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Please solve by hand, NOT MATLAB.Consider the PID-controlled system shown in Figure 8–19. The PID...

Please solve by hand, NOT MATLAB.

Consider the PID-controlled system shown in Figure 8–19. The PID controller is given by

 Gc(s) = K (s + a)2 /S 


It is desired to find a combination of K and a such that the closed-loop system will have 10% (or less) maximum overshoot in the unit-step response. 


Assume that the region to search for K and a is 

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