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    Root Locus

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    eeetist
    The document describes an experiment to analyze the stability of a system using root locus analysis. It involves: 1) Plotting the root locus of a transfer function and verifying the critical gain matches theoretical values. 2) Analyzing how the stability is affected by increasing the controller gain K. 3) Conducting sensitivity analysis by introducing small changes to poles and zeros. 4) Examining how adding poles and zeros impacts the system stability based on how they shift the root locus. The root locus is plotted in MATLAB for various controller gains to analyze the stability as gain increases. Sensitivity is analyzed using sisotool.

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    Root Locus

    Uploaded by

    eeetist
    95 views10 pages
    The document describes an experiment to analyze the stability of a system using root locus analysis. It involves: 1) Plotting the root locus of a transfer function and verifying the critical gain matches theoretical values. 2) Analyzing how the stability is affected by increasing the controller gain K. 3) Conducting sensitivity analysis by introducing small changes to poles and zeros. 4) Examining how adding poles and zeros impacts the system stability based on how they shift the root locus. The root locus is plotted in MATLAB for various controller gains to analyze the stability as gain increases. Sensitivity is analyzed using sisotool.

    Original Title

    ROOT LOCUS (1)

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    The document describes an experiment to analyze the stability of a system using root locus analysis. It involves: 1) Plotting the root locus of a transfer function and verifying the critical gain matches theoretical values. 2) Analyzing how the stability is affected by increasing the controller gain K. 3) Conducting sensitivity analysis by introducing small changes to poles and zeros. 4) Examining how adding poles and zeros impacts the system stability based on how they shift the root locus. The root locus is plotted in MATLAB for various controller gains to analyze the stability as gain increases. Sensitivity is analyzed using sisotool.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    95 views10 pages

    Root Locus

    Uploaded by

    eeetist
    The document describes an experiment to analyze the stability of a system using root locus analysis. It involves: 1) Plotting the root locus of a transfer function and verifying the critical gain matches theoretical values. 2) Analyzing how the stability is affected by increasing the controller gain K. 3) Conducting sensitivity analysis by introducing small changes to poles and zeros. 4) Examining how adding poles and zeros impacts the system stability based on how they shift the root locus. The root locus is plotted in MATLAB for various controller gains to analyze the stability as gain increases. Sensitivity is analyzed using sisotool.

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    EXPERIMENT NO:9

    PERFORMANCE ANALYSIS USING ROOT-LOCUS METHOD.

    AIM

    Plot the root locus of the given transfer function to analyse the following using simulation:

    A. Verification of the critical gain with the theoretical values.


    B. The effect of controller gain K on the stability.
    C. The sensitivity analysis by giving small perturbations in given poles and zeros
    D. The effect of the addition of poles and zeros on the given system.

    THEORY
    Root-locus defines as a graph of the poles of the closed-loop transfer function as the system
    parameter, such as the gain is varied The root locus of an (open-loop) transfer function is a
    plot of the locations (locus) of all possible closed-loop poles with some parameter, often a
    proportional gain , varied between 0 and . The figure below shows a unity-feedback
    architecture

    G(s)

    The closed-loop transfer function in this case is:

    and thus the poles of the closed-loop system are values of such that 1+K G(s)=0.
    PLOTTING THE ROOT LOCUS OF A TRANSFER FUNCTION
    Aim 1.
    Verification of the critical gain, wo with the theoretical values
    AIM : 2
    The effect of controller gain K on the stability.

    K=1
    STABLE SYSTEM K=10
    FREQ -2.83 rad/sec STABLE SYSTEM
    FREQ -2.83 rad/sec
    K=48
    Marginally STABLE
    K=40 SYSTEM
    STABLE SYSTEM

    K=60
    unSTABLE SYSTEM

    Value of k poles Damping overshoot frequency stability


    ratio

    Aim 3- The sensitivity analysis by giving small perturbations in given


    poles and zeros
    poles TF RiseTime SettlingTime Oversho PeakTi
    ot me
    Aim 4
    The effect of the addition of poles and zeros on the given system.

    Effect of addition of poles =>

    i) Root locus shift towards right half of the s-plane

    ii) system stability relatively decreases

    Effect of addition of zeros =>

    i) Root locus shift towards left half of the s-plane

    ii) system stability relatively increases


    PROGRAM

    clc
    s=tf('s')
    gh=1/((s)*(s+2)*(s+4))
    k=1
    t=gh*k
    den=[1 6 8 0]
    poles=roots(den)
    pzmap(t)
    m=feedback(gh*k,1)

    for k = 1:10:110;
    pzmap (feedback(gh*k,1));
    hold on;
    end
    figure
    rlocus(t)
    stepinfo(m)
    sisotool(gh)

    RESULT

    Root Locus Of The Given Transfer Function Is Ploted In Matlab And Analysed The Given Aims

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