Question 4 (15 marks) A third-order process is shown below: G(s) 3.5.(2-s) (5s + 1)(2s + 1)(s +5) a) Reduce this transfer function to a first-order-plus-deadtime (FOPDT) model by applying Skogestad's half rule [7 marks] b) Derive the PI tuning constants (to 2 decimal places) from the Integral of the absolute error (IAE) and the Integral of the time-weighted absolute error (ITAE) tuning relations provided in Table 1. Use K, t, and D obtained from part (a) [5 marks) c) Which PI controller would you recommend to the operator? Explain. [3 marks] Table 1: PI Tuning Rules IAE ITAE TI Kc TI -0.861 0.758D-0.861 . T D -= 1.02 -0.323- T 0.586 K h D = 1.03 -0.165 T K T