How can I represent a transfer function interms of symbolic variables? Apparently tf(num, den) can only take numeric values.

How can I represent a transfer function interms of symbolic variables. Apparently tf(num, den) can only take numeric values. I have also tried sym2poly() function, but that also generates errors.

syms theta(t) J b r I l B L F phi 
theta_p = diff(theta, t);
theta_pp = diff(theta, t, 2);

func = J*theta_pp + b*theta_p - 2*r*I*l*B == -L*F*sin(phi);
Sol = dsolve(func, theta(0)==0, theta_p(0)==0);
TF = laplace(Sol)
%pretty(TF);
[symNum,symDen] = numden(TF) %Get num and den of Symbolic TF      *****all is good untill this point****
%TFnum = sym2poly(symNum)    %Convert Symbolic num to polynomial
% TFden = sym2poly(symDen);    %Convert Symbolic den to polynomial
% ans =tf(TFnum,TFden);

Answer 1

[madhan ravi]

Might help :

https://www.mathworks.com/matlabcentral/answers/436037-i-want-to-use-inverse-laplace-with-tf-function-how-can-i-do-it-i-take-an-error-in-matlab-when-i-u#answer_352672

Note: sin is noticed in your equation so sym2poly cannot be used.

[Muhammad Umair Khan]

still doesnt work

Answer 2

[Walter Roberson]

syms theta(t) J b r I l B L F phi s
theta_p = diff(theta, t);
theta_pp = diff(theta, t, 2);
func = J*theta_pp + b*theta_p - 2*r*I*l*B == -L*F*sin(phi);
Sol = dsolve(func, theta(0)==0, theta_p(0)==0);
TF = laplace(Sol)
[symNum,symDen] = numden(simplify(TF)) %Get num and den of Symbolic TF
NumCoeff = coeffs(symNum,s,'all');
DenCoeff = coeffs(symDen,s,'all');

The transfer function would then logically be tf(NumCoeff, DenCoeff)

But only logically. The Control System Toolbox does not support symbolic coefficients.

The Control System Toolbox does support tuneable systems. See the discussion at https://www.mathworks.com/matlabcentral/answers/305339-how-to-create-a-transfer-function-with-gain-k#answer_236890 . These are not symbolic coefficients.