IC6501-Control Systems Engineering PDF

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www.rejinpaul.com VALLIAMMAI ENGINEERING COLLEGE ELECTRICAL AND ELECTRONICS ENGINEERING

ANNA UNIVERSITY CHENNAI III YEAR EEE / V SEMESTER  

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IC 6501 – CONTROL SYSTEM ENGINEERING (REGULATION 2013)

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www.rejinpaul.com UNIT - I SYSTEMS AND THEIR REPRESENTATION PART - A (2 MARKS) 1. What is control system? 2. What are the two major types of control system? 3. What are the components of feedback control system? 4. Define transfer function. 5. What are the basic elements used for modeling mechanical translational system? 6. What are the basic elements used for modeling mechanical rotational system? 7. Name two types of electrical analogous for mechanical system. 8. What is block diagram? 9. What is the basis for framing the rules of block diagram reduction technique? 10. What is a signal flow graph? 11. What is transmittance? 12. What is sink and source? 13. Define non-touching loop. 14. Write Masons Gain formula. 15. Write the analogous electrical elements in force voltage analogy for the elements of mechanical translational system. 16. Write the force balance equation of M ideal mass element. 17. Distinguish between open loop and closed loop system. 18. What is servomechanism? 19. Why is negative feedback invariably preferred in closed loop system? 20. What is synchro?

PART-B(16 MARKS)

1. (i) Derive the transfer function for Armature controlled DC motor. (ii)Derive the transfer function for Field controlled DC motor.

(8) (8)

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www.rejinpaul.com 2. Determine the transfer function Y2(S)/F(S) of the system shown in fig.

K1

f(t)

(16)

B

M1

y1 K2

M2

y2

3. Write the differential equations governing the Mechanical rotational system shown in fig. Draw the Torque-voltage and Torque-current electrical analogous circuits. (16) K1

B2

J1

K3

J2

J3

B1

T

4. Determine the overall transfer function C(S)/R(S) for the system shown in fig.

(16)

H2 R(S)

G1

+ -

+

G2

+

G4

G3

C(S)

H1

3

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www.rejinpaul.com 5. Obtain the closed loop transfer function C(S)/R(S) of the system whose block diagram is shown in fig. (16) H2 R(S)

G1

+

-

+

G3

G2

+

C(S)

+

-

+

H1 G4 6 . For the system represented by the block diagram shown in fig. Determine C1/R1 and C2/R1. (16) R1 + G1 G2 G3

C1

+

H2 H1 +

R2

C2

+

+

G4

G5

G6

-

7. (i).Find the overall gain C(s) / R(s) for the signal flow graph shown below.

(8)

-H 1 G5 G1

G2

1

G4

G3

R(S)

C(S)

4

2

5

3 -H2

G6

-H 3

4

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www.rejinpaul.com (ii).With neat diagram, explain the working of AC and DC servo motors.

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8. Find the overall gain of the system whose signal flow graph is shown in fig.

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-H1

G4

G6

G1 G2

1

G8

1

R(S)

C(S) G3

G7 G5

-H2

9. Draw a signal flow graph and evaluate the closed loop transfer function of a system whose block is shown in fig. (16) G2 R(S)

G1

+

G3

C(S)

+ + H2 -

H1

G4

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www.rejinpaul.com 10. Write the differential equations governing the mechanical systems shown below. Draw the force-voltage and force-current electrical analogous circuits and verify by writing mesh and node equations. (16) X1

X2 K1

f(t)

K2 M2

M1 B1

B12

B2

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www.rejinpaul.com UNIT – II TIME RESPONSE PART- A (2 MARKS) 1. What is transient response? 2. What is steady state response? 3. What is an order and type of a system. 4. Define Damping ratio. 5. List the time domain specifications. 6. Define Delay time, Rise time, peak time. 7. State the type and order of the following system. 

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8. What is the type and order of the system?

9. Define peak overshoot & settling time.

10. What is the need for a controller? 11. What are the different types of controllers? 12. What is proportional controller? 13. What is PI controller? 14. What is PD controller? 15. What is the significance of integral controller and derivative controller in a PID controller? 16. Why derivative controller is not used in control systems? 17. Define Steady state error. 18. What is the drawback of static coefficients? 19. What is step, ramp & parabolic signal? 20. What are the three constants associated with a steady state error?

PART B(16 MARKS) 1.(a) Derive the expressions and draw the response of first order system for unit step input.

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(b) Draw the response of second order system for critically damped case and when input is unit step. (8) 2. Derive the expressions for Rise time, Peak time, Peak overshoot, delay time

(16)

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www.rejinpaul.com 3. A positional control system with velocity feedback is shown in fig. What is the response of the system for unit step input. (16)

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4. (i) Measurements conducted on a Servomechanism show the system response to be c(t)=1+0.2 ê-60t -1.2 ê –10 t. when subjected to a unit step. Obtain an expression for closed loop transfer function. (8) (ii). A positional control system with velocity feedback is shown in fig. What is the response c(t) to the unit step input. Given that ς =0.5.and also calculate rise time, peak time, Maximum overshoot and settling time. (8)

5. Draw the root locus of the following system

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6. For a unity feedback control system the open loop transfer function G(s) = 10(s+2)/ s2 (s+1).Find (a) position, velocity and acceleration error constants. (b)the steady state error when the input is R(s) where R(s) =3/s –2/s2 +1/3s3 (16) 7. The open loop transfer function of a servo system with unity feedback system is G(s) = 10/ s(0.1s+1).Evaluate the static error constants of the system. Obtain the steady state error of the system when subjected to an input given Polynomial r(t) = a +a t +a /2 t2 (16) 8. The unity feedback system is characterized by an open loop transfer function is G(s)= K / s(s+10).Determine the gain K ,so that the system will have a damping ratio of 0.5.For this value of K, determine settling time,Peak overshoot and time to Peak overshoot for a unit-step input. (16) 9. (i) For a servomechanisms with open loop transfer function(S)=10/(S+2)(S+3).What type of input signal gives constant steady state error and calculate its value. (8) (ii) Find the static error coefficients for a system whose G(s) H(s) =10/ s (1+s) (1+2s) and also find the steady state error for r(t)=1+ t + t2/2. (8) 88

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www.rejinpaul.com 10. (i) Sketch the root locus of the system whose open loop transfer function is  Find the value of K so that damping ratio is 0.5

(8)

(ii) A unity feedback system has an amplifier with gain KA=10 and gain ratio G(s) = 1 / s (s+2) in the feed forward Path .A derivative feedback ,H(s)=s KO is introduced as a minor loop around G(s).Determine the derivative feed back constant ,KO ,so that the system damping factor is 0.6 (8)

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www.rejinpaul.com UNIT- III FREQUENCY RESPONSE PART- A (2 MARKS) 1. What is frequency response? 2. List out the different frequency domain specifications? 3. Define –resonant Peak? 4. Define –Resonant frequency? 5. What is bandwidth? 6. Define Cut-off rate? 7. Define –Gain Margin? 8. Define Phase cross over? 9. What is phase margin? 10. Mention some advantage and disadvantages of frequency response analysis 11. Define Gain cross over? 12. What is Bode plot? 13. draw the bode plot of a typical lag-lead compensator 14. Define Corner frequency? 15. What is Polar plot? 16. What type of compensator suitable for high frequency noisy environment? 17. What is non-minimum phase transfer function? 18. What is the transfer function of lag/lead compensator? 19. What is the correlation between phase margin and damping factor? 20. Draw the polar plot for  

PART B(16 MARKS) 1. Sketch the bode plot showing the magnitude in decibels and phase angle in degrees as a function Of log frequency for the transfer function,

From the bode plot, determine the gain cross over frequency.

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

Sketch the Polar plot and determine the Gain margin and Phase margin.

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www.rejinpaul.com 3.(i).Discuss the correlation between time and frequency response of second order system. (8) (ii).How does closed loop frequency response is determined from the open loop frequency response using Nichols chart? Explain how the gain adjustment is carried out on the Nichols chart. (8) 4. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. (16)

5. Sketch the polar plot for the following transfer function and finds Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. (16)

6. Construct the polar plot for the function,  Find Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. 7. Plot the Bode diagram for the following transfer function and obtain the gain and phase cross over frequencies G(s) =Ks2 / (1+0.2s) (1+0.02s).Determine the value of K for a gain cross over frequency of 20 rad/sec. (16) 8. 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) = 400/ s (s+2)(s+10)

(16)

9. Design a lead compensator for unity feedback system with open loop transfer function 

To statisfy the following specifications. (i).KV ≥ 50 (ii).Phase margin is 20o 10. Explain briefly about constant M and N circles.

(16) (16)

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www.rejinpaul.com UNIT- IV STABILITY AND COMPENSATOR DESIGN PART- A (2 MARKS) 1. What is Nyquist contour? 2. State Nyquist stability criterion. 3. Define Relative stability. 4. What are the two segments of Nyquist contour. 5. What are root loci? 6. What is a dominant pole? 7. What are the main significances of root locus? 8. What are the effects of adding a zero to a system? 9. State-Magnitude criterion. 10. State – Angle criterion. 11. Define Phase lag and phase lead? 12. What are the two types of compensation? 13. What are the uses of lag and lead compensator? 14. What is Compensation? 15. Why Compensation is necessary in feedback control system? 16. When lag/lead/lag-lead compensation is employed? 17. When is lag lead compensator is required? 18. What is a dominant pole? 19. Define BIBO stability. 20. What is the necessary condition for stability?

PART B(16 MARKS) 1. (i) Using Routh criterion determine the stability of the system whose characteristics equation is s4+8s3+18s2+16s+5 =0. (8) (ii).F(S) = s6 +s5-2s4-3s3-7s2-4s-4 =0.Find the number of roots falling in the RHS plane and LHS plane. (8) 2. Design suitable lead compensators for a system unity feedback and having open loop transfer function G(s)= K/ s(s+1) to meet the specifications.(i) The phase margin of the system ≥ 45º, (ii) Steady state error for a unit ramp input ≤1/15, (iii) The gain cross over frequency of the system must be less than 7.5 rad/sec. (16) 3. Describe the procedure for the design of lag compensator using bode plot.

(16)

4. (i).Design a Lag compensator for the unity feedback system whose closed loop transfer function C(s) / R(s) = K / (s (s+4) (s+80) + K) is to meet the following specifications P.M ≥33 º. And Kv ≥30. (8) (ii).What is compensation? Why it is need for control system? Explain the types of compensation? What is an importance of compensation?

(8) 22

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www.rejinpaul.com 5. Describe the procedure for the design of lead compensator using bode plot.

(16)

6. The open loop transfer function of a unity feedback control system is given by

(16)

 By applying the routh criterion,discuss the stability of the closed loop system as a function of K.

Determine the values of K which will cause sustained oscillations in the closed loop system. What are the corresponding oscillation frequencies? 7. Draw the Nyquist plot for the system whose open loop transfer function is G(s)= K / s(s+2)(s+10).Determine the range of k for which closed loop system is stable. (16) 8. Sketch the Nyquist Plot for a system with the open loop transfer function G(s) H(s)= K (1+0.5s)(1+s) / (1+10s)(s-1). Determine the range of k for which closed loop system is stable. (16) 9. (i) Determine the range of K for stability of unity feedback system whose open loop transfer function is G(s) = K / s (s+1)(s+2) (8) (ii) The open loop transfer function of a unity feed back system is given by G(s) = K (s+1) / s3+as2+2s+1. Determine the value of K and a so that the system oscillates at a frequency of 2 rad/sec. (8) 10.(i) Construct Routh array and determine the stability of the system represented by the characteristics 5 4 3 2 equation S +S +2S +2S +3S+5=0.Comment on the location of the roots of characteristic equation. (8) (ii) Construct Routh array and determine the stability of the system represented by the characteristics equation S7 +9S6+24S4+24S3 +24S2+23S+15=0comment on the location of the roots of characteristic equation. (8)

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www.rejinpaul.com UNIT - V STATE VARIABLE ANALYSIS PART- A (2 MARKS) 1. What is state? 2. What is state variable? 3. What is state vector? 4. What is state space? 5. What are the properties of state transition matrix. 6. What is controllability? 7. What is observability? 8. Name the methods of state space representation for phase variables. 9. What is the need for controllability test? 10. Define time invariant system. 11. List some advantages of phase variable method 12. List some disadvantages of phase variable method. 13. Define time invariant system. 14. Define time variant system. 15. List the four different types of realization. 16. What is the need for observability test? 17. What is Alias in sampling process? 18. What is meant by sampling theorem? 19. Define Time domain solution. 20. Write the transfer function of state model.

PART B(16 MARKS) 1. (i).Write the state equation for a mechanical system shown in fig

(8)

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www.rejinpaul.com (ii). For the given circuit shown in fig. Obtain State equations the input voltage source is u(t) and the output y(t) is taken across capacitor c2

(8)

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2. (i). Obtain and briefly explain the state space representation of (a).Armature controlled dc motor. (b).Field controlled dc motor. 3. (i). Find the controllable canonical realization of the following systems. Hence Obtain the state space model in controllable canonical form. (i).H(s)=s2+2s+3 / s4+3s3+12s2+9s+8 (ii).H(s)= 2s+9 / s3+8s2+12s+10 (ii). Find the observable canonical realization of the system. H(s)=s+2 / s4+4s3+3s2+12s+ 5 4. (i). Realize H(s)=s(s+2) / (s+1)(s+3)(s+4) in cascade form. Hence obtain the State model. (ii).Find observable canonical form for the transfer functions using Mason’s gain formula for the systems. (i).G(s) = 2 / s3+2s2+4s+8 (ii).G(s) = s+3 / s2+2s+7 Hence obtain the model matrix P and diagonalize the given state model. 5. Check the controllability of the following state space system.

6. For the given matrix find the diagonalization matrix.

(16)

(8)

(8)

(8) (8)

(16)

(16)

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www.rejinpaul.com 7. (i).A system is represented by the state equation X=AX+BU; Y=CX where A=

B=

(8)

C=

Determine the transfer function of the system. (ii).A system is characterized by the transfer function

(8)

Identify the first state of the output. Determine whether or not the system is completely Controllable and observable. 8. (i).Check the controllability of the following state space system. (8) A=

, B=

, C=

and D=

(ii).Obtain the state model of the system described by the following transfer functions. (8)

9. Obtain the state transition matrix for the state model whose system matrix A is given by A= 10. Briefly explain system realization and its types (any two).

(16) (16)

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