### EE 2365 CONTROL ENGINEERING Questions 2014

Anna University, Chennai

SRINIVASAN ENGINEERING COLLEGE, PERAMBALUR DEPT OF AERO

QUESTION BANK

SUBJECT CODE: EE 2365

SEM / YEAR: V/III

SUBJECT NAME: CONTROL ENGINEERING

PART – B (16 Marks)

1) With examples explain the concept of open loop and closed loop systems. Compare.(16)

2) Compare hydraulic systems with thermal systems. (16)

3) Compare electrical systems with mechanical systems (analogous). (16)

4) Compare open loop and closed loop systems. (16)

5) With a block diagram explain the concept of flight control systems. (16)

6) Write the differential equations governing the Mechanical system shown in fig .and determine the transfer function. (16)

7) Determine the transfer function Y2(S)/F(S) of the system shown in fig. (16)

8) Write the differential equations governing the Mechanical rotational system shown in fig.

Draw the Torque-voltage and Torque-current electrical analogous circuits. (16)

Note: Diagrams in these above referred problems are given separately. Only the type of the questions expected/asked in the previous year university end semester examinations are referred here

UNIT II

PART – B (16 Marks)

1. Determine the overall transfer function C(S)/R(S) for the system shown in fig. (16)

2. Obtain the closed loop transfer function C(S)/R(S) of the system whose block diagram is

shown in fig. (16)

3. For the system represented by the block diagram shown in fig. Determine C1/R1and C2/R1. (16)

4. Obtain the closed loop transfer function C(S)/R(S) of the system whose block diagram is

shown in fig. (16)

5. Find the overall gain of the system whose signal flow graph is shown in fig. (16)

6. Draw a signal flow graph and evaluate the closed loop transfer function of a system whose

block is shown in fig. (16)

Note: Diagrams in these above referred problems are given separately. Only the type of the questions expected/asked in the previous year university end semester examinations are referred here.

UNIT III

CHARACTERISTIC EQUATIONS AND FUNCTIONS PART – A (2 Marks)

1. What is time response?

It is the output of the closed loop system as a function of time. It is denoted by c(t).It is given by inverse of Laplace of product of input and transfer function of the system.

 L
 L
C (t) = -1

{(C(s)} = -1

{(R(s) G(s))/ (1+G(s) H(s))}

2. 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 at t=∞ is called steady state response

3. Name the test signals used in time response analysis.

Step signal, ramp signal, parabolic signal sinusoidal signal and impulse signal

4. Define step signal.

The step signal is a signal whose value changes from 0 to A and remains constant at A for t>0 The mathematical representation of step signal is r(t) = A u(t), where u(t) = 1 fort≥0 and u(t) =0 for t<0.

5. Define Ramp signal and parabolic 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 as r (t) = A t, where fort≥0 and r (t) =0 for t<0.

A parabolic signal is a signal in which the instantaneous value varies as square of the time from an initial value of zero at t=0.It is

2

mathematically represented as r (t) = A.t /2 for fort≥0 and r (t) =0 for t<0.

6. What is an impulse signal?

A signal which is available for very short duration is called impulse signal. Ideal impulse signal is a unit impulse signal which is defined as a signal having zero values at all-time except at t=0. At t=0, the magnitude becomes infinite.

7. How is system classified depending on the value of damping(ε)?

Undamped system (ε=0), under damped system (ε<1), critically damped system (ε=1) and over damped system (ε>1)

8. What is damped frequency of oscillation?

2

In under damped system, the response is damped oscillatory. The frequency of damed oscillation is given by wd=wn Sqrt of (1-ε ).

9. The closed-loop transfer function of second order system is C(S)/R(S) =10/ S2

+6S +10. What is the type of damping? Since ε<1, the system is under damped.

10. List the time domain specifications.

Delay time, rise time, peak time, and maximum over shoot and settling time.

11. Define rise time.

Rise time is the time taken for response tom raise from 0% to 100% for the very first time.

12. Define delay time..

Delay time is the time taken for response to reach 50% of the final value, for the very first time.

13. Define peak time.

It is the time taken for the response to reach the peak value for the very first time. It is the time taken for the response to reach the peak overshoot, Mp

14. What is steady state error?

The steady state error is the value of the error signal e (t), when (t) tends to infinity.

15. What are static error constants?

The Kp, Kv and Ka are called static error constants. The se constants are associated with steady state error in a particular type of a system and for a particular input.

16. What are generalized error constants?

They are the coefficients of generalized error series. They are also called as dynamic error coefficients.

17. List the advantages of generalized error constants.

Generalized error series gives error signal as a function of time. Using generalized error constants, the steady state error can be determined for any type of input. But static error constants are used to determine steady state error when the input is any one of the standard input.

PART B (16 Marks)

1. (a) Derive the expressions and draw the response of first order system for unit step input. (8) (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, and Peak overshoot. (16) 3. A potential control system with velocity feedback is shown in fig. What is the Response of the system for unit step input? (16) 4. 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. (16)

5. 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. (16)

6. A unity feedback control system has an open loop transfer function

G(S) = 10/S(S+2). Find the rise time, percentage over shoot, peak time and settling time. ( 16) 7. A closed loop servo is represented by the differential equation, where c is the

Displacement of the output shaft, r is the displacement of the input shaft and ( e= r-c) Determine undammed natural frequency, damping ratio and percentage maximum overshoot for unit step input. (16)

8. For a unity feedback control system the open loop transfer function

2

G(S) = 10(S+2)/ {S

(S+1)}. Find (a) position, velocity and acceleration error constants.

 S
 S
(b) The steady state error when the input is R(S) where R(S) =3/S –2/ 2

+1/3 3

(16)

9. 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 by the polynomial

2

r(t) = a0 +a1t +a2 /2 t

. (16)

PART – B (16 Marks)

1. Plot the Bode diagram for the following transfer function and obtain the gain and phase cross

over frequencies. G(S) = 10/ S(1+0.4S) (1+0.1S) (16)

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

G(S) = 1/ S(1+S)(1+2S) Sketch the Bode plot and determine the Gain margin and Phase margin. (16)

3. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency,

Gain margin and Phase margin(S) = 0.75(1+0.2S)/ S (1+0.5S) (1+0.1S) (16)

4. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency,

Gain margin and Phase margin. G(S) = 10(S+3)/ S(S+2) (S2+4S+100) (16)

5. Sketch the Bode plot for the following transfer function .and find Gain cross over frequency,

Phase cross over frequency, Gain margin and Phase margin.

G(S) = 10(S+2)(S+4)/ S (S2 -3S+10) (16)

6. Construct the Bode plot for the function GH(S) =2(S+1)/ S2. Find Gain cross over frequency,

Phase cross over frequency, Gain margin and Phase margin. (16)

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 Bode plot and hence find Gain cross over frequency, Phase cross over frequency,

Gain margin and Phase margin. G(S) = 10(1+0.1S)/ S(1+0.01S) (1+S). (16)

9. Write the short notes on correlation between the time and frequency response? (16)

10. Using Routh criterion, determine the stability of the system whose Characteristics equation

4 3 2 1

is S

+8S +18S

+16 +5 =0. (16)

11. F(S)=S6 +S5-2S4-3S3-7S2-4S1-4 =0.Find the number of roots falling in the RHS plane and LHS

plane. (16)

UNIT V

SAMPLED DATA SYSTEMS PART – A (2 Marks)

1. What is sampled data control system?

When the input or information at any or some points in a system is in the form of discrete pulses, then the system is called discrete data system or sampled data control system.

1) Systems are highly accurate, fast and flexible.

2) Use of time sharing concept in digital computers results in economic cost and space.

3) Digital transducers used in the system have better resolution.

4) The digital controllers are less affected by noise, non-linearity and transmission error of noisy channel.

3. State (Shanon’s) sampling theorem.

It states that a band limited continuous- time signal with highest frequency fm hertz, can be uniquely recovered from its samples provided that the sampling rate Fs is greater than or equal to (2fm) samples per second.

4. What is periodic sampling?

It is a sampling process in which the discrete- time signal or sequence is obtained by taking samples of continuous time signal periodically or uniformly at intervals of T seconds. Here T is called sampling period and (1/T) is called sampling frequency.

5. What are hold circuits?

Hold circuits are devices used to convert discrete time signals to continuous time signals.

6. What are the problems encountered in a practical hold circuits?

1) Errors in periodicity of sampling process.

2) Nonlinear variations in the duration of sampling aperture.

3) Droop (Changes) in the voltage held during conversions.

7. What are the methods available for the stability analysis of sampled data control system?

1) Jury’s stability test.

2) Bilinear transformation

3) Root locus technique.

8. What are the advantages of state space analysis?

1) It is applicable to any type of systems (linear/nonlinear/time variant/time invariant and multiple input & multiple output systems)

2) It can be performed with initial conditions.

3) The variables used to represent the system can be any variable in the system.

4) Using this analysis, the internal states of the system at any time instant can be predicted.

9. What is state and what are state variables?

The state is the condition of a system at any time instant (t). A set of variable which describes the state of the system at any time instant are called as state variables.

10. What is state diagram?

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

 PART B (16 Marks) 1. Compare analog control system with digital control systems. (16) 2. Explain sampling theorem briefly and sample & hold operation. (16) 3. Explain stability analysis of sampled control system and Jury’s stability. (16) 4. Explain Digital controllers with a neat block diagram . (16 5. Explain with a neat diagram digital PUID controllers. (16)

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