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Additional info for Control Systems Engineering, 4th Edition - Solutions Manual
Example text
K1 (J3 s2 + D3 s) ∆ Kt Tstall 100 Ea 50 1 = = = 2 ; Kb = = = Ra Ea 50 ω no− load 150 3 Also, Jm = 2+18 Thus, θ m (s) Ea (s) = ( 13 ) 2 = 4; Dm = 2+36 2 ( 13 ) = 6. 2/4 1/ 2 = 1 5 2 s(s + (6 + )) s(s + ) 4 3 3 Solutions to Problems 39 Since θL(s) = 1 θm(s), 3 θ L (s) Ea (s) = 1 6 5 . s(s + ) 3 43. 75) 4 3 1 3 Since θ2(s) = 1 θm(s), 4 1 θ 2 (s) 12 . 75) 44. The following torque-speed curve can be drawn from the data given: T 100 50 500 Therefore, 1000 v Kt Tstall 100 Ea 10 1 1 2 = = = 10 ; Kb = = = .
Using the standard form derived in the textbook, ⎡ 0 • ⎢ 0 x= ⎢ 0 ⎢⎣−10 0⎤ ⎡ 0⎤ 0⎥ ⎢ 0⎥ x+ r(t ) ⎢ 0⎥ 0 0 1⎥ ⎢⎣ 1⎥⎦ −5 −1 −2⎥⎦ 1 0 0 1 c = [10 5 0 0 0]x b. Using the standard form derived in the textbook, ⎡0 ⎢0 • x = ⎢0 ⎢0 ⎢0 ⎣ 1 0 0 0⎤ ⎡ 0⎤ ⎢ 0⎥ 0 1 0 0⎥ 0 0 1 0 ⎥ x + ⎢ 0⎥ r(t) ⎢ 0⎥ 0 0 0 1⎥ ⎢ 1⎥ 0 −8 −10 −9⎥⎦ ⎣ ⎦ c = [3 7 12 2 1]x 12. Program: 'a' num=[5 10]; den=[1 2 1 5 10] G=tf(num,den) [Acc,Bcc,Ccc,Dcc]=tf2ss(num,den); Af=flipud(Acc); A=fliplr(Af) B=flipud(Bcc) 60 Chapter 3: Modeling in the Time Domain C=fliplr(Ccc) 'b' num=[1 2 12 7 3]; den=[1 9 10 8 0 0] G=tf(num,den) [Acc,Bcc,Ccc,Dcc]=tf2ss(num,den); Af=flipud(Acc); A=fliplr(Af) B=flipud(Bcc) C=fliplr(Ccc) Computer response: ans = a den = 1 2 1 5 10 Transfer function: 5 s + 10 ---------------------------s^4 + 2 s^3 + s^2 + 5 s + 10 A = 0 0 0 -10 1 0 0 -5 0 1 0 -1 0 0 1 -2 5 0 0 9 10 8 B = 0 0 0 1 C = 10 ans = b den = 1 0 Transfer function: s^4 + 2 s^3 + 12 s^2 + 7 s + 3 -----------------------------s^5 + 9 s^4 + 10 s^3 + 8 s^2 A = 0 0 0 0 0 1 0 0 0 0 0 1 0 0 -8 0 0 1 0 -10 0 0 0 1 -9 0 Solutions to Problems 61 B = 0 0 0 0 1 C = 3 7 12 2 1 13.
766e004 ----------------------------------------------------s^5 - 4 s^4 - 32 s^3 + 148 s^2 - 1153 s - 4480 16. Program: syms s 'a' A=[0 1 3 0 0 0 1 0 0 0 0 1 -7 -9 -2 -3]; B=[0;5;8;2]; C=[1 3 4 6]; D=0; I=[1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1]; 'T(s)' T=C*((s*I-A)^-1)*B+D; T=simple(T); pretty(T) 'b' A=[3 1 0 4 -2 -3 5 -5 2 -1 0 1 -1 2 8 -7 6 -3 -4 0 -6 0 4 -3 1]; B=[2;7;6;5;4]; C=[1 -2 -9 7 6]; D=0; I=[1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1]; 'T(s)' T=C*((s*I-A)^-1)*B+D; T=simple(T); pretty(T) Computer response: ans = a Solutions to Problems 65 ans = T(s) 2 3 -164 s - 1621 s - 260 + 59 s -----------------------------4 3 2 s + 3 s + 2 s + 30 s + 7 ans = b ans = T(s) 2 3 4 14582 s + 1708 s - 408 s - 7 s + 27665 -----------------------------------------5 4 3 2 s - 4 s - 32 s + 148 s - 1153 s - 4480 17.
Control Systems Engineering, 4th Edition - Solutions Manual by Norman S. Nise
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