title: inverse Laplace with Matlab
body: <p>I have a problem with finding inverse laplace of function with Matlab. I obtained following transfer function :
  <img src="https://i.stack.imgur.com/Cgq1m.jpg" alt="enter image description here"></p>
  
  <p>I tried methods like </p>
  
  <pre><code>syms s t;
      num=[0 0 0 1.658e24 -1.163e14 6.076e15];
      den=[1 3.334e09 1.005e15 1.675e24 5.025e27 1.675e33];
      numsym=poly2sym(num);
      densym=poly2sym(den);
      transfer=numsym./densym;
      ilaplace(transfer,s,t)
  </code></pre>
  
  <p>but did not get an acceptable result. Meaning Matlab simply returns :
  <img src="https://i.stack.imgur.com/DypsC.jpg" alt="enter image description here"></p>
  
  <p>Also I tried to use partial fraction expansion and I wrote transfer function respect to poles and zeros but when I added all the pieces I did not get the original transfer function.</p>
  
  <pre><code>syms s t;
  num=[0 0 0 1.658e24 -1.163e14 6.076e15];
  den=[1 3.334e09 1.005e15 1.675e24 5.025e27 1.675e33];
  numsym=poly2sym(num);
  densym=poly2sym(den);
  transfer=numsym./densym;
  [z,p,r]=residue(num,den);
  transfer1=(z(1)/(s-p(1)))+(z(2)/(s-p(2)))+(z(3)/(s-p(3)))+(z(4)/(s-p(4)))+(z(5)/(s-p(5)));
  transfer1=vpa(simplifyFraction((transfer1),'Expand',true),2)
  the
  </code></pre>
  
  <p>The transfer1 variable after simplification is order 4 in numerator while the original transfer function is order 2. I would be very thankful if anyone help me  to find the transfer function of following expression by any method?</p>