II Ece

SyllabusEC6405-Control System Engineering

Class/Sem: III EEE / V Sem Unit I Control System Modeling 9Basic Elements of Control System – Open loop and Closed loop systems - Differential equation - Transfer function, Modeling of Electric systems, Translational and rotational mechanical systems - Block diagram reduction Techniques - Signal flow graph

Unit II Time Response Analysis 9Time response analysis - First Order Systems - Impulse and Step Response analysis of second order systems - Steady state errors – P, PI, PD and PID Compensation, Analysis using MATLAB

Unit III Frequency Response Analysis 9Frequency Response - Bode Plot, Polar Plot, Nyquist Plot - Frequency Domain specifications from the plots - Constant M and N Circles - Nichol‟s Chart - Use of Nichol‟s Chart in Control System Analysis. Series, Parallel, series-parallel Compensators - Lead, Lag, and Lead Lag Compensators, Analysis using MATLAB.

Unit IV Stability Analysis 9Stability, Routh-Hurwitz Criterion, Root Locus Technique, Construction of Root Locus, Stability, Dominant Poles, Application of Root Locus Diagram - Nyquist Stability Criterion - Relative Stability, Analysis using MATLAB

Unit V State Variable Analysis 9State space representation of Continuous Time systems – State equations – Transfer function from State Variable Representation – Solutions of the state equations - Concepts of Controllability and Observability – State space representation for Discrete time systems. Sampled Data control systems– Sampling Theorem – Sampler & Hold – Open loop & Closed loop sampled data systems.

TEXTBOOK:1. J.Nagrath and M.Gopal, “Control System Engineering”, New Age International Publishers, Edition, 2007.

REFERENCES:1. Benjamin.C.Kuo, “Automatic control systems”, Prentice Hall of India, 7th

Edition,1995.2. M.Gopal, “Control System – Principles and Design”, Tata McGraw Hill, 2nd Edition, 2002.3. Schaum‟s Outline Series, “Feed back and Control Systems” Tata Mc Graw-Hill, 2007.4. John J.D‟Azzo & Constantine H.Houpis, “Linear Control System Analysis and Design‟”, Tata Mc

Maharaja Engineering Institutions, Coimbatore & AvinashiDepartment of Electrical and Electronics Engineering

EC6405-Control System Engineering Question Bank-I (For Internal Assessment Purpose)

Class/Sem: II ECE /III Sem Max.Marks:100Unit-I Systems and Their Representation

Part A (10x2=20)1. Write Masons Gain formula.

Masons Gain formula states that the overall gain of the system isT = 1/ ∆Σk Pk ∆k k- no. of forward paths in the signal flow graph. Pk- Forward path gain of k th 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 ofAll possible combinations of three non touching loops] +… ∆k - ∆ for that part of the graph which is not touching k th forward path

2. Why negative feedback is preferred in control systems? The negative feedback results in better stability in steady state and rejects any

disturbance signals. It also has low sensitivity to parameter variations. Hence negative feedback is preferred in closed loop systems.

3. What is feedback? What type of feedback is employed in control system? The feedback is a property of the system by which it permits the output to be

compared with input so that appropriate controlling action can be decided. Negative is employed in control system.

4. What are the advantages of feedback control? i. Rejection of disturbance signal.ii. Accuracy in tracking steady state value. iii. Low sensitivity to parameter variations.

5. Distinguish between open loop and closed loop systems. S.No Open loop system Closed loop system

i. Inaccurate and unreliable Accurate and reliableii. Simple and economical Complex and costlier

iii.The changes in output due to external disturbance are not corrected

The changes in output due to external disturbances are corrected automatically

iv.They are generally stable Great efforts are needed to design

a stable System

6. Define Transfer Function. The transfer function of a system is defined as the ratio of the Laplace transform of

output to Laplace transform of input with zero initial conditions.

71

7. What are the advantages of closed loop control system? The closed loop systems are accurate.i. The closed loop systems are accurate even in the presence of non- linearities.ii. The closed loop systems are less affected by noise.iii. The sensitivity of the systems may be made small to make the system more stable.

8. What are the properties of Signal Flow Graphs? Signal flow graph is applicable to linear systems.i. It consists of nodes and branches.

A node is a point representing a variable or signal. A branch indicates functional dependence of one signal on the other.

ii. The algebraic equations must be in the form of cause and effect relationship.

9. List the basic elements used for modeling a mechanical rotational system. Mass with moment of inertia J Dash-pot with rotational frictional coefficient B Torsional spring with stiffness K.

10. What are the components of the block diagram? The basic elements are Block, branch and summing point.

Part- B (5X16=80)11. (a) Write the differential equations governing the mechanical system and determine

the transfer function.

12. Write the differential equations governing the mechanical rotational system. Obtain the transfer function of the system?

13. Using the block diagram reduction technique, find C/R.

72

14. Using Mason’s gain formula, find C/Rof the signal flow of the graph.

15. Derive the transfer function of armature controlled dc motor.

Question Bank –II (For Additional Study Purpose) Part- A (2x10=20)

1. What is signal flow graph?2. Give some examples for open and closed loop systems. 3. What are the advantages of closed loop control system?4. What is the effect of positive feedback on stability?5. What is servomechanism?6. State block diagram simplification rule for removing feedback loop 7. List two advantages of signal flow graph.8. Define non-touching loop.9. What is the sink and source? 10. Write the electrical analogous elements in torque – voltage analogy for the elements

of mechanical rotational system.

Part- B (5x16=80)11. Using Mason’s gain formula, find C/R of the signal flow graph shown in figure

.

12. The network shown figure modifies the error signal. It voltage Vi of a Servomechanism to a. Find the T.F. Vo/Vi neglecting any load on the output

73

terminals. Evaluate the function ((a) p r a sine signal voltage of 1.0 v at angular frequency w = 20 red/sec and (b) for a step function input signal voltage of 1.oV.

13. Use Mason’s gain formula for determining the overall T.F. of the system shown.

14. Write the differential equations governing the mechanical system. Draw the force-voltage and force current electrical analogous circuits and verify by writing mesh and node equations.

15. Reduce the given block diagram to its canonical form ‘D’ hence obtain the equivalent transfer function.

74

Question Bank-I (For Internal Assessment Purpose) Unit – II Time Response Analysis

` Part-A (10x2=20) 1. What is transient and steady state response?

The transient response is the response of the system when the input changes from one state to another. The response of the system t time infinity is called steady-state response.

2. Name the test signals used in time response analysis. The commonly used test input signals in control system are impulse, step, ramp,

acceleration and sinusoidal signals.

3. List the time domain specifications.(i) Delay time (ii) Rise time (iii) Peak time (iv) Maximum overshoot (v) Settling time.

4. Define rise time, delay time, peak time. Rise time is the time taken for response to rise from 0 to 100% for the very first

time. Delay time is the time taken for response to reach 50% of the final value, for the very first time. Peak time is the time taken for the response to reach the peak value for the very first time (or) It is the time taken for the response to reach peak overshoot, Mp

5. What is steady state error? List the static error constants. The 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 arise from the nature of inputs, type of system and from non-linearity of system components.(i) Positional error constant,(ii) Velocity error constant, (iii) Acceleration error constant

6. List the advantages of generalized error constants.i. Generalized error series gives error signal as a function of time.ii. Using generalized error constants the steady state error can be demean for any

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

7. What are generalized error constants? They are the coefficients of generalized series. The generalized error series is given

bye (t) = C0r(t) + C1dr(t)/dt + ( C2 / 2! ) dr2(t)/dt2 + ………….. + (Cn / n!) drn(t)/dtn…The coefficients C0, C1, C2,…,Cn are called generalized error coefficients or dynamic error coefficients.

8. 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 controllers not used in control systems.

9. What are zero and poles? The zero of a function, F(s) is the value at which the function, F(s) becomes zero, where F(s) is a function of complex variable s. The pole of a function, F(s) is the value

75

at which the function, F(s) becomes infinite, where F(s) is a function of complex variables.

10. What is meant by order of a system? The order of the system is given by the order of the differential equation

governing the system. If the system is governed by nth order differential equation then the system is called nth order system.

Part – B (5x16=80)11. (i) Draw the response of second order system for critically damped case and when input is unit step. (ii) Derive the expressions for second order system for under damped case and when The input is unit step. (iii)Derive the expressions for second order system for un damped case and when the

input is unit step.

12. (i) Derive the expressions for Rise time, Peak time, Peak overshoot, delay time. (ii) A positional control system with velocity feedback is shown in fig, what is the

response of the system for unit step input.

13. Measurements conducted on a servomechanism show the system response to be c(t)=1+0.2e-60t-1.2e-10t.when subjected to a unit step. Obtain an expression for closed loop transfer function.

14. A closed loop servo is represented by the differential equation d2c/dt2+8dc/dt

=64e.where c is the displacement of the output shaft r is the displacement of the input shaft and e=r-c. Determine un damped natural frequency, damping ratio and percentage maximum overshoot for unit step input.

15. Explain the P, I, PI, PD, PID controllers.

Question Bank –II (For Additional Study Purpose) Part-A (10x2=20)

1. What is Time Response? 2. Name the test signals used in Time Response Analysis. .3. Define step signal, Ramp signal and parabolic signal and impulse signal. 4. How is system classified depending on the value of damping?5. Sketch the response of a second order under damped system. 6. What is damped frequency of oscillation?7. What are static error constants? 8. What is the effect of adding a pole to a second order system?.9. Give two disadvantages of feedback in control.10. What is the integral time square error of the second order system with step input having

76

damping coefficient ξ and un damped natural frequency wn?

Part-B (5x16=80)11. (i) Obtain the steady state error for unit step, ramp input and parabolic input in terms of

the transfer function. (ii) Determine error coefficients for a system whose open loop transfer function

G(S)H(S)= . Also compute steady state error if the input to the system

is a0+a1t+a2t2.12. Figure shows PD controller used for the system. Determine the value of Td so that

system will be critically damped. Calculate it’s settling time

13. For a servomechanisms with open loop transfer function(S)= .What

type of input signal gives constant steady state error and calculate its value.

14. Determine the time response specifications and expression for output for unit step input to a system having equation as follows.

+5 +16y = 9x.

15. Find the steady state error system whose G(S) H(S) = and also find the

steady state error if the input is r(t) =1+ t +t2

Question Bank-I (For Internal Assessment Purpose)Unit – III Frequency Response Analysis

Part-A (10x2=20)1. What are the frequency domain specifications?

(i). Resonant peak (ii) Cut-off rate (iii). Resonant frequency (iv) Gain margin (v) Bandwidth (vi). Phase margin.

2. Define gain margin &phase margin.The phase margin is that amount of additional phase lag at the gain cross over

frequency, øgc required to bring the system to the verge of instability. It is given by, 180° +ø gc, where ø gc is the phase of G(jw) at the gain cross over frequency.

77

3. What is phase and gain cross over frequency? The gain cross-over frequency is the frequency at which the magnitude of the

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

4. What is corner frequency? The magnitude plot can be approximated by asymptotic straight lines. The

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

5. What is Nicholas chart? Nichol’s chart is a frequency response plot of the open loop transfer function of a

System. It is a graph between magnitude of G(jω) in dB and the phase of G(jω) in Degree, plotted on a ordinary graph sheet.

6. What is the importance of compensation? When the system is stable, compensation is provided to obtain the desired

performance. When the system is absolute unstable, then compensation is required to stabilize

the system and also to meet the desired performance.

7. Mention the need for lead compensation.The lead compensation increases the bandwidth and improves the speed of

response. When the given system is stable/unstable and requires improvement in transient state response then lead compensation is employed.

8. Name the commonly used electrical compensating networks. Lag compensation. Lead compensation and lag-lead compensation.

9. State the uses of Nicholas chart.The Nicholas chart is used to find the closed loop frequency response from the

open loop frequency response.

10. Define resonant frequency. The frequency at which the resonant peak occurs is called resonant frequency

Part –B (5x16=80)11. Plot the bode diagram for the following transfer function and obtain the gain and

phase cross over frequencies G(S) =

12. The open loop transfer function of a unity feedback system is

G(S) = Sketch the polar plot and determine the gain margin and

phase margin. 13. Sketch the polar plot for the following transfer function and find gain crossover

frequency, Phase cross over frequency ,Gain margin and phase margin

78

G(S) =

14. Draw the pole-zero diagram of a lead compensator. Propose lead compensation using electrical network. Derive the transfer function. Draw the bode plots

Question Bank –II (For Additional Study Purpose) Part-A (10x2=20)

1. What is frequency response?2. What is bode plot?3. What are the advantages of bode plot? 4. What is polar plot? Mention the advantages.5. What is cut off rate?6. What is bandwidth? 7. Define resonant frequency. 8. When lag /lead /lag-lead compensation?9. What is lag-compensation?10. What is lead compensation?

Part-B (5x16=80)11. Sketch the polar plot for the following transfer function and find gain cross over

frequency, phase cross over frequency, gain margin and phase margin.

G(S) =

12. A unity feedback system has an open loop transfer function

G(S) = Design a suitable phase lag compensators to achieve

the following specifications Kv = 8 and Phase margin 40 deg with usual notation.13. Explain the use of M circles and N circles for the study of frequency

response analysis of feedback system?14. Design a suitable lead compensator for a system with unity feedback and having

open loop transfer function G(S) = to meet the specifications as

damping ratio = 0.5 and un damped natural frequency = 2 rad / sec15. Discuss in detail about the design of a lag-lead compensator. Design the elements

of the network and sketch the bode plot.

Question Bank-I (For Internal Assessment Purpose)Unit – IV Stability Analysis

Part-A (10x2=20) 1. What is stability?

For a bounded input signal, if the output has constant amplitude oscillations may be stable

.2. State Routh stability criteri(a)

79

Routh condition states that the necessary and sufficient condition for stability is that all of the elements in the first column of routh array be positive. If this condition is not met, the system is unstable and the number of sign changes in the elements of the first column of routh array corresponds to number of roots of characteristic equation in the right half of s-plane.

3. Define BIBO Stability? A linear relaxed system is said to have BIBO stability if every bounded input

results in a bounded output.

4. What is root locus? The path taken by a root of characteristic equation when open loop gain K is

varied from 0 to infinity is called root locus.

5. What are root loci? The path taken by the roots of the open loop transfer function when the loop

gain is varied from 0 to α are called root loci.

6. What is a dominant pole? The dominant point is a pair of complex conjugate pole which decides

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

7. Define a breakaway& break in point. At breakaway point the root locus breaks from the real axis to enter into the complex plane. At breaking point the root locus enters the real axis from complex plane.

8. What are asymptotes? How will you find the angle of asymptotes? Asymptotes are straight lines which are parallel to root locus going to infinity an meet the root locus at infinity. Angle--+or - 180(2q+1)/n-m, q------0,1,2,----(n-m)

9. What is Nyquist stability criterion? If G(s) H(s) contour in the G(s) H(s) plane corresponding to Nyquist contour

in s-plane encircles the point -1+j0 in the anti clockwise direction as many times as the number of right half s-planes poles of G(s) H(s).Then the closed loop system is stable.

10. What is angle criterion for root locus? The angle criterion states that S=Sa will be a point on root locus if for that value of S argument or phase of G)S)H(S) is equal to an odd multiple of 180

Part - B (5x16=80)11. (i) F(S)= S6+2S5+8S4+12S3+20S2+16S+16=0. Find the number of roots falling in the RHS plane and LHS

(ii)Using Routh criterion Determine the stability of the system whose Characteristics equation is S5+S4+2S3+2S2 +3S+15=0

80

12. Sketch the root locus for the unity feedback system whose open loop transfer

function is G(S) = .

13. Sketch the root locus for the unity feedback system whose open loop

transfer function is G(S) = .

14. Using Routh criterion Determine the stability of the system whose characteristics equation is S5+S4+2S3+3S+5=0

15. Sketch the root locus for the unity feedback system whose open loop

transfer function is G(S) =

16. Sketch the Nyquist plot determine the stability of the system

G(S) H(S)= .

17. Sketch the Nyquist plot for a system with the open loop transfer function

G(S) = .Determine the range of values of K for which the

system is stable (ii) S5+6S4+15S3+30S2+44S+24.

Question Bank –II (For Additional Study Purpose)

Part-A (10x2=20) 1. What is characteristics equation?2. What is a centroid? 3. What is impulse response?4. What is guadrantal symmetry?5. In routh array what conclusion you can make when there is a row of all zeros?6. What is limitedly stable system?7. How will you find the gain K at a point on root locus?8. How will you find root locus on real axis? 9. What is the necessary condition for stability? 10. What will be the nature of impulse response when the roots of characteristic

equation are lying on imaginary axis?

Part – B (5x16=80)11. (i) Sketch the root locus for the unity feedback system whose open loop

transfer function is G(S) =

(ii) Using Routh criterion Determine the stability of the system whose characteristics equation is (a) S5+2S4+3S3+6S2+10S+15. (b) S5+6S4+15S3+30S2+44S+24.

81

12. (i) Draw the Nyquist plot for the system whose open loop transfer function

is G(S) H(S) =

(ii) Draw the Nyquist plot for the system whose open loop transfer function

is G(S) H(S) =

13. (i) Sketch the root locus for the unity feedback system whose open loop transfer

function is G(S) = .

(ii) Using Routh criterion Determine the stability of the system whose characteristics equation is (i) S5+2S4+3S3+6S2+10S+15.

(ii) S5+6S4+15S3+30S2+44S+24.

14. Using Routh criterion Determine the stability of the system whose characteristics equation is S5+S4+2S3+2S2 +3S+25=0. 15. Explain in detail about Root locus method.

(i) List the rules for constructing root locus. (ii) Write the procedure for constructing root locus.

Question Bank-I (For Internal Assessment Purpose)Unit –V State Variable Analysis

Part -A (10x2=20) 1. Write the Properties of State Transition Matrix?

Ф(0) = eA x 0 = 1 (Unit matrix) Ф(t) = (e-At)-1 = [Ф(-t)]-1 Ф(t1+t2) = eA(t

1+t

2) = eAt

1 eAt2 = Ф(t1) Ф(t2) = Ф(t2) Ф(t1)

2. Name the Methods of State Space Representation for Phase Variables. i. Bush form or companion form

ii. By using mason’s gain formulaiii. By using Laplace transform

3. How the Modal Matrix is Determined? The modal matrix M can be formed from eigenvectors. Let m1, m2, m3….. mn

be the eigenvectors of a nth order system. Now the modal matrix M is obtained by arranging all the eigenvectors column wise. ie M = [m1 m2 m3 …… mn]

4. What is Sampled Data Control System? In a control system, if the signal in any part of the system is discrete then the

entire system is said to be sampled data system.

5. State Sampling Theorem.

82

A continuous time signal can be completely represented in its samples and recovered back if the sampling frequency Fs≥2Fmax where Fs is the sampling frequency and Fmax is the maximum frequency present in the signal.

6. Define ‘State’ and ‘State Variables’. The state is the condition of a system at any instant, t. A set of variable which

describes the state of the system at any time instant are called state variables

7. What is meant by Quantization? For processing the sampled signals by digital means, it has to be converted to

binary codes and this conversion process is called quantization. The process of converting a discrete time continuous valued signal into a discrete value signal is called quantization.

8. What is Hold Circuit? A device used to convert digital signal into analog signal.The function of the hold circuit is to reconstruct the signal which is applied as

input to the sampler. The simplest holding device holds the signal between two consecutive instants at its preceded value, till next sampling instant is reached.

9. What is Acquisition Time? Time taken by an analog to digital converter to sample the signal, to quantize it

and to code it is known as acquisition time.

10. What is Settling Time? It is the time taken by a digital to analog converter to convert the given digital

signal into analog signal magnitude and be remain within the tolerance is called settling time.

Part- B (5x16=80) 11. For the following transfer functions obtain the state space representation of this systems in controllable canonical form

G(s) =

12. Find the state variable equation for a mechanical system (spring – mass – damper system shown below.

13. (i) Consider the system given by below. Obtain state space representation in diagonal canonical form.

83

=

(ii) A sampled data control system is shown in the figure below

Find the open loop pulse transfer function, if the controller gain is

unity with sampling period time 0.5 seconds.

14. Determine state space representation of network shown below.

15. Write state space representation of mechanical system shown in fig.

Question Bank –II (For Additional Study Purpose) Part –A (10x2=20)

1. What are the problems that may occur in a practical hold circuit? 2. How the high frequency noise in the output hold circuits can be filtered? 3. What is pulse transfer function? 4. What is hold mode droop? 5. Distinguish between analog and digital controllers. 6. What is the condition to be satisfied for a sampled data system to be stable? 7. What is the characteristic equation of a sampled data system? 8. When a control system can be called as sampled data control system?9. List the methods used to test the stability of discrete time system. 10. What are the advantages of state space analysis?

84

Part –B (5x16=80)11. (i) Explain sampling theorem and Sample & Hold operation briefly.

(ii) Explain state space representation for discrete time system.12. (i) Explain state space representation for continuous time system.

(ii) Explain the solution for state equation for discrete time system.13. (i) Determine the state variable representation of the system whose transfer

function given as Y(S) / U(S) = 2S2+8S+7 / (S+2)2 (S+1)

(ii) Given the transfer function of a system, determine a state variable representation for the system Y(S) / U(S) = 1/ (S+2) * (S+3) * (S+4)

14. Explain Jury’s stability test in root loci 15. Explain the importance of controllability and observability of the control system model in the design of the control system.

------------------------------------------- ALL THE BEST -----------------------------------

85