Apply the controller synthesis formula (19.2.6) for the following process transfer func- tions: (a) G(s) = (b) G(s) = (c) G(s) = k(1+tos) (ts +1)(+1)(T38+1) ' k(1-tos) (ts+1)(+1)(t3s k (Ts+1)(Ts+1) -0s e +1) ' To >0, T0, T > 0, T3 > 0 To > 0, T > 0, T > 0, T > 0 T > 0, T > 0, 0>0 3 For the last transfer function, under the assumption of small dead time, apply a first- order Pad approximation to derive an approximate rational controller transfer function. In all cases, determine if the controller transfer function is PID.