system and establishes the LINK for input and output COMPARISON and subsequent error correction.

Discussion

69.	Assertion (A): Z-transform is used to analyze discrete time systems and it is also called pulsed transfer function approach.Reason (R): The sampled signal is assumed to be a train of impulses whose strengths, or areas, are equal to the continuous time signal at the sampling instants.(a) Both A and R are true and R is correct explanation of A(b) Both A and R are true and R is not correct Explanation of A(c) A is True and R is false(d) A is False and R is trueThis question was posed to me during an online exam.This is a very interesting question from The inverse z-transform and Response of Linear Discrete Systrems in section Digital Control Systems of Control Systems
Answer» Correct answer is (a) Both A and R are true and R is correct explanation of A The BEST explanation: Z-transform is USED to convert the discrete TIME systems into the z domain and it is also called pulsed TRANSFER function approach that is justified only at the sampling instants.

Discussion

70.	If a periodic function f(t) of period T satisfies f(t) = −f (t + T/2) , then in its Fourier series expansion(a) The constant term will be zero(b) There will be no cosine terms(c) There will be no sine terms(d) There will be no even harmonicsThe question was asked during an online exam.My query is from The z- and s-Domain Relationship topic in chapter Digital Control Systems of Control Systems
Answer» Right option is (b) There will be no cosine terms For explanation I would SAY: The FOURIER series will contain the cosine terms if the PERIODIC function f (t) of period T satisfies f (t) = -f(t+T/2), and this can be PROVED by the basic definition of the fourier transform.

Discussion

71.	If G( f) represents the Fourier Transform of a signal g (t) which is real and odd symmetric in time, then G (f) is(a) Complex(b) Imaginary(c) Real(d) Real and non-negativeThis question was posed to me during an interview.This interesting question is from The z- and s-Domain Relationship in chapter Digital Control Systems of Control Systems
Answer» Correct OPTION is (b) Imaginary The best I can explain: For the real and odd SYMMETRIC SIGNAL in time DOMAIN on the FOURIER transform the resulting signal is always imaginary.

Discussion

72.	A bandpass sampling extends from 4-6 kHz. What is the smallest sampling frequency required to retain all the information in the signal.(a) 1 kHz(b) 2 kHz(c) 3 kHz(d) 4 kHzThis question was addressed to me in final exam.My question is taken from Spectrum Analysis of Sampling Process in portion Digital Control Systems of Control Systems
Answer» The CORRECT answer is (d) 4 KHZ The best I can explain: FH =6 kHz Bandwidth = 2 kHz Fs =4 kHz.

Discussion

73.	A band limited signal with a maximum frequency of 5 KHz to be sampled. According to the sampling theorem, the sampling frequency which is not valid is:(a) 5 KHz(b) 12 KHz(c) 15 KHz(d) 20 KHzI had been asked this question in quiz.This intriguing question comes from Spectrum Analysis of Sampling Process in chapter Digital Control Systems of Control Systems
Answer» The correct ANSWER is (a) 5 KHz To EXPLAIN I would SAY: FS (min) =2fm fs (min) =2*5 =10 KHz So, fs >=1o KHz.

Discussion

74.	The characteristic equation of the control system is s^5+15s^4+85s^3+225s^2+274s+120=0 . What are the number of roots of the equation which lie to the left of the line s+1 = 0?(a) 2(b) 3(c) 4(d) 5I had been asked this question during an internship interview.Origin of the question is Compensation Techniques topic in division Digital Control Systems of Control Systems
Answer» The CORRECT option is (C) 4 To explain: The solution is obtained with the HELP of the Routh-Hurwitz table and in this the solution is obtained by equating the VALUE as s-1 in the GIVEN equation.

Discussion

75.	The probability cumulative distribution function must be monotone and(a) Increasing(b) Decreasing(c) Non-increasing(d) Non-decreasingI have been asked this question during an interview for a job.This intriguing question comes from The Z-transform Analysis of Sampled-Data Control Systems in section Digital Control Systems of Control Systems
Answer» CORRECT answer is (d) Non-decreasing Easy EXPLANATION: The CUMULATIVE DISTRIBUTION function that is monotone and non-decreasing or can be increasing.

Discussion

76.	Which of the following techniques is utilized to determine at the actual point at which the root locus crosses the imaginary axis?(a) Nyquist technique(b) Routh-Hurwitz technique(c) Nichol’s technique(d) Bode techniqueI had been asked this question by my school teacher while I was bunking the class.My question is from Stability Analysis in portion Digital Control Systems of Control Systems
Answer» Right option is (b) Routh-Hurwitz TECHNIQUE The best I can explain: Routh-Hurwitz technique is utilized to DETERMINE at the actual point at which the root LOCUS crosses the IMAGINARY AXIS.

Discussion

77.	_______________ isa sampling pattern which is repeated periodically(a) Single order sampling(b) Multi order sampling(c) Zero order sampling(d) Unordered samplingThis question was addressed to me during an interview.I need to ask this question from Signal Reconstruction topic in section Digital Control Systems of Control Systems
Answer» RIGHT answer is (b) MULTI ORDER sampling To EXPLAIN I would say: Multi-order sampling is a sampling pattern in which the sampling is of different SIGNALS and which is repeated periodically.

Discussion

78.	Difference equation in discrete systems is similar to the _____________ in continuous systems.(a) Difference equation(b) Differential equation(c) Quadratic equation(d) None of the mentionedI have been asked this question during an interview.My question comes from Difference Equations in portion Digital Control Systems of Control Systems
Answer» Correct choice is (B) Differential equation To elaborate: DIFFERENCE equation are the equations used in discrete time systems and difference equations are SIMILAR to the differential equation in CONTINUOUS systems.

Discussion

79.	Unit step response of the system described by the equation y(n) +y(n-1) =x(n) is:(a) z^2/(z+1)(z-1)(b) z/(z+1)(z-1)(c) z+1/z-1(d) z(z-1)/z+1I got this question by my school principal while I was bunking the class.I want to ask this question from The inverse z-transform and Response of Linear Discrete Systrems in section Digital Control Systems of Control Systems
Answer» Right choice is (a) z^2/(z+1)(z-1) For explanation I would say: RESPONSE of the SYSTEM is CALCULATED by taking the z-transform of the equation and input to the TRANSFER function in the step input.

Discussion

80.	The region of convergence of the z-transform of a unit step function is:(a) \|z\|>1(b) \|z\|0(d) (Real part of z)
Answer» The correct option is (a) \|Z\|>1 The best I can explain: h[n] =U[n] Hence, Region of CONVERGENCE is the region for which the VALUES of the roots in z transform are lying in the function and is the range of values of z for which \|z\|>1.

Discussion

81.	A continuous-time periodic signal x(t), having a period T, is convolved with itself. The resulting signal is(a) Not periodic(b) Periodic having a period T(c) Periodic having a period 2T(d) Periodic having a period T/2The question was posed to me during an interview.Query is from The Z-transform Analysis of Sampled-Data Control Systems in division Digital Control Systems of Control Systems
Answer» The CORRECT ANSWER is (B) Periodic having a period T The best I can explain: Periodic having a period T CONVOLUTION of a periodic signal (period T) with itself will give the same period T.

Discussion

82.	For the successful reconstruction of signals :(a) Sampling frequency must be equal to the message signal(b) Sampling frequency must be greater to the message signal(c) Sampling frequency must be less to the message signal(d) Sampling frequency must be greater than or equal to the message signalI had been asked this question by my school teacher while I was bunking the class.Question is from Signal Reconstruction in section Digital Control Systems of Control Systems
Answer» Right option is (d) Sampling frequency MUST be greater than or EQUAL to the message signal To explain: Reconstruction of signals refers to the CONVERSION of the discrete time signals into continuous tiem signals and for the succesful reconstruction of signals sampling frequency must be greater than or equal to the message signal but ideally it is always preferred to be greater.

Discussion

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If X(z) =(z+z^-3)/(z+z^-1), then x(n) series has:(a) Alternate 0s(b) Alternate 1s(c) Alternate 2s(d) Alternate -1sI have been asked this question in an interview.Origin of the question is Difference Equations in section Digital Control Systems of Control Systems

The ROC of z-transform of the discrete time sequence x(n) = is:(a) 1/3>|z|1/2(c) |z||z|

Difference equation is used in :(a) Discrete time analysis(b) Continuous time analysis(c) Digital analysis(d) None of the mentionedI have been asked this question during an interview for a job.This key question is from Difference Equations in division Digital Control Systems of Control Systems

If the region of convergence of x1[n]+x2[n] is 1/>|z||z||z||z||z|

Which of the following may result in instability problem?(a) Large error(b) High selectivity(c) High gain(d) NoiseI had been asked this question in my homework.The query is from Compensation Techniques topic in portion Digital Control Systems of Control Systems

The region of convergence of the z-transform of a unit step function is:(a) |z|>1(b) |z|0(d) (Real part of z)