Question 1:

G= 1

H=6

(a) Give ONE (1) application of Least Square method in Adaptive Control Systems. Justify your answer by describing one structure of controller. [Berikan SATU (1) penggunaan kaedah kuasa dua terkecil dalam system kawalan suai. Berikan justifikasi terhadap jawapan anda dengan menerangkan satu struktur pengawal:] (5 Marks/ Markah) (b) Data in Table 2 is obtained from a system in general form: [Data dalam Jadual 2 diperolehi daripada sebuah system dalam bentuk am:] y(k) 1 + bz-1 + az-zu(k) Table 2 (Jadual 2] k 1 2 3 2.9 1.3 3.4 2.2 y 0.h 0.2 0.1 4 0.3 Please refer Table 1 for the value of g and h. If g=0, then u(1)=2.5, and if h=0, then y(1)=0.5. Use the Recursive Least Square algorithm to find:- [Gunakan algorithma Rekursif kuasa dua terkecil (RLS) bagi mencari:-) (1) The regression model of the system. [Model regresi system tersebut.] (4 Marks/ Markah) (11) Identify the estimated value of the parameters a, b and c after k = 2 ONLY. The forgetting factor, p, is given b the following equation : [Anggaran nilai parameter a, b dan c setelah k = 2 SAHAJA. Nilai forgetting factor, p. diberi oleh persamaan berikut:] p(k) = pop(k 1) + (1 - Po) where (di mana] Po = p(0) = (0.98) Use the following initial values: [Gunakan nilai permulaan berikut: @0) = 10,P [100 [100 0 100] 0 100 The calculation must be in 4 decimal places [Pengiraan hendaklah dalam 4 titik perpuluhan:] (10 Marks/ Markah) (11)Determine and explain the performances of the system based on value of the parameters a, b and c in Question 1(b)(ii) [Tentukan dan terangkan prestatsi system berdasarkan ke atas nilai parameter a, b dan c dalam Soalan 1(b)(i)] 6 Marks/ Markah)