# Reduce block diagrams symbolically

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Aleem Andrew on 6 Feb 2021
Answered: Paul on 6 Feb 2021
Can the code below be modified to find the transfer function in terms of symbolic functions g1 to g5 instead of numeric functions? I tried passing symbolic arrays as arguments to tf but I get an error message stating that the values of num and den must be numeric arrays. Is there a way to write code similar to the code below but with g1, g2, g3, g4, and g5 being passed as symbolic arguments?
g1 = tf(1,[1 0 0]);
num2 = 50; den2 = [1 1];
g2 = tf(num2,den2);
g3 = tf(2,[1,0]); g4 = tf([1 0],1);
g5 = tf(2,);
sys1 = parallel(g4,-g5);
sys2 = feedback(g2,g3,-1);
sys4 = series(sys2,sys1);
sys5 = series(sys4,g1);
sys6 = feedback(sys5,)

Paul on 6 Feb 2021
Assuming you want final result in terms of the gi(s):
syms g1(s) g2(s) g3(s) g4(s) g5(s)
symsys1 = g4(s)-g5(s);
symsys2 = g2(s)/(1 + g3(s)*g2(s));
symsys4 = symsys2*symsys1;
symsys5 = symsys4*g1(s);
symsys6 = symsys5/(1 + symsys5);
symsys6 = simplify(symsys6,50);
[num,den] = numden(symsys6);
symsys6 = num/den;
symsys6
symsys6 =
(g1(s)*g2(s)*g4(s) - g1(s)*g2(s)*g5(s))/(g2(s)*g3(s) + g1(s)*g2(s)*g4(s) - g1(s)*g2(s)*g5(s) + 1)