Question: A first-order system is represented by the time domain differential equation A feedback controller is to be designed such that u(t) = -kx, and the
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A feedback controller is to be designed such that
u(t) = -kx,
and the desired equilibrium condition is x(t) = 0 as t -> oo. The performance integral is defined as
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and the initial value of the state variable is x(0) = ˆš2 Obtain the value of k in order to make J a minimum. Is this k physically realizable? Select a practical value for the gain k and evaluate the performance index with that gain. Is the system stable without the feedback due to u(t)l
J = | x@dt,
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