Possible Inverse Laplace Transform Error?

Rocky Gonzalez

2020 7 9

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3 次查看（30 天）

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Hello,

I get an error: "Undefined function or variable 's'."

I am not too sure why. I am wondering if this is due to symbolic notation of the inverse laplace transform (even though I converted the equation into function notation). I am trying to compute an inverse laplace transform so I can plot 'Vb' as the y-axis and 't' as the x-axis. I defined 's' to have a value without any luck. Here is my code that is able to reproduce this error. I am also not sure if laplace domain equation is 'too' complicated to compute. If so, are there any alternatives to consider for computing an numerical approximation for an inverse laplace transform? Thank you in advance.

Program:

% Written: Rocky Y. Gonzalez (07/09/2020)
% University of Nevada Las Vegas
% Department of Electrical and Computer Engineering
% Program: N/A
clear all, close all, clc
% Variables ---------------------------------------------------------------
V0 = 5000;     
Rtotal = 50;    
ic = V0/Rtotal; 
Rd = 0;         
Gd = 0;         
Ld = 6E-6;      
Cd = 12E-9;     
C = 3.3E-6;    
Rs = Rtotal;    
Rf = 1E9;       
RL = 1E9;       
la = 12;        
lb = 22;        
z = 22;         
% Laplace Domain Equations ------------------------------------------------
syms s
Z0 = sqrt((s*Ld+Rd)/(s*Cd+Gd));
Z0a = Z0;
Z0b = Z0;
gamma = sqrt((s*Ld+Rd)*(s*Cd+Gd));
Zina = Z0a*(RL*cosh(gamma*la) + Z0a*sinh(gamma*la))/...
           (RL*sinh(gamma*la) - Z0a*cosh(gamma*la));
ZLb = (Rf*Zina)/(Rf+Zina);
Zinb = Z0b*(ZLb*cosh(gamma*lb) + Z0b*sinh(gamma*lb))/...
           (Z0b*sinh(gamma*lb) - Z0b*cosh(gamma*lb));
Qb_plus = (2*V0*Z0b*(ZLb+Z0b)*C)/...
          ((1+s*(Rs+Zinb)*C)*(ZLb*sinh(gamma*lb) + Z0b*cosh(gamma*lb)));
Qb_minus = Qb_plus*(ZLb-Z0b)/(ZLb+Z0b);
Qa_plus = Qb_plus*(RL+Z0a)*ZLb/...
          ((ZLb-Z0b)*(RL*cosh(gamma*la) + Z0a*sinh(gamma*la)));
Qa_minus = Qa_plus*(RL-Z0a)/(RL+Z0a);
Vb = (Qa_plus*exp(-gamma*(z-la)) + Qa_minus*exp(gamma*(z-la)))/2;
% Inverse Laplace Transforming / Plotting ---------------------------------
t = 0:1:2;
figure(1)
Vb = simplify(Vb, 'Steps',20);
Vb = vpa(Vb, 5)
vb = ilaplace(Vb)
vb_ = matlabFunction(vb)
s = 1
plot(t,vb_(t))