A third-order process is shown below: G(S) 3.5.(2-) (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 KO TI K T -0.861 T -0.861 0.586 0.758 TD K 1 D = 1.02 -0.323 T TO T D -=1.03 0.165 I T