An engineering laboratory has presented a plan to operate an Earth-orbiting satellite that is to be controlled from a ground station. A block diagram of the proposed system is shown in Figure CP9.7.

It takes T seconds for a signal to reach the spacecraft from the ground station and the identical delay for a return signal. The proposed ground-based controller is a proportional-derivative (PD) controller, where

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).

Ge(s) = Kp + Kps. (a) Assume no transmission time delay (i.e., T = 0), and design the controller to the following spec- ifications: (1) percent overshoot P.O. < 20% to a unit step input and (2) time to peak Tp = 30 s. (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 Pad approximation to the time delay, determine the maximum allowable delay Tmax for system stability by developing a