TRANSFER FUNCTION IN PARALLEL CONNECTION

The physically realizable form of the PD transfer function is given in the first equation of Exercise 8.1.
(a) Show how to obtain this transfer function with a parallel arrangement of two much simpler functions in Figure: 

(b) Find expressions for K1, K2, and t1 that can be used to obtain desired values of Kc, tD, and a.
(c) Verify [he relations for Kc = 3, tD = 2, a = 0.1.