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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?

4

GTU Paper Analysis (New Syllabus)

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

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

GTU Paper Analysis (New Syllabus)

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

2.

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

7

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.

7

GTU Paper Analysis (New Syllabus)

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

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.

7

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

GTU Paper Analysis (New Syllabus)

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

block diagram reduction.

7.

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

GTU Paper Analysis (New Syllabus)

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

8.

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

4

9.

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

7

GTU Paper Analysis (New Syllabus)

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

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.

7

GTU Paper Analysis (New Syllabus)

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

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.

GTU Paper Analysis (New Syllabus)

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

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

7

GTU Paper Analysis (New Syllabus)

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

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.

7

GTU Paper Analysis (New Syllabus)

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

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.

7

GTU Paper Analysis (New Syllabus)

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

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

GTU Paper Analysis (New Syllabus)

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

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.

7

GTU Paper Analysis (New Syllabus)

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

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.

7

GTU Paper Analysis (New Syllabus)

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

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

GTU Paper Analysis (New Syllabus)

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

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

GTU Paper Analysis (New Syllabus)

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

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.

4

GTU Paper Analysis (New Syllabus)

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

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.

7

GTU Paper Analysis (New Syllabus)

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

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

GTU Paper Analysis (New Syllabus)

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

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.

7

GTU Paper Analysis (New Syllabus)

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

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

GTU Paper Analysis (New Syllabus)

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

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

GTU Paper Analysis (New Syllabus)

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

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