GTU Paper Analysis (New Syllabus) · GTU Paper Analysis (New Syllabus) Control Engineering (2151908) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

GTU Paper Analysis (New Syllabus)

Control Engineering (2151908) Department of Mechanical Engineering Darshan Institute of Engineering & Technology

Ch. 1 Basic concepts of control system:

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1. With a suitable example, explain following terms related to a control system. (a) Control Variable (b) Manipulated Variable (c) Plant (d) Process

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2. State and explain conditions for a system to be a linear system 3

3. Derive transfer function of room heating system with usual notations. 7

4. Differentiate between open loop and close loop control systems 7

5. Discuss about the requirements of good control system. 3

6. Define Controlled variable and Manipulated variable. State requirements of a good control system.

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7. Briefly classify control systems. Write comparison between Open loop system and Closed loop system.

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8. Write note on “ Significance of Control Engineering” 3

9. Define transfer function. List important characteristics of transfer function. 3

10. What is a time varying system? Give suitable examples. How is it different from the time invariant system?

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Ch. 2 Mathematical modelling of systems:

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Theory

1. Derive the Analogous relationship between Mechanical and Electrical system based on Force-Current analogy.

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2. Derive the analogous relationship between Mechanical and Electrical systems based on Force-Voltage analogy.

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3. What does a block diagram represent? List its salient characteristics 4

4. Find transfer function equation for simple mass-spring-dashpot system with usual notation.

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5. Tabulate the various analogous elements in mechanical and electrical systems. 4

6. What does a block diagram represent? Explain it in detail. 3

7. List its salient characteristics of Block Diagram. Explain the following: Summing point, take off point.

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8. What is signal flow graph? Can the gain formula be applied between any two nodes of a SFG?

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9. Compare block diagram representation versus Signal flow graph representation. 4

Examples

1. From the block diagram in Figure 1, to obtain a transfer function C(S) / R(S). 7



2.

Obtain the transfer function Y(s)/U(s) of the system shown in Figure 2. The displacement input is u(t).

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3. A mechanical system (Figure 3(a)), is subjected to a step input of 200 N. The response curve for the same is shown in Figure 3(b). Determine mass m, spring constant k and damping coefficient b of the system from this response curve.

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4.

A system is described by following a set of linear algebraic equations. Draw signal flow graph and obtain transfer function of the system using Mason’s gain formula.

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5.

Draw the analogous electric circuit considering Force-Voltage analogy for the mechanical system shown in figure 1 where xi is the input displacement, x0 is the output displacement, y is the displacement of the spring, D1, D2 are the viscous damping coefficients and K1, K2 are the compliances of the springs. Also obtain the transfer function for this mechanical system.

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6. Determine the overall transfer function for the block diagram shown in figure 2 using 7



block diagram reduction.

7.

Determine the transfer function by the Mason’s Gain formula for the Signal Flow Graph shown in figure 3.



8.

Obtain the Transfer function C/R from the signal flow graph as shown in figure1.

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9.

Obtain the overall transfer function of the system whose block diagram is as given infigure 2 using block diagram reduction technique.

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10.

Obtain Differential Equation for the mechanical system shown in figure3. Also obtain analogus circuit using Force-Voltage analogy.

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11.

In a mechanical vibratory system when 2N of force (step input) is applied to the system, the mass oscillates as shown in figure 4. Determine the values of M, B and K of the system from this response curve. The displacement is measured from equilibrium position.

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12.

Obtain overall transfer function of the system whose block diagram is shown in Figure 1, explaining the major steps of reduction involved.

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13.

Obtain overall transmittance of the system whose signal flow graph is shown in Figure 2 by using Masson’s gain formula

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14.

Derive the differential equation for the mechanical system shown in Figure 3.



15.

Using Force-Voltage analogy, draw electrical analogous circuit of the mechanical system shown in Figure I and write the differential equations governing the system shown in figure.

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16.

What do you mean by Signal Flow graph? The block diagram representation of a control system is shown in Figure II. Draw the signal flow graph and determine overall transfer function using Mason’s gain formula.

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17.

Obtain the transfer function of a mechanical network shown in Figure III

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18.

Reduce block diagram as shown in Figure IV and obtain overall transfer function

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19.

Obtain the transfer function Y(s)/U(s) of the system shown in figure 1. The displacement input is u(t).

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20. Reduce block diagram as shown in figure 2 by using block diagram reduction rules and obtain overall transfer function.

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21.

For the signal flow graph of a multiple loop system shown in figure 3, determine C(s)/R(s) using Mason’s gain formula.

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Ch. 3 Time Response Analysis

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1. Derive expressions of rise time and peak time for a second order under damped system excited by a unit step input.

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2.

A closed-loop control system is represented by the differential following equation, where e is the error signal given as (r – c). (d2c/dt2)+ 4(dc/dt) = 16e. Determine un-damped natural frequency, percentage of maximum overshoot for unit-step input, damping ratio and percentage of maximum overshoot for unit-step input.

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3. For a second-order system with a sinusoidal transfer function, derive the expression of the resonant peak.

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4. Derive unit-step response for first-order control system. Discuss salient features of the response curve and error curve with a neat sketch.

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5.

For the system shown in figure, determine the value of gain K and velocity-feedback constant Kh so that the maximum overshoot in the unit-step response is 0.2 and the peak time is 1 sec. With these values of K and Kh, obtain the rise time and settling time for 2% criterion. Assume that J = 1kg-m2 and B = 1 N-m/rad/sec.

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6. Derive unit impulse response for a generalized second order system for underdamped, critically damped and overdamped cases with usual notations. Also derive the relation of maximum overshoot (for underdamped case).

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7. Discuss the effect of time constant on 1st order system response for unit step input. 3

8. Discuss the effect of damping on the position of closed loop poles of the 2nd order 4



system with diagram.

9. Draw generalized unit step response for 2nd order system and define following: Rise time, Delay time, Settling time.

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10. Explain about the transient and steady state response of the system. Also list out the standard test signals and explain any one of them.

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11. Obtain the transient response of first order system subjected to unity step input. Also draw the response curve of the same explaining the terms involved.

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12. Discuss the effect of time constant on first order system response for unit step input. 3

13. Explain the effect on steady state error when a step input applied to Type 0 systems. 4

14. Define following terms in context with the transient response specifications of second order system using neat sketch: Delay time, Rise time, Peak time, Maximum overshoot, settling time

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15. Explain the ramp input mathematically and graphically. 3

16.

The overall transfer function of a control system is given below eq. Determine the rise time, peak time and maximum overshoot.

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17. Discuss about an On-Off control action type automatic industrial controller with differential gap.

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18. What is meant by Step input, Impulse input and Ramp input? 3

19. Explain PI controller and its effect on the system performance. 3

20.

The closed loop transfer functions of certain second order unity feedback control systems are given below. Determine the type of damping in the systems.

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21. What is a time varying system? Give suitable examples. How is it different from the time invariant system?

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22. Derive expressions of rise time and peak time for a second order under damped system excited by a unit step input.

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23. Define following terms in context with the transient response specifications of second order system using neat sketch: Delay time, Rise time, Peak time, Maximum overshoot, settling time.

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Ch. 4 Frequency Response Analysis

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1. Explain frequency response specifications (1) Resonant peak (2) Band width (3) Resonant frequency. Also write the equation of each.

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2. Explain the terms Gain Margin and Phase Margin related to Frequency response analysis of Control Systems.

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3. Briefly discuss performance specifications of frequency response analysis for linear controls systems.

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4. Discuss about gain margin and phase margin for frequency response of control system. 4

5. What do you mean by Frequency Response analysis? What are the methods used response analysis.

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6. Define the following terms: (1) Resonant peak (2) Gain Margin 3

7. Find the frequency domain specifications with a unity feedback having,

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8. State advantages and limitations of Frequency Response Analysis. 4



Ch. 5 Stability

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1. (1) Enlist limitations of Routh’s stability criterion. (2) Consider following characteristic equation. Using Routh’s stability criterion, determine the range of K for stability. S4 + 2S3 + (4+K)S2 + 9S + 25 = 0

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2. Enlist steps for plotting root locus. 7

3.

Assuming gain K to be positive, plot root loci for the system shown in Figure. Is system stable?

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4.

Determine the stability of a system whose overall transfer function is given below. If the system is found unstable, how many roots it has with positive real part ?

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5. Discuss stepwise procedure of plotting the root-locus for a given open-loop transfer function.

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6. A close loop system is characterized by the following transfer function, s4+5s3+5s2+4s+K=0. Determine the range of K for which the system is stable.

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7. Draw root locus diagram for the system with transfer function. 7



8. Using Routh criterion, discuss about the stability for the system having characteristics equation is given as 3s7 + 9s6 + 6s5 + 4s4 + 7s3 + 8s2 + 2s + 6 = 0.

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9. Check stability of the system whose characteristics equation is given as by s3+8s2+14s+24=0 using Hurwitz criterion.

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10. Draw the Root Locus diagram of a system with transfer function is

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11.

For Unity feedback control system has given G(s). Sketch the root locus. Also determine the value of K so that the damping ration ζ, of a pair of complex conjugate closed loop pole is 0.5.

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12.

Unity feedback control system has given G(S). Find the range of K for the stability of the system Using stability criterion.

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13. Enlist limitations of Routh’s stability criterion. 3

14. Using R-H criterion determine the stability of the system whose characteristic equation is given by : s5+1.5s4+2s3+4s2+5s+10=0.

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15.

Draw root locus diagram for the system with transfer function, Obtain value of k when ζ =0.6 from root locus. Determine the value of k for stability and critical damping.

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16. State ‘Angle condition’ and ‘Magnitude condition’ of root locus method. 3

17. Determine the stability of the system represented by the characteristic equation by means of the R-H Criterion. Also find root lying in right half of s-plane.: s6+3s5+5s4+9s3+8s2+6s+4=0.

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18.

The open loop transfer function of unity feedback control system is given as below. Draw the root locus. Determine the value of k for which the system becomes critically damped and also the value of k for which the system become unstable.

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Ch. 6 Hydraulic Control System

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1. Compare the hydraulic system with the pneumatic system. 3

2. Explain working principle of a dashpot system (hydraulic damper). 4

3. Draw a neat sketch of a hydraulic servomotor and prove that it acts as an integral controller. 7

4. Explain the schematics to achieve Hydraulic Proportional-Plus-Derivative Control action with a neat sketch in brief. Draw block diagram and obtain transfer function for the same.

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5. Draw a neat sketch of generalized hydraulic control system. Explain the elements of hydraulic control system in brief.

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6. In a 4/3 Direction control valve 4 stands for_____ and 3 stands for___? 1

7. List the basic elements of a Hydraulic circuit. Explain any one in brief. 3

8. Explain Hydraulic Integral Control and derive its transfer function. 4

9. Draw the schematic diagram of Hydraulic PID controller. Explain its working and derive its transfer function.

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10. Draw the block diagram of PID controller. 1

11. Give names of any TWO basic elements of hydraulic system. 1

12. What is the function of Pressure Relief Valve? 1

13. With the help of neat diagrams, explain how the direction control valves are classified. 4

14. Explain PI controller and its effect on the system performance. 3

15. Enlist basic elements of Hydraulic circuit and Pneumatic circuit. 4



16. Write comparison between (1) Hydraulic and Electrical control system (2) Pneumatic and Hydraulic control system

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17. Explain Hydraulic PID controller with neat sketch. 4

18. Compare hydraulic control system with pneumatic control system in detail. 3

19. Draw the schematic diagram of Hydraulic PID controller. Explain its working and derive its transfer function.

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Ch. 7 Pneumatic Control System

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1. With the help of a neat sketch, explain how proportional control is achieved in a force-balance type pneumatic controller. Derive the expression for gain for the same.

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2. Draw a neat sketch of a pneumatic PID controller, its block diagram and state the transfer function for the same.

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3. Explain Force-Distance type Pneumatic Proportional controller and derive transfer function for it.

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4. Explain working of schematics to achieve Pneumatic PID controller in brief with a neat sketch. Draw block diagram and obtain transfer function for the same.

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5. What does FRL stands for in a Pneumatic system. 1

6. Draw the schematic diagram of Pneumatic PI controller. Explain its working and derive its transfer function.

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7. Write the comparison between a Pneumatic system and Hydraulic system. 3

8. With the help of necessary diagram, explain Pneumatic nozzle- flapper amplifier. 4

9. Draw the symbol of Variable Throttle Valve. 1

10. List out the basic elements of a Pneumatic system. 3

11. Describe with neat sketch of a pneumatic proportional controller. 4

12. Explain Pneumatic PID controller with a schematic diagram. 4

13. Write short note on pneumatic nozzle-flapper amplifier with diagram. 3

14. With the help of necessary diagram, explain Pneumatic nozzle flapper amplifier. 4

15. Draw the schematic diagram of Pneumatic PI controller. Explain its working and derive its 7



transfer function.

Ch. 8 State space analysis

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1. Obtain a state-space representation of the mechanical system shown in Figure 4. Consider u1 and u2 as inputs and y1 and y2 as outputs.

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2. Explain the concept of state used in modern control theory and briefly explain the state

space representation of Mechanical system. 7

3. Discuss the advantages of State Space analysis over Classical Technique used for control

systems analysis. Also explain the state space representation of second order differential

equation.

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4. State the advantages of state-space representation over conventional control system

analysis method. 3

5. Explain the following terms: (i) State (ii) State variables (iii) State-space (iv) state

transition matrix. 4

6. Obtain the state space representation of system as shown in figure 5 7



7. For an RLC circuit, Derive the state model. 7

8. State the advantages of State-space Analysis over conventional control system analysis

methods. 3

9. For series R-L-C circuit, obtain the state-space model.

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10. State the advantages of state-space approach for analysis and design of Control systems. 3

11.

Define State vector in the context of state-space approach. Obtain state model for the transfer

function:

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12. State the advantages of state-space representation over conventional control system analysis

method. 3

13. Explain the following terms: (i) State (ii) State variables (iii) State-space (iv) state transition

matrix 4

Documents

GTU Paper Analysis (New Syllabus) · GTU Paper Analysis (New Syllabus) Control Engineering (2151908) Department of Mechanical Engineering Darshan Institute of Engineering & Technology