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    Experiment 5 AIM:Write A Program To Design Proportional, Proportional+Integral, Proportional+

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    saumya desai

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    Experiment 5 AIM:Write A Program To Design Proportional, Proportional+Integral, Proportional+

    Uploaded by

    saumya desai
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    Experiment 5 Template

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    24 views4 pages

    Experiment 5 AIM:Write A Program To Design Proportional, Proportional+Integral, Proportional+

    Uploaded by

    saumya desai

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 4

    EXPERIMENT 5

    AIM:Write a program to design Proportional, Proportional+Integral, Proportional+


    Derivative and P-I-D Controller for second order system.

    SOFTWARE: MATLAB

    PROCEDURE:

    1. Enter the Command window of the MATLAB.


    2. Create a new file by selecting file new m-file.
    3. Type and save the program.
    4. Execute the program by selecting Save and Run.
    5. View the result

    THEORY:

    The transfer function of the PID controller looks like the following:
    𝐾𝑖 𝐾𝐷 𝑠 2 + 𝐾𝑝 𝑠 + 𝐾𝑖
    𝐾𝑝 + + 𝐾𝐷 𝑠 =
    𝑠 𝑠
    𝐾𝑝 = Proportional gain
    𝐾𝑖 = Integral gain
    𝐾𝐷 = Derivative gain
    A proportional controller (Kp) will have the effect of reducing the rise time and will reduce
    ,but never eliminate, the steady-state error. An integral control (Ki) will have the effect of
    eliminating the steady-state error, but it may make the transient response worse. A
    derivative control (Kd) will have the effect of increasing the stability of the system,
    reducing the overshoot, and improving the transient response. Effects of each of controllers
    Kp, Kd, and Ki on a closed-loop system are summarized in the table shown below.

    Note that these correlations may not be exactly accurate, because Kp, Ki, and Kd are
    dependent of each other. In fact, changing one of these variables can change the effect of
    the other two. For this reason, the table should only be used as a reference when you are
    determining the values for Ki, Kp and Kd.
    1
    PROBLEM STATEMENT:

    Design the Proportional, Proportional+ Integral, Proportional+ Derivative and P-I-D


    1
    Controller for 𝐺(𝑠) = 𝑠2 +10𝑠+20 and H(s)=1.

    SOLUTION:
    1. Proportional Controller:

    With 𝑲𝒑 =300, the closed loop transfer is,

    𝐶(𝑠) 𝐾𝑝
    = 2
    𝑅(𝑠) 𝑠 + 10𝑠 + (20 + 𝐾𝑝 )

    𝐶(𝑠) 300
    = 2
    𝑅(𝑠) 𝑠 + 10𝑠 + 320

    2. Proportional+ Derivative Controller:


    Now, let's take a look at a PD control. From the table shown above, the derivative
    controller (Kd) reduces both the overshoot and the settling time.

    The closed-loop transfer function of the given system with a PD controller is,

    𝐶(𝑠) (𝐾𝑝 + 𝑠𝐾𝐷 )


    = 2
    𝑅(𝑠) 𝑠 + (10 + 𝐾𝐷 )𝑠 + (20 + 𝐾𝑝 )
    With 𝑲𝒑 =300 and 𝑲𝑫 =10,
    𝐶(𝑠) (300 + 10𝑠)
    = 2
    𝑅(𝑠) 𝑠 + 20𝑠 + 320
    2
    3. Proportional+ Integral Controller:
    From the table, we see that an integral controller (Ki) decreases the rise time, increases
    both the overshoot and the settling time, and eliminates the steady-state error. For the
    given system, the closed-loop transfer function with a PI control is:

    With 𝑲𝒑 =30 and 𝑲𝑰 =70,


    𝐶(𝑠) (𝐾𝑝 + 𝐾𝐼 /𝑠)
    = 3
    𝑅(𝑠) 𝑠 + 10𝑠 2 + (20 + 𝐾𝑝 )𝑠 + 𝐾𝐼

    𝐶(𝑠) (𝑠𝐾𝑝 + 𝐾𝐼 )
    = 3
    𝑅(𝑠) 𝑠 + 10𝑠 2 + (20 + 𝐾𝑝 )𝑠 + 𝐾𝐼

    𝐶(𝑠) (30𝑠 + 70)


    = 3
    𝑅(𝑠) 𝑠 + 10𝑠 2 + 50𝑠 + 70

    4. Proportional+ Integral +Derivative Controller:

    The closed-loop transfer function of the given system with a PID controller is,

    𝐶(𝑠) (𝐾𝐷 𝑠 2 + 𝐾𝑝 s + 𝐾𝐼 )
    =
    𝑅(𝑠) 𝑠 3 + (10+𝐾𝐷 )𝑠 2 + (20 + 𝐾𝑝 )𝑠 + 𝐾𝐼

    3
    With 𝐾𝑝 =350, 𝐾𝑑 =50 and 𝐾𝐼 =300,
    𝐶(𝑠) (50𝑠 2 + 350s + 300)
    = 3
    𝑅(𝑠) 𝑠 + 60𝑠 2 + 370𝑠 + 300

    CONCLUSION:
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