JUNE 2014 Solved Question Paper - Navodaya Institute of ... ?· JUNE 2014 Solved Question Paper ...…

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  • JUNE 2014 Solved Question Paper

    1 a: Explain with examples open loop and closed loop control systems. List merits and demerits

    of both. Jun. 2014, 10 Marks

    Open & Closed Loop System - Advantages & Disadvantages [Control System].

    In control systems engineering, a system is actually a group of objects or elements capable of

    performing individual tasks. They are connected in a specific sequence to perform a specific

    function.

    A system is of 2 types:

    1. Open loop system which is also called as Manual control system.

    2. Closed loop system which is also named as automatic control system.

    In this post, we will be discussing various advantages and disadvantages of the 2 types of control

    systems.

    Open Loop System:

    Advantages: 1. Simplicity and stability: they are simpler in their layout and hence areeconomical and stable too due to their simplicity.

    2. Construction: Since these are having a simple layout so are easier to construct.

    Disadvantages: 1. Accuracy and Reliability: since these systems do not have a feedback mechanism, so they are very inaccurate in terms of result output and hence they are

    unreliable too.

    2. Due to the absence of a feedback mechanism, they are unable to remove the disturbances occurring from external sources.

    Closed Loop System:

    Advantages: 1. Accuracy: They are more accurate than open loop system due to their complex construction. They are equally accurate and are not disturbed in the presence of non-

    linearities.

    2. Noise reduction ability: Since they are composed of a feedback mechanism, so they clear out the errors between input and output signals, and hence remain unaffected to

    the external noise sources.

    Disadvantages: 1. Construction: They are relatively more complex in construction and hence it adds up to the cost making it costlier than open loop system.

  • 2. Since it consists of feedback loop, it may create oscillatory response of the system and it also reduces the overall gain of the system.

    3. Stability: It is less stable than open loop system but this disadvantage can be striked off since we can make the sensitivity of the system very small so as to make the

    system as stable as possible.

    Open Loop Control System

    A control system in which the control action is totally independent of output of the system then it

    is called open loop control system. Manual control system is also an open loop control system.

    Fig - 1 shows the block diagram of open loop control system in which process output is totally

    independent of controller action.

    Open-loop Motor Control

    So for example, assume the DC motor controller as shown. The speed of rotation of the motor

    will depend upon the voltage supplied to the amplifier (the controller) by the potentiometer. The

    value of the input voltage could be proportional to the position of the potentiometer.

    If the potentiometer is moved to the top of the resistance the maximum positive voltage will be

    supplied to the amplifier representing full speed. Likewise, if the potentiometer wiper is moved

    to the bottom of the resistance, zero voltage will be supplied representing a very slow speed or

    stop.

    Then the position of the potentiometers slider represents the input, i which is amplified by the

    amplifier (controller) to drive the DC motor (process) at a set speed N representing the

    output,o of the system. The motor will continue to rotate at a fixed speed determined by the

    position of the potentiometer.

    As the signal path from the input to the output is a direct path not forming part of any loop, the

    overall gain of the system will the cascaded values of the individual gains from the

    potentiometer, amplifier, motor and load. It is clearly desirable that the output speed of the motor

  • should be identical to the position of the potentiometer, giving the overall gain of the system as

    unity.

    However, the individual gains of the potentiometer, amplifier and motor may vary over time with

    changes in supply voltage or temperature, or the motors load may increase representing external

    disturbances to the open-loop motor control system.

    But the user will eventually become aware of the change in the systems performance (change in

    motor speed) and may correct it by increasing or decreasing the potentiometers input signal

    accordingly to maintain the original or desired speed.

    The advantages of this type of open-loop motor control is that it is potentially cheap and

    simple to implement making it ideal for use in well-defined systems were the relationship

    between input and output is direct and not influenced by any outside disturbances. Unfortunately

    this type of open-loop system is inadequate as variations or disturbances in the system affect the

    speed of the motor. Then another form of control is required.

    Practical Examples of Open Loop Control System

    1. Electric Hand Drier Hot air (output) comes out as long as you keep your hand under the

    machine, irrespective of how much your hand is dried.

    2. Automatic Washing Machine This machine runs according to the pre-set time

    irrespective of washing is completed or not.

    3. Bread Toaster - This machine runs as per adjusted time irrespective of toasting is

    completed or not.

    4. Automatic Tea/Coffee Maker These machines also function for pre adjusted time only.

    5. Timer Based Clothes Drier This machine dries wet clothes for pre adjusted time, it

    does not matter how much the clothes are dried.

    6. Light Switch lamps glow whenever light switch is on irrespective of light is required or

    not.

    7. Volume on Stereo System Volume is adjusted manually irrespective of output volume

    level.

    Closed Loop Control System

    Control system in which the output has an effect on the input quantity in such a manner that the

    input quantity will adjust itself based on the output generated is called closed loop control

    system. Open loop control system can be converted in to closed loop control system by

    providing a feedback. This feedback automatically makes the suitable changes in the output due

    to external disturbance. In this way closed loop control system is called automatic control

    system. Figure below shows the block diagram of closed loop control system in which feedback

  • is taken from output and fed in to input.

    Closed-loop Motor Control

    Any external disturbances to the closed-loop motor control system such as the motors load

    increasing would create a difference in the actual motor speed and the potentiometer input set

    point.

    This difference would produce an error signal which the controller would automatically respond

    too adjusting the motors speed. Then the controller works to minimize the error signal, with zero

    error indicating actual speed which equals set point.

    Electronically, we could implement such a simple closed-loop tachometer-feedback motor

    control circuit using an operational amplifier (op-amp) for the controller as shown.

    Closed-loop Motor Controller Circuit

  • Practical Examples of Closed Loop Control System

    1. Automatic Electric Iron Heating elements are controlled by output temperature of the

    iron.

    2. Servo Voltage Stabilizer Voltage controller operates depending upon output voltage of

    the system.

    3. Water Level Controller Input water is controlled by water level of the reservoir.

    4. Missile Launched & Auto Tracked by Radar The direction of missile is controlled by

    comparing the target and position of the missile.

    5. An Air Conditioner An air conditioner functions depending upon the temperature of the

    room.

    6. Cooling System in Car It operates depending upon the temperature which it controls.

    Comparison of Closed Loop And Open Loop Control System

    Sr. No. Open loop control system Closed loop control system

    1 The feedback element is absent. The feedback element is always present.

    2 An error detector is not present. An error detector is always present.

    3 It is stable one. It may become unstable.

    4 Easy to construct. Complicated construction.

    5 It is an economical. It is costly.

    6 Having small bandwidth. Having large bandwidth.

    7 It is inaccurate. It is accurate.

    http://www.electrical4u.com/voltage-or-electric-potential-difference/

  • 8 Less maintenance. More maintenance.

    9 It is unreliable. It is reliable.

    10 Examples: Hand drier, tea maker Examples: Servo voltage stabilizer,

    perspiration

    1 b: Draw the electrical network based on torque-current analogy give all the perfor-mance

    equations for Figure. 1 Jul. 2014, 10 Marks

    T 1 k1

    2 k2

    J1 J2

    f1 f2

    Figure 1:

  • 3 a: Draw the transient response characteristics of a control system to a unit step input

    and define the following: i) Delay time; ii) Rise time; iii) Peak time;

    iv)Maximum overshoot; v) Settling time 5 Marks

  • 3 b: Derive the expressions for peak time tp for a second order system for step input. 5 Marks

    Jun. 2014, 4 Marks

  • 3 c: The response of a servo mechanism is c(t) = 1 + 0.2e 60t

    +1.2e 10t

    when subjected

    to a unit step input. Obtain an expression for closed loop transfer function. Determine

    the undamped natural frequency and damping ratio. 6Marks Jun. 2014, 4 Marks

  • 3 d: The open loop transfer function of a unity feedback system is given by G(s) =K/S(ST+1)

    K

    ,

    s(Ts + 1)

    where K and T are positive constant. By what factor should the amplifier, gain K be re-

    duced so that the peak overshoot of unit step response of the system is reduced from 75%

    to 25%. 4 Marks Jun. 2014, 6 Marks

  • 4 a: Explain Routh-Hurwitz criterion in stability of a control system. What are the disad-

    vantages of RH criterion on stability of control system? Jun. 2014, 4+4 Marks

  • 4 b: The characteristics equation for certain feedback control system is given below. Deter-mine

    the system is stable or not and find the value of K for a stable system

    s3 + 3Ks

    2 + (K + 2)s + 4 = 0. Jun. 2014, 6 Marks

  • 4 c: The open-loop TF of a unity negative feedback system is given by

    G(s) =

    K(s + 3)

    s(s2 + 2s + 3)(s + 5)(s + 6)

    Find the value of K of which the closed loop system is stable. Jun. 2014, 6 Marks

  • 5 a: For a unity feedback system, the open-loop transfer function is given by

    K

    G(s) =

    . Jun. 2014, 15 Marks

    s(s + 2)(s2 + 6s + 25)

    (i) Sketch the root locus for K .

    (ii) At what value of K the system becomes unstable.

    (iii) At this point of instability, determine the frequency of oscillation of the system.

  • 5 b: Consider the system with G(s)H(s) =

    K

    using angle condition find

    s(s + 2)(s + 4)

    whether s = 0.75 and s = 1 + j4 are on the root locus or not. Jun. 2014, 5 Marks

  • (or)

  • s = 0.75 and s = 1 + j4 are not on the root locus.

    6 a: Explain the procedure for investigating the stability using Nyquist criterion. Jun. 2014, 8 Marks, 6 Marks

    Nyquist Stability Criterion The Nyquist plot allows us also to predict the stability and performance of a closed-loop system

    by observing its open-loop behavior. The Nyquist criterion can be used for design purposes

    regardless of open-loop stability (remember that the Bode design methods assume that the

  • system is stable in open loop). Therefore, we use this criterion to determine closed-loop

    stability when the Bode plots display confusing information.

    The Nyquist diagram is basically a plot of G(j* w) where G(s) is the open-loop transfer function

    and w is a vector of frequencies which encloses the entire right-half plane. In drawing the

    Nyquist diagram, both positive and negative frequencies (from zero to infinity) are taken into

    account. We will represent positive frequencies in red and negative frequencies in green. The

    frequency vector used in plotting the Nyquist diagram usually looks like this (if you can imagine

    the plot stretching out to infinity):

    However, if we have open-loop

    poles or zeros on the jw axis, G(s)

    will not be defined at those points,

    and we must loop around them

    when we are plotting the contour.

    Such a contour would look as

    follows:

    Please note that the contour loops

    around the pole on the jw axis. As

    we mentioned before, the Matlab

    nyquist command does not take

    poles or zeros on the jw axis into

    account and therefore produces an

    incorrect plot.

    The Cauchy criterion

    The Cauchy criterion (from complex analysis) states that when taking a closed contour in the

    complex plane, and mapping it through a complex function G(s), the number of times that the

    plot of G(s) encircles the origin is equal to the number of zeros of G(s) enclosed by the frequency

  • contour minus the number of poles of G(s) enclosed by the frequency contour. Encirclements of

    the origin are counted as positive if they are in the same direction as the original closed contour

    or negative if they are in the opposite direction.

    When studying feedback controls, we are not as interested in G(s) as in the closed-loop transfer

    function:

    G(s)

    ---------

    1 + G(s)

    If 1+ G(s) encircles the origin, then G(s) will enclose the point -1.

    Since we are interested in the closed-loop stability, we want to know if there are any closed-loop

    poles (zeros of 1 + G(s)) in the right-half plane.

    Therefore, the behavior of the Nyquist diagram around the -1 point in the real axis is very

    important; however, the axis on the standard nyquist diagram might make it hard to see what's

    happening around this point

    To view a simple Nyquist plot using Matlab, we will define the following transfer function and

    view the Nyquist plot:

    0.5

    -------

    s - 0.5

    Closed Loop Stability

    Consider the negative feedback system

  • Remember from the Cauchy criterion that the number N of times that the plot of G(s)H(s)

    encircles -1 is equal to the number Z of zeros of 1 + G(s)H(s) enclosed by the frequency contour

    minus the number P of poles of 1 + G(s)H(s) enclosed by the frequency contour (N = Z - P).

    Keeping careful track of open- and closed-loop transfer functions, as well as numerators and

    denominators, you should convince yourself that:

    the zeros of 1 + G(s)H(s) are the poles of the closed-loop transfer function

    the poles of 1 + G(s)H(s) are the poles of the open-loop transfer function. The Nyquist criterion then states that:

    P = the number of open-loop (unstable) poles of G(s)H(s)

    N = the number of times the Nyquist diagram encircles -1

    clockwise encirclements of -1 count as positive encirclements

    counter-clockwise (or anti-clockwise) encirclements of -1 count as negative encirclements

    Z = the number of right half-plane (positive, real) poles of the closed-loop system The important equation which relates these three quantities is:

    Z = P + N

    Note: This is only one convention for the Nyquist criterion. Another convention states

    that a positive N counts the counter-clockwise or anti-clockwise encirclements of -1. The

    P and Z variables remain the same. In this case the equation b...