Question (3) (25 Marks) The following sixth-order transfer function was obtained by linearizing the original set of ordinary differential equations used to model an industrial chemical reactor: G(s)=(1.5s+1)5(15s+1)10.3 The indicated time constants are in minutes. For the purposes of designing a practical controller, this model was further simplified to: G(s)=(15s+1)10.3e7.5s (a) Design an IMC controller G for the system write the transfer function (c=5)(6 marks). (b) Design a PID controller for the sixth-order process, based on the approximated transfer function. (7 Marks) (c) Simulate and compare this controller to th illustrate about the relationship between the IMC strategy, Direct Syntheses and the PID derived from IMC tuning? (12 marks)