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    Design a series controller

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    The process of a unity-feedback control system has the transfer function
    Gp(s) = ------------------------
    s^2 + 10 s + 100

    Design a series controller (a PD, PI or PID) so that the following performance specifications are satisfied.

    Steady-state error due to a step input = 0
    Maximum overshoot < 2 percent
    Rise time < 0.02 second

    Carry out the design in the frequency domain and check the design in the time domain.

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    Solution Preview

    Since the unity-feedback transfer function is , we have the open loop transfer function as .

    For a type 1 system, which means there is a free integrator in , the steady-state error due to a step input is if is kept after G(s) is in series with a controller . Hence, PI or PID controller, which can increase the type of the system to eliminate the steady-state error, is not necessary in our case.

    For a second order ...

    Solution Summary

    The response explains how it is natural to use a PD controller in this question.