k b T 1 |k3 '3. b T 2 02 2 |k, 4. Use k = 3, 6, =2, K2=4,K3=2, 63 = 1, J = 2, J2=5, find the impulse and step response of o, (+) due to one input at a time, use matlab 5. (a) Formulate T (5) = (kp+ S* kJ) * (RE)-0, (5)) ; Using Mason's rule find Z, and Z which satisfy ()=2, R(s) + Z2 * T (s) (b) Formulate T ) = ( kp + 5 # kj + ki/s) * (R(S)-(s)); Using Mason's rule Find Z3 and zi M which satisfy 0 (5) = 23 * R(S) + Zy *T, (s) 6. Take the model from 5a of a proportional, Jerivative controller. Obtain the characteristic eavation, Choose kp=2 and then using Routh array, find the value of K, when the roots of the denominator Polynomial become unstable. What are the valves of the roots at this transition? 7. Still using the motel from 59, choose Kp = 2, K=5, Use the final value theorem and find the steady state valve of 9, (+) For: (a) r) = step function and for (b) T, (+) = step function 8. Draw the step response till steady state occurs for each of the above cases in 7a and 7b. Use matlab for this part. 9. Take the model from 5b of a proportional, derivative, integral controller, choose Kp=2, k = 5 and then using Routh array, find the value of k; when the roots of the denomination polynomial become unstable. What are the values of the roots at this transition? 10. Still using the model from 56, choose Kp=2, K=5, K; = 3. Use the final value theorem and Find the steady State value of 0, (+) For: (a)(t) = step function, and for (6) T, (+) = Step Function 11. Draw the Step response till steady state occurs for each of the above cases in loa and lob, use matlab for this part.