engrmae 170 2015 uci homework 2
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>> %Question P2.50 b. >> [r, p] = residue( 12000, [1 25 4100 24500] ) r = 1.5361 + 0.0806i 1.5361 0.0806i 3.0722 + 0.0000i p = 9.4253 +62.4119i 9.4253 62.4119i 6.1495 + 0.0000i >> %Question P2.50 c. >> [r, p] = residue( 12000, [1 25 4100 24500 0] ) r = 0.0049 + 0.0239i 0.0049 0.0239i 0.4996 + 0.0000i 0.4898 + 0.0000i p = 9.4253 +62.4119i 9.4253 62.4119i 6.1495 + 0.0000i 0.0000 + 0.0000i >> k=r(1) k = 0.0049 + 0.0239i >> D=2*abs(k) D =
0.0487 >> phi=angle(k) + (pi/2) phi =
2.9393 >> sys = tf( 12000, [1 25 4100 24500] )
sys = 12000 s3 + 25 s2 + 4100 s + 24500 Continuoustime transfer function. >> Question P2.50 d, >> step(sys)
>> ENGRMAE170Homework2 _________________________________________________________ %This is the .m file %Defining the blocks sys_1 = tf( 4, 1); sys_2 = tf( 1, [1, 1]); sys_3 = tf( [1, 0, 0], [1, 0, 1]); sys_4 = tf( 1, [1, 0, 0]); sys_5 = tf( [4, 2], [1, 2, 1]); sys_6 = tf( 50, 1); sys_7 = tf( [1, 0, 2], [1, 0, 0, 14]); %Reducing the diagram
sys_a = feedback( sys_4, sys_6, +1); sys_b = series( sys_2, sys_3); sys_c = feedback( sys_b, sys_5, 1); sys_d = series( sys_c, sys_a); sys_e = feedback( sys_d, sys_7); system = series( sys_1, sys_e); %system is the closed loop transfer function system %To show the pzmap pzmap(system) ___________________________________________________________ system = 4 s7 + 8 s6 + 4 s5 + 56 s4 + 112 s3 + 56 s2 s10 + 3 s9 42 s8 130 s7 354 s6 885 s5 2163 s4 5604 s3 4184 s2 2100 s 700 Continuoustime transfer function. >> pls = pole(system) pls = 7.0699 + 0.0000i 7.0695 + 0.0000i 1.2065 + 2.0864i 1.2065 2.0864i 2.4120 + 0.0000i 1.0778 + 2.1336i 1.0778 2.1336i 0.5762 + 0.0000i 0.1348 + 0.5343i 0.1348 0.5343i >> zro = zero(system) zro = 0.0000 + 0.0000i 0.0000 + 0.0000i 1.2051 + 2.0872i 1.2051 2.0872i 2.4101 + 0.0000i 1.0000 + 0.0000i
1.0000 0.0000i