Trying to solve for analysis of system stability with transfer functions where 1 + Gol = 0, x represents the S variable. It says "unable to find explicit solution".

syms x
Gd = 1/((573.5*x)+1);
Gc = (1.09)*(1+((1/693.51*x)));
Gv = (0.020*(exp(-24*x))/((180*x)+1));
Gp = 1417.15/((573.51*x)+1);
Gm = [0.08*exp(-1*180*x)]/(1 + 505.6*x);
Gol = Gc*Gv*Gp*Gm;

eqn = 1 + Gol == 0

sol = solve (eqn, x)

Output:

Warning: Unable to find explicit solution. For options, see

help.

> In sym/solve (line 317)

In untitled (line 11)

sol =

Empty sym: 0-by-1

Answer 1

[Walter Roberson]

format long g
syms x
Gd = 1/((573.5*x)+1);
Gc = (1.09)*(1+((1/693.51*x)));
Gv = (0.020*(exp(-24*x))/((180*x)+1));
Gp = 1417.15/((573.51*x)+1);
Gm = [0.08*exp(-1*180*x)]/(1 + 505.6*x);
Gol = Gc*Gv*Gp*Gm;
eqn = 1 + Gol == 0

eqn = 

SE = simplify(eqn)

SE = 

sol = solve(SE, x)

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

sol = 

double(limit(lhs(eqn), x, sol))

ans = 
     -1.23106198916657e-32

double(subs(lhs(eqn), x, sol))

ans = 
      1.41426664083306e-38

So slightly numerically unstable, but close enough to 0 that you are getting down to round-off error.