IV. Disturbance Accommodating Controller (DAC): Use the same (A,B,C) as in Problem II. (x=. =Ax+ Bu+Tup Let [up=0zD with Disturbance Generator &r= y=Cx ZD=FZD = a) Let u, sint+, cost (sint & cost). Find (F,0). Ans: F = =[0] =[10] Justify this. b) Check (A)(F) = $. c) Solve the Matching Conditions: (S, S) [S,FAS,+BS+ = [CS = 0 Be Careful: S, is 2x2 & S, is 1x2 and A will be 4x4 [0]=[C O] is observable. F d) Determine that (4= e) Find G(A+BG) = {1, 1} . f) Find K(A-KC) = {1, 1, 1, 1}. Define K = .(Use MatLab here) KD g) Design the DAC Controller: [u = G+G; G = S-GS, =Ax+Bu++K(y-); y = C Plant State Estimator \ = 0; = F+K, (y-) Disturbance Estimator So that All Gains (G,G,K,K)(Closed-Loop) = {-1,-1,-1,-1,-1,-13 Put all specific information into the above controller.