An engineering laboratory has presented a plan to operate an Earth-orbiting satellite that is to be controlled
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Gr(s) = KD + KDs.
(a) Assume no transmission time delay (i.e., T = 0), and design the controller to the following specifications: (1) percent overshoot less than 20% to a unit step input and (2) time to peak less than 30 seconds.
(b) Compute the phase margin with the controller in the loop but assuming a zero transmission time delay. Estimate the amount of allowable time delay for a stable system from the phase margin calculation.
(c) Using a second-order Pade approximation to the time delay, determine the maximum allowable delay Tmw for system stability by developing a m file script that employs the pade function and computes the closed-loop system poles as a function of the time delay T. Compare your answer with the one obtained in part (b).
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