A pilot feedback control scheme, based on the following disturbance and transfer function models:

∇???????? = ????????

(1 − ????????)Y???? = ????0????????−1+ − ????1????????−2+

was operated, leading to a series of adjustments ???????? and errors ????????. It was believed that the noise model was reasonably accurate, but that the parameters of the transfer function model were of questionable accuracy.

(a) Given the first 10 values of the ????????, ???????? series shown below:
t ???????? ???????? t ???????? ????????
1 25 −7 6 −30 1 2 42 −7 7 −25 3 3 3 −6 8 −25 4 4 20 −7 9 20 0 5 5 −4 10 40 −3 set out the calculation of the residuals ???????? (???? = 2, 3, … , 10) for ???? = 0.5, ????0 = 0.3, ????1 = 0.2, and for arbitrary starting values ????0 1 and ????0 0.

(b) Calculate the values ????1, ̂????0 of ????0 1 and ????0 0 that minimize the sum of squares ∑10 ????=2(????????|???? = 0.5, ????0 = 0.3, ????1 = 0.2, ????0 1 , ????0 0 )
2 and the value of this minimum sum of squares.