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    Control Systems Complex Controller

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    Problem 1:
    Consider the closed-loop transfer function

    T(s) = 10K/(s2 + 20s + K)

    1. Obtain the family of step responses for K=10, 100, and 500. Co-plot the responses and develop a table that includes the following:

    a. Percent overshoot
    b. Settling time
    c. Steady-state error.

    Figure 1
    Problem 2:
    A negative feedback control system is depicted in Figure 1. Suppose that your design is to find a controller, Gc(s), of minimal complexity such that your closed-loop system can track a unit step input with steady-state error of zero.

    1. As a first try, consider a simple proportional controller: Gc (s) = K,
    where K is a fixed gain. Let K = 2. Using MATLAB, plot the unit step response.

    2. Determine the steady-state error from the plot above. Calculate the theoretical steady-state error and compare your results.

    3. Now consider a more complex controller: Gc (s) = K0 + K1/s

    where K0 = 2, and K1 = 20. This type of controller is known as a proportional, integral (PI) controller. Plot the unit step response using this controller.

    4. Determine the steady-state error from the plot. Calculate the theoretical steady-state error and compare your results.

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    https://brainmass.com/engineering/electrical-engineering/control-systems-218371

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    Solution Summary

    A negative feedback control system is analyzed. The design for a complex controller is given for minimal complexity such that the closed-loop system can track a unit step input with steady-state error of zero.

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