Variables of type "sym" cannot be combined with other models. Please help

I want to solve this set of equations:

Here is my code:

syms mu_u N_a; % Variables to Solve for
P = tf(1,[1 1]);
F_r = tf(1,[1 1]);
C = 1;
sigma_r = 1;
f = x ;
mu_r =1;
P_o = 1;
C_o = 1;
sys = (F_r * C) / ( 1 + (P * N_a * C) );
n = norm(sys); % H2 Norm Calculation 
sigma_u = n * sigma_r;
fun_n =  ( (diff(f)) / (sqrt(2*pi)*mu_u) ) * (exp ( -1* ((x-(mu_u))^2) / (2*(sigma_u)^2)) );
F_N = int(fun_n, x, -inf, inf);
%N_a - F_N = 0; % Equation 14 of Assignment
fun_m =  ( (f) / (sqrt(2*pi)*mu_u) ) * (exp ( -1* ((x-(mu_u))^2) / (2*(sigma_u)^2)) );
F_M = int(fun_m, x, -inf, inf);
%(mu_r / P_o) - (mu_u / C_o * P_o) - F_M = 0; % Equation 15 of Assignment
eqn1 = N_a - F_N == 0;
eqn2 = (mu_r / P_o) - (mu_u / C_o * P_o) - F_M == 0;
eqns = [eqn1 eqn2];
S = solve(eqns,[N_a mu_u]);
ans_1 = S.N_a
ans_2 = S.mu_u

And the error is:

Error using *

Invalid operand. Variables of type "sym" cannot be combined with other models.

Error in Test (line 13)

sys = (F_r * C) / ( 1 + (P * N_a * C) );

Please help me resolve this error.

[Dyuman Joshi]

The error is clear, you can not combine transfer function model with symbolic variables.

Why not define P and F_r as symbolic variables?

sys = tf([1 0],[1 2 3])

sys =
 
        s
  -------------
  s^2 + 2 s + 3
 
Continuous-time transfer function.

[Num,Den] = tfdata(sys);
syms s
sys_syms = poly2sym(Num{:},s)/poly2sym(Den{:},s)

sys_syms = 

Also, "x" is un-defined.

f = x;

Unrecognized function or variable 'x'.

Answer 1

[Walter Roberson]

The functions in the Control System Toolbox do not use the Symbolic Toolbox, and cannot be mixed with the symbolic toolbox at all. You need to convert your tf into symbolic formulas

Your "x" is not defined in your code, so I cannot test much.

syms mu_u N_a; % Variables to Solve for
syms s
P_tf = tf(1,[1 1]);
F_r_tf = tf(1,[1 1]);
P = poly2sym(P_tf.Numerator{1},s) / poly2sym(P_tf.Denominator{1},s)

P = 

F_r = poly2sym(F_r_tf.Numerator{1},s) / poly2sym(F_r_tf.Denominator{1},s)

F_r = 

C = 1;
sigma_r = 1;
f = x ;

Unrecognized function or variable 'x'.

mu_r =1;
P_o = 1;
C_o = 1;
sys = (F_r * C) / ( 1 + (P * N_a * C) );
n = norm(sys); % H2 Norm Calculation 
sigma_u = n * sigma_r;
fun_n =  ( (diff(f)) / (sqrt(2*pi)*mu_u) ) * (exp ( -1* ((x-(mu_u))^2) / (2*(sigma_u)^2)) );
F_N = int(fun_n, x, -inf, inf);
%N_a - F_N = 0; % Equation 14 of Assignment
fun_m =  ( (f) / (sqrt(2*pi)*mu_u) ) * (exp ( -1* ((x-(mu_u))^2) / (2*(sigma_u)^2)) );
F_M = int(fun_m, x, -inf, inf);
%(mu_r / P_o) - (mu_u / C_o * P_o) - F_M = 0; % Equation 15 of Assignment
eqn1 = N_a - F_N == 0;
eqn2 = (mu_r / P_o) - (mu_u / C_o * P_o) - F_M == 0;
eqns = [eqn1 eqn2];
S = solve(eqns,[N_a mu_u]);
ans_1 = S.N_a
ans_2 = S.mu_u

[Ahmad]

My function f is a saturation function. How should i model it and solve it?

[Walter Roberson]

Unfortunately at the moment I have no idea what saturation models look like.

You can convert tf() to symbolic form using the approach I show here of fetching the numerator and denominator, or using Dyuman's suggestion of tfdata.

Likewise if you have a symbolic laplace transform that does not involve any exp() forms and which involves only s and no other symbolic variable, then there are ways to convert that into a tf() that are not bad. (delays coded with exp take more work to detect and extract from the laplace)

If you start needing state space form then conversion of symbolic to ss is harder.

If you have a symbolic laplace that involves another symbolic variable beyond s (perhaps you are trying to tune the equation) then unfortunately, Control System Toolbox cannot handle that situation.

What Control System Toolbox can handle is systems involving entities that are marked as being subject to change. So you might get a system that you write in terms of (say) k, but internally at every point the control system toolbox has a definite value for k, along with tools that can change the definite value easily. The resulting internals cannot "reason" about k