40 + Interview Questions in Mathematical Models Of Physical Systems in Control Systems Page 1 InterviewSolution

1.	A signal flow graph is the graphical representation of the relationships between the variables of set linear algebraic equations.(a) True(b) FalseI got this question in homework.Question is from Signal Flow Graphs topic in section Mathematical Models of Physical Systems of Control Systems
Answer» CORRECT answer is (a) True The explanation is: By definition SIGNAL FLOW GRAPHS are the graphical representation of the relationships between the variables of set LINEAR algebraic equations.

Discussion

2.	The overall transfer function of two blocks in parallel are :(a) Sum of individual gain(b) Product of individual gain(c) Difference of individual gain(d) Division of individual gainThis question was posed to me during an interview.I'd like to ask this question from Block diagram Algebra topic in division Mathematical Models of Physical Systems of Control Systems
Answer» Correct option is (a) Sum of INDIVIDUAL gain Easy EXPLANATION: The GAINS get added as the blocks are CONNECTED in parallel with the summer in between and they are connected with the same sign.

Discussion

3.	The advantage of block diagram representation is that it is possible to evaluate the contribution of each component to the overall performance of the system.(a) True(b) FalseThis question was addressed to me during an interview.This is a very interesting question from Block diagram Algebra topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» Correct answer is (a) True The EXPLANATION: The advantage of the block DIAGRAM is that it is POSSIBLE to get the CONTRIBUTION of each block to the OVERALL performance of the system.

Discussion

4.	The closed loop gain of the system shown in the given figure is :(a) -9/5(b) -6/5(c) 6/5(d) 9/5I got this question in semester exam.Question is from Block diagram Algebra topic in section Mathematical Models of Physical Systems of Control Systems
Answer» CORRECT choice is (B) -6/5 The EXPLANATION: C(s)/R(s)=-3/1+3/2=-6/5.

Discussion

5.	Which of the following is not the feature of modern control system?(a) Quick response(b) Accuracy(c) Correct power level(d) No oscillationThe question was asked during an internship interview.The above asked question is from Transfer Functions topic in section Mathematical Models of Physical Systems of Control Systems
Answer» The correct OPTION is (d) No oscillation Easiest explanation: For a good CONTROL system the speed of response and stability MUST be HIGH and for the slow and sluggish response is not used and undesirable.

Discussion

6.	The transfer function from D(s) to Y(s) is :(a) 2/3s+7(b) 2/3s+1(c) 6/3s+7(d) 2/3s+6The question was asked in homework.Asked question is from Block diagram Algebra topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» CORRECT ANSWER is (a) 2/3s+7 Explanation: Y(s)/D(s)=2/3s+1/1+3*(2/3s+1)=2/3s+7.

Discussion

7.	A transfer function has two zeroes at infinity. Then the relation between the numerator(N) and the denominator degree(M) of the transfer function is:(a) N=M+2(b) N=M-2(c) N=M+1(d) N=M-1The question was posed to me during an interview.I'm obligated to ask this question of Transfer Functions topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» Right CHOICE is (b) N=M-2 To explain: Zeroes at infinity IMPLIES two poles at origin hence the TYPE of the SYSTEM is two and degree of denominator is M=N+2.

Discussion

8.	The principle of homogeneity and superpositionare applied to:(a) Linear time invariant systems(b) Nonlinear time invariant systems(c) Linear time variant systems(d) Nonlinear time invariant systemsI have been asked this question in unit test.My doubt stems from Transfer Functions in chapter Mathematical Models of Physical Systems of Control Systems
Answer» Correct choice is (c) Linear time variant SYSTEMS For explanation I would say: SUPERPOSITION THEOREM states that for TWO signals additivity and homogeneity property must be satisfied and that is applicable for the LTI systems.

Discussion

9.	Assertion (A): Servomotors have heavier rotors and lower R/X ratio as compared to ordinary motors of similar ratings.Reason (R): Servomotor should have smaller electrical and mechanical time constants for faster response.Reason (R): Servomotor should have smaller electrical and mechanical time constants for faster response.(a) Both A and R are true and R is the correct explanation of A(b) Both A and R are true but R is not correct explanation of A(c) A is true but R is false(d) A is false but R is trueThe question was asked in examination.My question is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in portion Mathematical Models of Physical Systems of Control Systems
Answer» RIGHT option is (d) A is FALSE but R is true To explain: AC servomotors are essentially induction motor with low X/R RATIO for the ROTOR which has very low inertia.

Discussion

10.	Backlash in a stable control system may cause:(a) Under damping(b) Over damping(c) High level oscillations(d) Low level oscillationsThe question was posed to me in an online quiz.My question is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms in division Mathematical Models of Physical Systems of Control Systems
Answer» The correct option is (d) Low LEVEL OSCILLATIONS To elaborate: In a servo system, the GEAR BACKLASH may cause sustained oscillations or chattering phenomenon and the system may even turn UNSTABLE for large backlash.

Discussion

11.	A tachometer is added to servomechanism because:(a) It is easily adjustable(b) It can adjust damping(c) It reduces steady state error(d) It converts velocity of the shaft to a proportional Dc voltageThe question was posed to me in quiz.This intriguing question originated from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in section Mathematical Models of Physical Systems of Control Systems
Answer» Right choice is (B) It can adjust damping To explain I would SAY: A tachometer is a device to CONTROL the speed and adjust damping and it is used in SERVOMECHANISM to adjust damping and mainly is used in AC SERVOMOTORS.

Discussion

12.	Consider a simple mass spring friction system as given in the figure K1, K2 are spring constants f-friction, M-Mass, F-Force, x-Displacement. The transfer function X(s)/F(s) of the given system will be :(a) 1/(Ms^2+fs+K1.K2)(b) 1/(Ms^2+fs+K1+K2)(c) 1/(Ms^2+fs+K1.K2/K1+K2)(d) K2/(Ms^2+fs+K1)I have been asked this question in an online quiz.My query is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in portion Mathematical Models of Physical Systems of Control Systems
Answer» CORRECT choice is (b) 1/(Ms^2+fs+K1+K2) EASIEST explanation: FORCE BALANCE equations are formed where force from both the springs will be balanced by the MASS system.

Discussion

13.	A gantry robot consists of a manipulator mounted on an overhead system that allows movement only in ________ plane.(a) Horizontal(b) Inclined(c) Vertical(d) None of the mentionedThe question was asked in an international level competition.My question comes from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in division Mathematical Models of Physical Systems of Control Systems
Answer» Correct OPTION is (a) Horizontal To explain: Gantry ROBOT allows motion only in horizontal plane and this is made in this geometry to fulfill the RESPECTIVE WORK.

Discussion

14.	The relationship between an input and output variable of a signal flow graph is given by the net gain between the input and output node is known as the overall______________(a) Overall gain of the system(b) Stability(c) Bandwidth(d) SpeedThe question was asked by my college professor while I was bunking the class.My question is taken from Signal Flow Graphs in portion Mathematical Models of Physical Systems of Control Systems
Answer» RIGHT answer is (a) OVERALL gain of the SYSTEM Easiest explanation: The RELATIONSHIP between input and output VARIABLE of a signal flow graph is the overall gain of the system.

Discussion

15.	Gear train in the motor is used to reduce the gear ratio?(a) True(b) FalseI got this question by my school principal while I was bunking the class.Question is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms in division Mathematical Models of Physical Systems of Control Systems
Answer» The correct option is (B) False The EXPLANATION is: Gear RATIO REFERS to the ratio of the number of teeths in the respective GEARS and gear train in the motor is specifically used to increase the gear ratio.

Discussion

16.	Use mason’s gain formula to find the transfer function of the following signal flow graph:(a) abcd+efg/1-cd-fg-cdfg(b) acdfg+bcefg/1-cd-fg-cdfg(c) abef+bcd/1-cd-fg-cdfg(d) adcdefg/1-cd-fg-cdfgI got this question by my college professor while I was bunking the class.The question is from Signal Flow Graphs in section Mathematical Models of Physical Systems of Control Systems
Answer» Correct option is (b) acdfg+bcefg/1-cd-fg-cdfg To EXPLAIN I would SAY: Using mason’s gain formula transfer FUNCTION from signal flow graph can be CALCULATED which RELATES the forward path gain to the various paths and loops.

Discussion

17.	In the following block diagram, G1=10/s G2=10/s+1 H1=s+3, H2=1. The overall transfer function is given by :(a) 10/11s^2+31s+10(b) 100/11s^2+31s+100(c) 100/11s^2+31s+10(d) 100/11s^2+31sI got this question during a job interview.The doubt is from Block diagram Algebra topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» The CORRECT CHOICE is (B) 100/11s^2+31s+100 The BEST EXPLANATION: C/R=G2G1/1+G2H2+G1G2H2 C/R=100/11s^2+31s+100.

Discussion

18.	A node having only outgoing branches.(a) Input node(b) Output node(c) Incoming node(d) Outgoing nodeI had been asked this question in an interview.My enquiry is from Signal Flow Graphs topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» CORRECT OPTION is (a) INPUT node Explanation: Nodes are the point by which the branches are OUTGOING or ingoing and this can be input or OUTPUT node and input node is the node having only outgoing branches.

Discussion

19.	In case of DC servomotor, the back emf is equivalent to an “electric friction” which tends to:(a) Slowly decrease the stability of the system(b) Improve stability of the system(c) Very rapidly decrease the stability of the system(d) Have no effect of stabilityThe question was posed to me in a national level competition.The question is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» RIGHT answer is (b) IMPROVE stability of the system Explanation: As Back emf in DC servomotors provides necessary CENTRIFUGAL force to control the SPEED of the motor that increases the stability of the system.

Discussion

20.	Use mason’s gain formula to calculate the transfer function of given figure:(a) G1/1+G2H(b) G1+G2/1+G1H(c) G2/1+G1H(d) None of the mentionedI got this question in final exam.Enquiry is from Signal Flow Graphs in chapter Mathematical Models of Physical Systems of Control Systems
Answer» Right answer is (B) G1+G2/1+G1H The best I can EXPLAIN: Use mason’s gain formula to solve the SIGNAL flow graph and by using mason’s gain formula transfer FUNCTION from signal flow graph can be calculated which relates the forward path gain to the VARIOUS paths and loops.

Discussion

21.	Signal flow graphs are reliable to find transfer function than block diagram reduction technique.(a) True(b) FalseThe question was asked in class test.My doubt stems from Signal Flow Graphs in portion Mathematical Models of Physical Systems of Control Systems
Answer» Right ANSWER is (a) True The BEST EXPLANATION: As one set technique and formula is used here but in block diagram technique various methods are involved which increases COMPLEXITY.

Discussion

22.	Loop which do not possess any common node are said to be ___________ loops.(a) Forward gain(b) Touching loops(c) Non touching loops(d) Feedback gainThe question was posed to me in class test.This question is from Signal Flow Graphs in division Mathematical Models of Physical Systems of Control Systems
Answer» Correct choice is (c) Non TOUCHING loops Best explanation: Loop is the part of the network in which the BRANCH starts from the node and comes BACK to the same node and non touching loop must not have any node in COMMON.

Discussion

23.	Transfer function of the system is defined as the ratio of Laplace output to Laplace input considering initial conditions________(a) 1(b) 2(c) 0(d) infiniteI have been asked this question at a job interview.I'd like to ask this question from Block diagram Algebra in division Mathematical Models of Physical Systems of Control Systems
Answer» Right option is (C) 0 The best explanation: By definition transfer FUNCTION is the ratio of the laplace output to the input but the initial conditions MAINLY the stored energy is ZERO.

Discussion

24.	The overall transfer function from block diagram reduction for cascaded blocks is :(a) Sum of individual gain(b) Product of individual gain(c) Difference of individual gain(d) Division of individual gainThe question was posed to me in an internship interview.Query is from Block diagram Algebra in chapter Mathematical Models of Physical Systems of Control Systems
Answer» The correct choice is (b) PRODUCT of individual gain To explain I WOULD say: Gain of BLOCK get MULTIPLIED when they are cascaded where cascaded means that the blocks are in series COMBINATION with no summer in between.

Discussion

25.	A linear system at rest is subject to an input signal r(t)=1-e^-t. The response of the system for t>0 is given by c(t)=1-e^-2t. The transfer function of the system is:(a) (s+2)/(s+1)(b) (s+1)/(s+2)(c) 2(s+1)/(s+2)(d) (s+1)/2(s+2)The question was asked during an interview for a job.The doubt is from Transfer Functions in chapter Mathematical Models of Physical Systems of Control Systems
Answer»

Discussion

26.	Use mason’s gain formula to find the transfer function of the given signal flow graph:(a) abd/1-(ac)(b) abdeg/1-(bc+ef)+bcef(c) abd/1-(bc+ef)+bcef(d) adcdef/1-(bc+ef)+bcefI got this question in semester exam.I need to ask this question from Signal Flow Graphs in portion Mathematical Models of Physical Systems of Control Systems
Answer» RIGHT choice is (b) abdeg/1-(bc+ef)+bcef The best I can explain: Using mason’s gain formula TRANSFER FUNCTION from signal flow graph can be CALCULATED which relates the forward path gain to the various PATHS and loops.

Discussion

27.	The output of the feedback control system must be a function of:(a) Reference input(b) Reference output(c) Output and feedback signal(d) Input and feedback signalI had been asked this question in final exam.This intriguing question originated from Transfer Functions topic in section Mathematical Models of Physical Systems of Control Systems
Answer» The correct answer is (d) INPUT and FEEDBACK signal Easiest EXPLANATION: Feedback control system has the property of reducing the ERROR and that is by differencing the output with the DESIRED output and as the equation of the output of the system is C=GR/1+GH.

Discussion

28.	The below figure represents:(a) Lead network(b) Lag network(c) PI controller(d) PD controllerI had been asked this question in an interview.Question is taken from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms in portion Mathematical Models of Physical Systems of Control Systems
Answer» Right option is (b) Lag network To explain I WOULD SAY: The EQUATIONS of performance are B1(dX1/dt-dX2/dt)+k1(X1-X0)=k2X0 T=k1(1+B1s/K1)/k1+k2(1+sB1/k1+k2) X0(s)/X1(s)=1/a(1+aTs/1+Ts).

Discussion

29.	Which of the following is an example of an open loop system?(a) Household Refrigerator(b) Respiratory system of an animal(c) Stabilization of air pressure entering into the mask(d) Execution of program by computerI have been asked this question during an online exam.This interesting question is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in portion Mathematical Models of Physical Systems of Control Systems
Answer» Right choice is (d) EXECUTION of program by computer Easy EXPLANATION: Execution of a program by a computer is an example of an open loop SYSTEM as the feedback mechanism is not TAKEN by the computer program and set programs are USED to get the set output.

Discussion

30.	For the block diagram given in the following figure, the expression of C/R is:(a) G1G2G3/1-G2G1(b) G1G2/1-G1G2G3(c) G1G2G3/1-G1G2G3(d) G1G2/G3(1-G1G2)The question was asked in an online interview.This question is from Block diagram Algebra topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» Right option is (a) G1G2G3/1-G2G1 Easy explanation: Block diagram is being CONVERTED into signal flow GRAPHS by considering each take off point as a NODE and each forward transfer function as forward GAIN.

Discussion

31.	For a tachometer, if a(t) is the rotor displacement, e(t) is the output voltage and K is the tachometer constant, then the transfer function is given by:(a) Ks^2(b) K/s(c) Ks(d) KThe question was posed to me in final exam.My question is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in portion Mathematical Models of Physical Systems of Control Systems
Answer» RIGHT choice is (C) KS To EXPLAIN: e(t)=Kw E(s)=Ksa(s) E(s)/a(s)=Ks.

Discussion

32.	A control system whose step response is -0.5(1+e^-2t) is cascaded to another control block whose impulse response is e^-t. What is the transfer function of the cascaded combination?(a) 1/(s+2)(s+1)(b) 1/(s+1)s(c) 1/(s+3)(d) 0.5/(s+1)(s+2)The question was asked in a job interview.Query is from Transfer Functions topic in section Mathematical Models of Physical Systems of Control Systems
Answer» Right choice is (a) 1/(s+2)(s+1) To elaborate: Solution: Laplace transform is the transformation that transforms the time DOMAIN into FREQUENCY domain and of both the cascaded systems are 1/(s+1)(s+2).

Discussion

33.	Tachometer feedback in a D.C. position control system enhances stability?(a) True(b) FalseThis question was posed to me in a job interview.The doubt is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms in section Mathematical Models of Physical Systems of Control Systems
Answer» Correct answer is (a) True Explanation: Tachometer feedback is derivative feedback and hence INCREASES the STABILITY and speed of response, so tachometer adds ZERO at ORIGIN.

Discussion

34.	Signal flow graphs:(a) They apply to linear systems(b) The equation obtained may or may not be in the form of cause or effect(c) Arrows are not important in the graph(d) They cannot be converted back to block diagramThis question was posed to me in an international level competition.I would like to ask this question from Signal Flow Graphs topic in section Mathematical Models of Physical Systems of Control Systems
Answer» The correct OPTION is (a) They apply to LINEAR systems Easiest explanation: Signal FLOW GRAPHS are used to find the transfer FUNCTION of control system by converting the block diagrams into signal flow graphs or directly but cannot be used for nonlinear systems.

Discussion

35.	A synchro Transmitter is used with control transformer for:(a) Feedback(b) Amplification(c) Error detection(d) Remote sensingI had been asked this question by my school principal while I was bunking the class.This intriguing question originated from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms in chapter Mathematical Models of Physical Systems of Control Systems
Answer» RIGHT option is (c) ERROR detection Easiest explanation: Synchro transmitter is USED as the error detector to get the desired speed and it is ACCOMPAINED with the synchro transformer which is used as an amplifier.

Discussion

36.	When deriving the transfer function of a linear element(a) Both initial conditions and loading are taken into account(b) Initial conditions are taken into account but the element is assumed to be not loaded(c) Initial conditions are assumed to be zero but loading is taken into account(d) Initial conditions are assumed to be zero and the element is assumed to be not loadedThe question was posed to me in an online quiz.The doubt is from Transfer Functions topic in division Mathematical Models of Physical Systems of Control Systems
Answer» The correct answer is (c) Initial conditions are ASSUMED to be zero but loading is TAKEN into account The best I can EXPLAIN: When deriving the transfer function of a LINEAR ELEMENT only initial conditions are assumed to be zero, loading cannot be assumed to be zero.

Discussion

37.	Assertion (A): DC servomotors are more commonly used in armature controlled mode than field controlled mode.Reason (R): Armature controlled Dc motors have higher starting torque than fiels controlled motors.(a) Both A and R are true and R is the correct explanation of A(b) Both A and R are true but R is not correct explanation of A(c) A is true but R is false(d) A is false but R is trueI have been asked this question during an interview for a job.The question is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in division Mathematical Models of Physical Systems of Control Systems
Answer» CORRECT answer is (a) Both A and R are true and R is the correct explanation of A The BEST explanation: To get higher SPEED in FIELD controlled dc motor, field current is decreased with DECREASE in torque.

Discussion

38.	In regenerating the feedback, the transfer function is given by(a) C(s)/R(s)=G(s)/1+G(s)H(s)(b) C(s)/R(s)=G(s)H(s)/1-G(s)H(s)(c) C(s)/R(s)=G(s)/1+G(s)H(s)(d) C(s)/R(s)=G(s)/1-G(s)H(s)I had been asked this question in unit test.The query is from Transfer Functions topic in chapter Mathematical Models of Physical Systems of Control Systems
Answer» Correct option is (d) C(s)/R(s)=G(s)/1-G(s)H(s) EASIEST explanation: REGENERATING feedback is positive feedbackand it increases the infinitely and hence the speed of response of the system reduces.

Discussion

39.	The output of an first order hold between two consecutive sampling instants is:(a) Constant(b) Quadratic Function(c) Ramp Function(d) Exponential FunctionThe question was asked in my homework.Query is from Differential Equations of Physical Systems and Dynamics of Robotic Mechanisms topic in section Mathematical Models of Physical Systems of Control Systems
Answer» Correct answer is (c) Ramp Function The best I can EXPLAIN: Inverse LAPLACE of the equation of first order hold GIVES the ramp function and hence the output of an first order hold between TWO consecutive sampling is ramp function.

Discussion

40.	In continuous data systems:(a) Data may be continuous function of time at all points in the system(b) Data is necessarily a continuous function of time at all points in the system(c) Data is continuous at the inputs and output parts of the system but not necessarily during intermediate processing of the data(d) Only the reference signal is continuous function of timeI have been asked this question in an online quiz.The above asked question is from Transfer Functions topic in portion Mathematical Models of Physical Systems of Control Systems
Answer» Right option is (b) Data is necessarily a continuous FUNCTION of time at all points in the system To elaborate: Continuous SIGNALS are the signals having values for the continuous time and if impulse response DECAYS to zero as time approaches infinity, the system is stable.

Discussion

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A signal flow graph is the graphical representation of the relationships between the variables of set linear algebraic equations.(a) True(b) FalseI got this question in homework.Question is from Signal Flow Graphs topic in section Mathematical Models of Physical Systems of Control Systems

The closed loop gain of the system shown in the given figure is :(a) -9/5(b) -6/5(c) 6/5(d) 9/5I got this question in semester exam.Question is from Block diagram Algebra topic in section Mathematical Models of Physical Systems of Control Systems

The transfer function from D(s) to Y(s) is :(a) 2/3s+7(b) 2/3s+1(c) 6/3s+7(d) 2/3s+6The question was asked in homework.Asked question is from Block diagram Algebra topic in chapter Mathematical Models of Physical Systems of Control Systems

A node having only outgoing branches.(a) Input node(b) Output node(c) Incoming node(d) Outgoing nodeI had been asked this question in an interview.My enquiry is from Signal Flow Graphs topic in chapter Mathematical Models of Physical Systems of Control Systems

Use mason’s gain formula to calculate the transfer function of given figure:(a) G1/1+G2H(b) G1+G2/1+G1H(c) G2/1+G1H(d) None of the mentionedI got this question in final exam.Enquiry is from Signal Flow Graphs in chapter Mathematical Models of Physical Systems of Control Systems

Signal flow graphs are reliable to find transfer function than block diagram reduction technique.(a) True(b) FalseThe question was asked in class test.My doubt stems from Signal Flow Graphs in portion Mathematical Models of Physical Systems of Control Systems