How can I solve this expression for Qi_s/thetha_s = ....?

clc,clear
syms theta_s s C Qi_s R theta_a
Transfer=solve(Qi_s/C-theta_s/(R*C)+theta_a/(R*C)==s*theta_s,...)

Hi, I was wondering if you can help me with this exercise, I must get my transfer function, I need to obtain "Qi_s/thetha_s" and the expression, can anyone help me please. I think solve can't do this so I am looking for a new tool that could help me.

[Sam Chak]

@Jhoao Venegas, please check if your Laplace equation looks like this:

[Jhoao Venegas]

@Sam Chak

Hi, yes that is exactly what I have.

Answer 1

[Sulaymon Eshkabilov]

To get a transfer function, you should divide both sides of the equation by theta_s, and you will get this:

% Qi_s/C-theta_s/(R*C)+theta_a/(R*C)==s*theta_s
% Qi_s/(C*theta_s)-1/(R*C)+theta_a/(R*C) = s
% Qi_s/(C*theta_s) = s+(1/R*C)-theta_a/(R*C)
% Qi_s/theta_s = s/C + (1-theta_a)/(R*C^2)
% Qi_s/theta_s = (s*R*C+1-theta_a)/(R*C^2)
% TF = (s*R*C+1-theta_a)/(R*C^2)
% Analytical solution of the found TF and its reverse using the inverse and
% Laplace transforms
% Some numerical values assigned to the unknowns:  
R = 100;
C = 5;
theta_a = pi;
syms s
Solution1 = ilaplace((s*R*C+1-theta_a)/(R*C^2))

Solution1 = 

fplot(Solution1, [-10, 10])

% Note that this is an improper TF. Presuming it to be reverse: 
% TF = (R*C^2)/(s*R*C+1-theta_a)

% Some numerical values
R = 100;
C = 5;
theta_a = pi;
s = tf('s');
TF = (R*C^2)/(s*R*C+1-theta_a);
% Step response
step(TF, 10)

% analytical solution of the found TF and its reverse using the inverse and
% Laplace transforms
syms s
Solution2 = ilaplace((R*C^2)/(s*R*C+1-theta_a))

Solution2 = 

fplot(Solution2, [-10, 10])

[Torsten]

@Jhoao Venegas comment moved here:

I think in the second line there should be: %Qi_s/(C*theta_s)-1/(R*C)+theta_a/(theta_s*R*C) = s

Although, thanks.