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    Feedback Control Systems: Systems Specifications

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    Find a second order model to achieve the following response to a step output disturbance of height 0.5. Minimum value 0.05 after 0.1s. Make a rough sketch of the bode magnitude plot and the step response.

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    Posting 23525:

    Ty/do is high-passing

    Note from then class notes you attached:

    Ty/di = P/(1+L), since P* = P
    Ty/do = 1/(1+L), since P* = 1
    and hence, Ty/do = [Ty/di]/P
    Typically P(s) = k/(s+a)
    Now, we know from previous postings and the normalized curves,
    Ty/di is of the form:

    Ty/di = bs/[s^2 + cs +d ]

    Now, Ty/do = [Ty/di]/P
    = bs/[s^2 + cs +d ]/[k/(s+a)]
    = (s+a)(bs)/[k{s^2 + cs +d}]
    = (bs^2+abs)/[k{s^2 + cs +d}]
    This is the general form ofn the TF.

    Find a second-order model:

    Step output disturbance of height 0.5

    Output: Minimum value: 0.05 after 0.1 Sec

    If d is the damping coefficient and Wn is the undamped angular velocity (in rad/sec),
    Transfer function from output disturbance to output:

    Y(s)/Do(s) = s*(s+2dWn)/[s^2 + 2dWn*s + Wn^2]

    do = 0.5U(t)

    Do(s) = 0.5/s

    Hence, Y(s) = ...

    Solution Summary

    In 560 words, this solution provides a step-by-step response which clearly indicates how to approach this feedback control system problem.