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5- (10 bonous points) A PID controller/Regulator is designed for an plant G(s) based on the Ziegler-Nichols second tuning method called "ultimate sensivity method". R(S) E(s) C(s) 401 +1/is+G(s) As you know in the ultimate sensivity method"the following table is being used for finding the optimum gains of a P, PI or PID gains that results in a quarter delay response. Ziegler-Nichols Tuning for the Regulator DC) - k,(1 + 1/T: + Tos). Based on the Ultimate Sensitivity Method Type of Controller Optimum Gain Proportional k, = 0.5K. PI k,-0.45K, T- • Per ke 0.6K PID To be The optimum Gains of the PID controller are found to be Kp = 2, T, = 2, Tp = 0.5. Using a PID could be more expensive than using a P and PI controller. As a result the design enginner wants to find equivalent Pand PI controllers for the system using the table. Please help her find: 1- Kp of a P-Controller that will result in a quarter decay response using the table mentioned above 2- Kp and T, of a PI -Controller that will result in a quarter decay response using the table mentioned above