Question

5.10 Use the MATLAB series and feedback functions to obtain the transfer functions C(s)/R(s) and C(s)/D(s) for the block diagram shown in Figure P5.7

Answer 1

Program Screen Shot:

clc, clear G1 = tf(6,[1 0]); $ 6/5 block G2 = tf(1, [41]) 1/ (45+1) block G3 = tf(1, [32]); $ 1/ (33+2) block H1 = tf(10,1) 10 block H2 = tf(1,1); $i block/line HHHHHHHHH 400 99 8% compute C(s)/R(S) by setting D(s) = 0 G2G3 = series (G2, G3); G2G3H1 = feedback (G2G3, Hl); G1G2G3H1 = series (G1,G2G3H1); CsRs = feedback (G1G2G3H1, H2); 8% compute C(s)/D (s) by setting R(s) = 0 G1H2 = series (G1, H2) H = series ( G2, (G1H2+Hl) ) CsDs = - feedback (G3, H)

Sample Output:

Command Window CsRs = 12 3^3 + 11 s^2 + 12 S + 6 Continuous-time transfer function. CsDs = - 4 3 2 - 3 12 s^3 + 11 s^2 + 12 S + 6 Continuous-time transfer function. fy >>

Program Code to Copy:

clc,clear
%%
G1 = tf(6,[1 0]); % 6/s block
G2 = tf(1,[4 1]); % 1/(4s+1) block
G3 = tf(1,[3 2]); % 1/(3s+2) block
H1 = tf(10,1); % 10 block
H2 = tf(1,1); % 1 block/line

%% compute C(s)/R(s) by setting D(s) = 0
G2G3 = series(G2,G3);
G2G3H1 = feedback(G2G3,H1);
G1G2G3H1 = series(G1,G2G3H1);
CsRs = feedback(G1G2G3H1,H2)
%
%% compute C(s)/D(s) by setting R(s) = 0
G1H2 = series(G1,H2);
H = series( G2, (G1H2+H1) );
CsDs = - feedback(G3,H)

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