Plotting inverse laplace function in matlab

Question

I'm currently working on an assignment where we want to plot an output function.

Since our input signal( v(t) )is in the Time domain and our transfer function ( H(s) ) is in the S domain. we want to bring our input signal to the S domain so we can simply use multiplication and then bring it back to the time domain to plot.

The error I'm getting is: Error using plot Data must be numeric, datetime, duration or an array convertible to double.

syms s C R L T n

C = (36)*10^(-6); % Our given values for capacitance, inductance and resistance
L = 0.18;
R = 100;
T = 1/50; % Period
H = 1/(C*R*s + C*L*s^2 + 1);        %Transfer function
y = 3/2;                           %c_0

for n = -5:1:5
    c_k = (((-1)^n)/(pi*(2*n+1)))*exp(1i*(2*n+1)*100*pi*t);
    y = y + c_k;
end
V = laplace(y);
Vc = V * H;
vc = ilaplace(Vc);

vpa(vc);
plot(t,vc);```

Answer 1

I see different issues in this RLC filter circuit.

Here are the modifications you should operate at the end of your program:

vc = real(ilaplace(Vc));%"real" is compulsory even if... it is already real (very small imaginary parts way cree on) 
vvc = string(vc);
close all;hold on;axis([-1,1,-3,3]);
f=str2func(['@(t)(',vvc,')']);%in order to get a function
for t=-1:0.1:1
    plot(t,f(t),'.')
end; 

1. You have to change types : "syms" type has to be converted into "string" type

2. You have to convert to real.

3. "t" is symbolic: Matlab cannot use it as it is; you know that you must give to $t$ a range of values, for example $t=-1:0.1:1$.

4. We use here the so-called "immediate definition" of a function (https://uk.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html)

5. What is this function $y$ ? It looks like a truncated Fourier series expansion of a ramp function ?

6. vpa(...) isn't useful. Instead of for example $2/3$, it gives you $0.66666666666666666666666666...$ with thirty decimals... It's better to keep the fractional form.

7. The value of T isn't used.