Control System ECE

8/6/2019 Control System ECE

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SELVAM COLLEGE OF TECHNOLOGY, NAMAKKAL

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

II YEAR /IV SEM

UNIT I

CONTROL SYSTEM MODELING

1. What is system and control system?A number of components are connected in a sequence to perform a

specific function, the group is called system.In a system when the output quantity is controlled by varying the input

quantity then the system is called control system.

2. List out the advantages of closed loop transfer function. (AU, May-10) The closed loop systems are accurate. The closed loop systems are accurate even in the presence of non-

linearity. The sensitivity of the systems may be made small to make the

system more stable. The closed loop systems are less affected by noise.

3. Compare open loop system with closed loop system? (AU, May-10)S.No. Open loop system Closed loop system

1 Inaccurate Accurate2 Simple and economical Complex and costlier3 The changes in output due to

external disturbance are notcorrected

The changes in output due toexternal disturbance are correctedautomatically

4 May oscillate and become unstable They are generally stable. Greatefforts are needed to design astable

4. Give two examples for open loop and closed systems. (AU, Dec-09) Temperature control system. Traffic control system. Numerical control system.

Position control system.5. Define transfer function. (AU, May-10)

The Transfer function of a system is defined as the ratio of the laplacetransform of output to Laplace transform of input with zero initial conditions.


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6. What are the basic elements used for modeling mechanical rotationalsystem(AU,Dec-09)

Moment of inertia J, Kg-m2/rad Dashpot with rotational frictional coefficient B, N-m/(rad/sec) Torsional spring with stiffness K ,N-m /rad.

7. Name two types of electrical analogous for mechanical system. (AU, Dec-09) Force - voltage analogy. Force -current analogy.

8. Write the force equation for the system shown (AU, Dec-07)

F(t) = M d2x/dt2 +Bdx/dt + kx

9. What are the basic elements used for modeling mechanical translational system? Mass M, Kg, Stiffness of spring K, N/m Viscous friction coefficient dashpot B, N-sec/m

10.What is feedback? What type of feedback is employed in control system?The feedback is a control action in which the output is sampled and a

proportional signal is given to input for automatic correction of any changes indesired output. Negative feedback is employed in control system.

11.State whether transfer function technique is applicable to non-linear system andwhether the transfer function is independent of the input of a system.(AU, Dec-09)

The transfer function technique is not applicable to non-linearsystem.

The transfer function of a system is independent of input anddepends only on system parameters but the output of a systemdepends on input.

12.Prove the rule for eliminating negative and positive feedback loop. (AU, May-07)Positive feedbackProof:

C = (R-CH) GC = RG-CHGC + CHG = RGC (1+HG) = RGC/R = G/ (1+GH)


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Negative feedback

Proof:C = (R+CH) GC = RG+CHGC - CHG = RGC (1-GH) = RG

C/R = G/ (1-GH)

13.What is block diagram? What are the basic components of block diagram? (AU,Dec-07)

A block diagram of a system is a pictorial representation of the functionsperformed by each component of the system and shows the flow of signals. Thebasic elements of block diagram block, branch point and summing point.

14.Write any two advantage and disadvantages of block diagramrepresentation?(AU, Dec)

Advantage Very simple to construct the block diagram for complicated systems. The function of individual element can be visualized from block

diagram.Disadvantage

Block diagram does not include any information about the physicalconstruction of the system.

Source of energy is generally not shown in the block diagram. Sonumber of different block diagrams can be drawn depending upon thepoint of view of analysis. So block diagram for given system is notunique.

15.State Masons Gain formula. (AU, Dec-09)The formula can be stated as

= KK

PTgainOverall , .

Where k= no. of forward paths in the signal flow graphPK= forward path gain of the Kth forward path = 1-[sum of individual loop gains] + [sum of gain products of all possible Combinations of two non touching loops]-[sum of gain

products of all possible combinations of three non touching loops]+k= ( for that part of the graph which is not touching Kth forwardpath)


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16.What is an input node, forward path gain, Transmittance in case of a signal flowgraph?

Input node is a node that has only outgoing branches. Forward path gain is a path from an input node to an output node that

does not cross any node more than once. The gain acquired by the signal when it travels from one node to

another is called transmittance.17.What is signal flow graph?A signal flow graph is a diagram that represents a set of simultaneous algebraic

equations .By taking L.T the time domain differential equations governing a controlsystem can be transferred to a set of algebraic equations in s-domain.

18. What is source and sink?

Source is the input node in the signal flow graph and it has onlyoutgoing branches.

Sink is an output node in the signal flow graph and it has onlyincoming branches.19.Define non-touching loop.If there is no node common in between the two or more loops, such loops are said to

be non- touching loops.

20.What are the basic properties of signal flow graph? (AU, Dec-10)The basic properties of signal flow graph are

Signal flow graph is applicable to linear systems. It consists of nodes and branches. A node adds the signal of all incoming branches and transmits this sum

to all outgoing branches. Signals travel along branches only in the marked direction and is

multiplied by the gain of the branch.


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II YEAR /IV SEM

UNIT II

TIME RESPONSE ANALYSIS

1. What is time response?The response given by the system which is function of the time, to the applied

excitation is called time response of a control system.

2. Name the test signals used in control systems? (AU, Dec-09)The commonly used test input signals in control system are impulse, step,

ramp, acceleration and sinusoidal signals.

3. What do you mean order of a control system? (AU,Jun-10)The order of the system is given by the order of the differential equation

governing the system. It is also given by the maximum power of s in thedenominator polynomial of transfer function. The maximum power of s also givesthe number of poles of the system and so the order of the system is also given bynumber of poles of the transfer function.

4. List the time domain specifications. (AU, Dec-09)The time domain specifications are

Delay time Rise time Peak time Peak overshoot

5. Define rise time, delay time settling time. (AU, May-08)Rise Time:The time taken for response to raise from 0% to 100% for the very first time isrise time.Delay Time:The time taken for response to reach 50% of final value for the very first time isdelay time.Settling Time:Settling time is defined as the time taken by the response to reach and stay withinspecified error


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6. Define: Peak time and Peak over shoot. (AU, Jun-09)Peak Time:The time taken for the response to reach the peak value for the first time is peaktime.Peak over shoot:Peak overshoot is defined as the ratio of maximum peak value measured from theMaximum value to final value

7. Second order system has a damping ratio of 0.5 and a damped frequency of 4.2rad/sec. Find the 5% settling time in the step response.

(AU, Dec-07)

Settling time, ts = 3/n = 3/(0.5*4.2) = 1.42 second.

8. How can we classify second order system based on damping ratio? (AU, Dec-09) Undamped system, = 0 Underdamped system, 0 < < 1 Critically damped system, = 1 Over damped system, > 1.

9. What is damped frequency of oscillation and damping ratio? (AU, Jun-09)Damped Frequency of Oscillation

In under damped system the response is damped oscillatory. The frequency ofdampedOscillation is given by d = n (1-

2)Damping RatioThe damping ratio is defined as the ratio of the actual damping to critical damping

10.What is mean by dynamic error coefficient? Mention its significance.(AU, Dec-07)They are the coefficients of generalized error series. The generalized error

series is given bye(t) = C0r(t) + C1 r (t) + (C2/2!) r\'\'(t) + (C3/3!) r\'\'\'(t) + ............. + (Cn/n!)rn\'(t).The coefficients C0, C1, C2 , ......,Cn are called generalized error coefficients ordynamic error coefficients.

Significance:

Steady state is function of time. Steady state can be determined from any type of input.11.What are the different types of controller? (AU, Dec -09)

P-controller PI controller PD controller PID controller


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12. Give the relation ship between generalized and static error coefficients.

The following expressions shows the relation between generalized andstatic error coefficient

C0=1/(1+Kp); C1=1/Kv C2=1/KaWhere, the Coefficients C0, C1, C2are called generalized error coefficient or

dynamic error coefficients.The Kp, Kv and Ka are called static error constants.

13. Mention two advantages of generalized error constants over static errorconstants:

Generalized error series gives error signal as a function of time. Using generalized error constants the steady state error can be detena for

any type of input but static error constants are used to determine m stateerror when the input is anyone of the standard input.

14. Why derivative controller is not used in control systems?The derivative controller produces a control action based on rate of change

of error signal and it does not produce corrective measures for any constant error.Hence derivative controller is not used in control systems.

15. Define Transient response and steady state response.Transient Response

The output variation during the time, it takes to achieve its final value iscalled as transient response. The time required to achieve the final value is calledtransient period.Steady State Response

It is that part of the time response which remains after complete transientresponse vanishes from the system output.

16. Give the effects of PI, PD controller.The PI controller increases the order of the system by one, which results in

reducing the steady state error .But the system becomes less stable than theoriginal system.

The effect of PD controller is to increase the damping ratio of the systemand so the peak overshoot is reduced.

17.What are the various static error constants? What is steady state error?(AU, May-08)

Positional Error Constant (Kp) Velocity error constant ( Kv) Acceleration Error Constant (Ka)

Steady State ErrorThe steady state error is the value of error signal e (t), when t tends to

infinity. The steady state error is a measure of system accuracy. These errors arisefrom the nature of inputs, type of system and from non-linearity of systemcomponents.


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18.What will be the nature of response of a second order system with different types

of damping?

For Undamped system the response is oscillatory. For Under damped system the response is damped oscillatory. For Critically damped system the response is exponentially rising. For over damped system the response is exponentially rising but the rise

time will be very large.

19.Define Ramp signal:A ramp signal is a signal whose value increases linearly with time from an

initial value of zero at t = 0. It is mathematically represented asr (t) = A t, t > 0= 0, t < 0

20.What is the importance of test signals?The test signals can be easily generated in test laboratories and the

characteristics of test signals resembles the characteristics of actual input signals.The test signals are used to predetermine the performance of the system. If theresponse of a system is satisfactory for a test signal, then the system will besuitable for practical applications.


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II YEAR /IV SEM

UNIT II

TIME RESPONSE ANALYSIS

1. What is time response?The response given by the system which is function of the time, to the applied

excitation is called time response of a control system.

2. Name the test signals used in control systems? (AU, Dec-09)The commonly used test input signals in control system are impulse, step,

ramp, acceleration and sinusoidal signals.

3.

What do you mean order of a control system? (AU,Jun-10)The order of the system is given by the order of the differential equation

governing the system. It is also given by the maximum power of s in thedenominator polynomial of transfer function. The maximum power of s also givesthe number of poles of the system and so the order of the system is also given bynumber of poles of the transfer function.

4. List the time domain specifications. (AU, Dec-09)The time domain specifications are

Delay time

Rise time Peak time Peak overshoot

5. Define rise time, delay time settling time. (AU, May-08)Rise Time:The time taken for response to raise from 0% to 100% for the very first time isrise time.Delay Time:The time taken for response to reach 50% of final value for the very first time isdelay time.

Settling Time:Settling time is defined as the time taken by the response to reach and stay withinspecified error

6. Define: Peak time and Peak over shoot. (AU, Jun-09)Peak Time:

The time taken for the response to reach the peak value for the first time is peaktime.


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Peak over shoot:Peak overshoot is defined as the ratio of maximum peak value measured from theMaximum value to final value

7. Second order system has a damping ratio of 0.5 and a damped frequency of 4.2rad/sec. Find the 5% settling time in the step response.

(AU, Dec-07)Settling time, ts = 3/n = 3/(0.5*4.2) = 1.42 second.

8. How can we classify second order system based on damping ratio? (AU, Dec-09) Undamped system, = 0 Underdamped system, 0 < < 1 Critically damped system, = 1 Over damped system, > 1.

9. What is damped frequency of oscillation and damping ratio? (AU, Jun-09)Damped Frequency of OscillationIn under damped system the response is damped oscillatory. The frequency ofdampedOscillation is given by d = n (1-

2)Damping Ratio

The damping ratio is defined as the ratio of the actual damping to critical damping

10.What is mean by dynamic error coefficient? Mention its significance.(AU, Dec-07)

They are the coefficients of generalized error series. The generalized errorseries is given by

e(t) = C0r(t) + C1 r (t) + (C2/2!) r\'\'(t) + (C3/3!) r\'\'\'(t) + ............. + (Cn/n!)rn\'(t).The coefficients C0, C1, C2 , ......,Cn are called generalized error coefficients ordynamic error coefficients.

Significance:

Steady state is function of time. Steady state can be determined from any type of input.

11.What are the different types of controller? (AU, Dec -09) P-controller PI controller PD controller PID controller

12. Give the relation ship between generalized and static error coefficients.


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The following expressions shows the relation between generalized andstatic error coefficient

C0=1/(1+Kp); C1=1/Kv C2=1/KaWhere, the Coefficients C0, C1, C2are called generalized error coefficient ordynamic error coefficients.The Kp, Kv and Ka are called static error constants.

14.Mention two advantages of generalized error constants over static errorconstants:

Generalized error series gives error signal as a function of time. Using generalized error constants the steady state error can be detena for

any type of input but static error constants are used to determine m stateerror when the input is anyone of the standard input.

14. Why derivative controller is not used in control systems?The derivative controller produces a control action based on rate of change

of error signal and it does not produce corrective measures for any constant error.Hence derivative controller is not used in control systems.

15. Define Transient response and steady state response.Transient Response

The output variation during the time, it takes to achieve its final value iscalled as transient response. The time required to achieve the final value is calledtransient period.Steady State Response

It is that part of the time response which remains after complete transientresponse vanishes from the system output.

16. Give the effects of PI, PD controller.The PI controller increases the order of the system by one, which results in

reducing the steady state error .But the system becomes less stable than theoriginal system.The effect of PD controller is to increase the damping ratio of the system

and so the peak overshoot is reduced.

17.What are the various static error constants? What is steady state error?(AU, May-08)

Positional Error Constant (Kp) Velocity error constant ( Kv) Acceleration Error Constant (Ka)

Steady State ErrorThe steady state error is the value of error signal e (t), when t tends to

infinity. The steady state error is a measure of system accuracy. These errors arisefrom the nature of inputs, type of system and from non-linearity of systemcomponents.

18.What will be the nature of response of a second order system with different typesof damping?


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For Undamped system the response is oscillatory. For Under damped system the response is damped oscillatory. For Critically damped system the response is exponentially rising. For over damped system the response is exponentially rising but the rise

time will be very large.

19.Define Ramp signal:

A ramp signal is a signal whose value increases linearly with time from aninitial value of zero at t = 0. It is mathematically represented asr (t) = A t, t > 0= 0, t < 0

20.What is the importance of test signals?

The test signals can be easily generated in test laboratories and thecharacteristics of test signals resembles the characteristics of actual input signals.

The test signals are used to predetermine the performance of the system. If theresponse of a system is satisfactory for a test signal, then the system will besuitable for practical applications.


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II YEAR /IV SEM

UNIT III

FREQUENCY RESPONSE ANALYSIS

1. Define resonance peak and bandwidth of the system? (AU, Dec-10)Resonance Peak

The maximum value of the magnitude of closed loop transfer function iscalled resonant peak.Bandwidth

The bandwidth is the range of frequencies for which the system gain Ismore than 3 dB. The bandwidth is a measure of the ability of a feedback system toreproduce the input signal, noise rejection characteristics and rise time.

2. What is frequency response? (AU, Dec-09)A frequency response is the steady state response of a system when the

input to the system is a sinusoidal signal.

3. Give example for frequency response plot. (AU, Dec-09) Bode plot Polar plot Nichols plot M and N circles Nichols chart

4. Define phase cross over frequency and gain cross over frequency. (AU, Dec-09)Phase Cross Over Frequency

The gain cross-over frequency is the frequency at which the magnitude ofthe open loop transfer function is unity.Gain Cross Over Frequency

The phase cross-over frequency is the frequency at which the phase of theopen loop transfer function is 180.

5. List the Frequency domain specifications? (AU, Jun-07)The frequency domain specifications are

Resonant peak. Resonant frequency. Bandwidth Cut-off rate Gain margin Phase margin


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6. Define phase margin and gain margin. (AU, Dec-07)Gain Margin.

The gain margin, Kg is defined as the reciprocal of the magnitude of openloop transfer function, at phase cross-over frequency, pc.

Gain margin,Kg =Phase MarginThe phase margin, is that amount of additional phase lag at the gain

cross over frequency, gc required to bring the system to the verge of instability. Itis given by, 180 + gc, where gc is the phase of G(j) at the gain cross overfrequency.Phase margin, = 180 + gc ; Where, gc = < G(j) =gc

7. Define Cut-off rate? Resonant frequency (r)?The slope of the log-magnitude curve near the cut-off frequency is called cut-Off

rate.The frequency at which the resonant peak occurs is called resonant frequency.The resonant peak is the maximum value of the magnitude of closed loop transferfunction.

8. Define Corner frequency (AU, Jun-09)The magnitude plot can be approximated by asymptotic straight lines. The

frequencies corresponding to the meeting point of asymptotes are called cornerfrequency. The slope of the magnitude plot changes at every corner frequencies.

9. Define polar plot.The polar plot of a sinusoidal transfer function G(j) is a plot of the

magnitude of G(j) versus the phase angle/argument of G(j) on polar orrectangular coordinates as is varied from zero to infinity.

10. What are the advantages of bode plot. (AU, Jun-09) The magnitudes are expressed in db and so a simple procedure is to add

magnitude of each term one by one. The approximate bode plot can be quickly sketched, and the c: can be

made at corner frequencies to get the exact plot. The frequency domain specifications can be easily determined. The bode plot can be used to analyse both open loop and close loop

system.

11.Write the expression to determine the resonant peak and resonant frequencyResonant peak, Mr= Resonant frequency,


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12.Mention the advantage of Nichols chart? (AU, Jun-10) It is used to find closed loop frequency response from open loop frequency

response. The frequency domain specifications can be determined from Nichols

chart. The gain of the system can be adjusted to satisfy the given specification.13.What are M and N circle? (AU, Dec 09)

M circleThe magnitude M of closed loop transfer function with unity feedback will

be in the form of circle in complex plane for each constant value of M. The familyof these circles is called M circles.N circle

Let N = tan where a is the phase of closed loop transfer function withunity feedback. For each constant value of N, a circle can be drawn in the

complex plane. The family of these circles is called N circles.14.What is compensator? (AU, Dec 09)

A device inserted into the system for the purpose of satisfying thespecifications is called as a compensator.

15.What are the uses of lead compensator? The uses of lead compensator are speeds up the transient response Increases the margin of stability of a system Increases the system error constant to a limited extent.

16.What is Nichols chart?The Nichols chart consists of M and N contours superimposed on ordinary graph.

Along each M contour the magnitude of closed loop system, M will be a constant.Along each N contour, the phase of closed loop system will be constant. Theordinary graph consists of magnitude in db, marked on the y-axis and the phase indegrees marked on x-axis. The Nichols chart is used to find the closed loop frequencyresponse from the open loop frequency response.

17.When lag/lead/lag-lead compensation is employed? Lag compensation is employed for a stable system for improvement in

steady state performance. Lead compensation is employed for stable/unstable system for

improvement in transient state performance.


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The lag lead compensator is required when both the transient andsteady state response of a system has to be improved

18.What are the advantages of frequency response analysis? The absolute and relative stability of the closed loop system can be

estimated from the knowledge of the open loop frequency response.

The practical testing of system can be easily carried with availablesinusoidal signal generators and precise measurement equipments.19.What is bode plot?

The bode plot is a frequency response plot of the transfer function of asystem. It consists of two plots-magnitude plot and phase plot.

The magnitude plot is a graph between magnitude of a system transferfunction in db and the frequency () .The phase plot is a graph between the phaseor arguments of a system transfer function in degrees and the frequency ().

Usually, both the plots are plotted on a common x-axis in which the frequenciesare expressed in logarithmic scale.

20.What are the three types of compensators?The three types of compensators are

Lag compensator. Lead compensator. Lag-Lead compensator.


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II YEAR /IV SEM

UNIT-IV

STABILITY ANALYSIS

1. What are the main significance of root locus? (AU, Dec-09) The root locus technique is used for stability analysis. Using root locus technique the range of values of K, for as stable system

can be determined

2. What is limitedly and absolutely stable system? (AU, Dec-09) For a bounded input signal,if the output has constant amplitude

oscillations the the system may be stable or unstable under some

limited constraints.Such a system is called Limitedly stable system. If a system output is stable for all variations of its parameters,then

the system is called absolutely stable system.

3. What is the necessary and sufficient condition for stability? (AU, Dec-10) The necessary condition for stability is that all the coefficients of

the characteristic polynomial be positive. The necessary and sufficient condition for stability is that all of the

elements in the first column of the routh array should be positive.

4. What is relative stability (AU, Dec-10)The Relative stability indicates the closeness of the system to stable.

It is an indication of the strength or degree of stability

5. What is a principle of argument?The principles of arguments states that let F(S) are analytic function and if an

arbitrary closed contour in a clockwise direction is chosen in the S-plane so thatF(S) is analytic at every point of the contour. Then the corresponding F(S) planecontour mapped in the F(S) plane will encircle the origin N times in the anticlockwise direction, where N is the difference between number of poles and zeros

of F(S) that are encircled by the choosen closed contour in the S-plane

6. State Routh stability criterion. (AU, Dec-09)Routh criterion states that the necessary and sufficient condition for stability is

that all of the elements in the first column of the routh array is positive. If thiscondition is not met, the system is unstable and the number of sign changes in the


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elements of the first column of routh array corresponds to the number of roots ofcharacteristic equation in the right half of the S-plane.

7. What is BIBOstability? (AU, Jun-10)

A linear relaxed system is said to have BIBO stability if every bounded

input results in a bounded output.8. What is root locus? (AU, Dec-09)

The path taken by a root of characteristic equation when open loop gain Kis varied from 0 to infinity is called root locus.

9. State Nyquist stability criterion? (AU, May-08)If G(s) H(s) contour in the G(s) H(s) palne corresponding to Nyquist

contour in s-plane encircles the point -1+j0 in the anticlockwise direction as many

times as the number of right half s-planes poles of G(s) H(s).Then the closed loopsystem is stable.

10.What is breakaway and breakin point in root locus. (AU, May-08) At breakaway point the root locus breaks from the real axis to enter into

the complex plane. At breakin point the root locus enters the real axis from complex plane

11.Define root loci (RL) (AU, Jun-09)The path taken by the roots of the open loop transfer function when the loop gainis varied from 0 to infinity are called root loci.

12.What do you mean by dominant pole? (AU, Dec-09)The dominant point is a pair of complex conjugate pole which decides

transient response of the system. In higher order systems the dominant poles arevery close to origin and all other poles of the system are widely separated and sothey have less effect on transient response of the system.

13.Define the terms Asymptotes and centroid in root locus.AsymptotesAsymptotes are straight lines which are parallel to root locus going toinfinity an meet the root locus at infinity. Angle +or - 180(2q+1)/n-m, q------0,1,2,----(n-m)Centroid

The meeting point of the asymptotes with the real axis is called centroid.The centroid is given by

Centroid = (sum of poles sum of zeros) / (n-m)


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n-number of poles.m-number of zeros.

14.What is characteristic equation?The denominator polynomial C(s)/R(s) is the characteristic equation of thesystem.

15.What is auxiliary polynomial? (AU, Dec-10)In the construction of routh array a row of all zero indicates the existence

of an even polynomial as a factor of the given characteristic equation. In an evenpolynomial the exponents of s are even integers or 0 only. This even polynomialfactor is called auxiliary polynomial.

16.How will you find the root locus on real axis?To find the root loci on real axis, choose the test point on real axis. If the

total number of poles and zeros on the real axis to the right of this test point is odd

number then the test point lie on the root locus. If it is even then the test pointdoes not lie on the root locus.

17.How the roots of characteristic are related to stability?If the root of characteristic equation has positive real part then the impulse

response of the system is not bounded. Hence the system will be unstable. If theroot has negative real parts then the impulse response is bounded. Hence thesystem will be stable.

18.What is nyquist contourThe contour that encloses entire right half of S plane is called nyquist

contour.

19.How the roots of characteristic equation are related to stability?If the roots of characteristic equation has positive real part then the impulse

response of the system is not bounded,Hence the system will be unstable .If theroots has negative real parts then the impulse response is bounded. Hence thesystem will be stable.

20.What is the relation between stability and coefficient of characteristicpolynomial?

If the coefficients of characteristic polynomial are negative or 0, then some ofroots lies on half of s-plane. Hence the system is unstable. If the coefficients ofcharacteristic polynomial are positive and if no coefficient is 0 the there is apossibility of the system to be stable provided all the roots lie on left half of s-plane.


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II YEAR /IV SEM

UNIT-VSTATE VARIABLE ANALYSIS

1. What is state vector? (AU, Dec-10)The state vector is a (nx1) column matrix (or vector) whose elements are

state variables of the system. (Where n is the order of the system).It is denoted byX(t).

2. What is input and output space? (AU, Dec-10)The set of all possible values which the input vector U(t) can have (or

assume) at time t forms the input space of the system.

The set of all possible values which the output vector Y(t) can have (orassume) at time t forms the output space of the system.

3. What are the three basics elements used to form state diagram? (AU, Nov-10)The basic elements used to construct the state diagram are Scalar Adder Integrator.

4. What are the advantages of state space analysis?

The state space analysis is applicable to any type of systems. They can beused for modeling and analysis of linear & non linear systems, timeinvariant & time variant systems and multiple input & multiple outputsystems.

The state space analysis can be performed with initial conditions. The variables used to represent the system can be any variables in the

system. Using this analysis the internal states of the system at any time instant can

be predicted.5. What is a state and state variable? (AU, Jun-10)

The state is the condition of a system at any time instant. A set of variable which describes the state of the system at any

time instant are called state variables.


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6. Give the need for controllability test and observability test? (AU, Jun-10) The controllability test is necessary to find the usefulness of a state

variable. If the state variables are controllable then by controlling(i.e. varying) the state variables the desired outputs of the systemare achieved.

The observability test is necessary to find whether the statevariables are measurable or not. If the state variables aremeasurable then the state of the system can be determined bypractical measurements of the state variables.

7. State sampling theorem? (AU, Jun-10)Sampling theorem states that a band limited continuous time signal with

highest frequency fm, hertz can be uniquely recovered from its samples providedthat the sampling rate Fs is greater than or equal to 2fm samples per second.

8. State the duality between controllability and observability? (AU, Jun-10)The concept of controllability and observability are dual concepts and it is

proposed by kalman as principle of duality. The principle of duality states that asystem is completely state controllable if and only if its dual system is completelystate controllable if and only if its dual system is completely observable or viceversa.

9. What are all the methods of modeling for phase variables? Controllable canonical form. Observable canonical form. Diagonical canonical form. Jordan canonical form.

10. What are phase variables?

The phase variables are defined as those particular state variables whichare obtained from one of the system variable and its derivatives. Usually thevariable used is the system output and the remaining state variables are thenderivatives of the output.

11. State the various properties of state transition matrix.The properties of the state transition matrix of discrete time system are

given below, (0)=1 -1 (k) =(-k) (k,k0)= (k-k0)= A(k-k0) ; where k> k0


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12.What are the types of solution of state equations? Homogeneous state equations. Non-homogeneous state equations.

13. Define is controllability and is observability.

A system is said to be completely state controllable if it is possible totransfer the system state from any initial state X(t0) at any other desired state X(t),in specified finite time by a control vector U(t).

A system is said to be completely observable if every state X(t) can becompletely identified by measurements of the output Y(t) over a finite timeinterval.

14. What are the disadvantages of state space modeling using physical variable?

The advantages of choosing the physical variable are the following,

The state variable can be utilized for the purpose of feedback The implementation of design with state variable feedback

becomes straight forward. The solution of state equation gives time variation of variables

which have direct relevance to the physical system.

15. What are the drawbacks in transfer function model analysis? Transfer function is defined under zero initial conditions. Transfer function is applicable to linear time invariant systems. Transfer function analysis is restricted to single input and output systems. Does not provide information regarding the internal state of the system.

16. What are the different methods available for computing eAt?

The various methods available for computing eAt are,

Computation of eAt using matrix exponential. Computation of eAt using laplace-transform Computation of eAt by canonical transformation Computation of eAt using cayley-hamilton theorem.

17. What is state diagram?

The pictorial representation of the state model of the system is called statediagram. The state diagram of the system can be either in block diagram or insignal flow graph form.


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18. Write the state model of nth order system?

The state model of a system consists of state equation and output equation.the state model of a nth order system with m-inputs and p-outputs are

X (t) =AX (t) +BU (t) ..State Equation.Y (t) =CX (t) +DU (t) ..Output Equation.

Where X (t) =state vector of order (nx1), U (t) =Input vector of order (mx1)A= system matrix of order (nxn), B=Input matrix of order (nxm)Y (t) =output vector of order (px1), C=output matrix of order (pxn),D= Transmission matrix of order (pxm).

19. What is sampled data control system?

When the signal or information at any or some points in a system is in theform of discrete pulses, then the system is called discrete data system or sampleddata system.

20. What are the methods available for the stability analysis of sampled data controlsystem?

The following three methods are available for the stability analysis ofsampled data control system

Juris stability test. Bilinear transformation. Root locus technique.

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