Question

Use MATLAB to write a function that takes inputs R, L, C, TO, Tf, DeltaT and f and produces as output the charge on the capacitor in a driven RLC series circuit where the input voltage source is v(t) = cos(21 ft). Here f is the frequency of the voltage source in Hz. This function returns the inverse Laplace Transform of (1) L (s2 + 2) ($2 + 2as +B) where a = # and B = Lc. Note that there is assumed to be no charge or current in the circuit at time t = 0. For R = 2012, L = 80 mH, C = 20 uF and f = 20 Hz make a graph that shows both the input voltage source and the voltage drop across the capacitor. Your plot must clearly show both the transient response and steady state response of the capacitor voltage.

Answer 1

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% prompt the user to enter the parameters
R = input('Enter R: ');
L = input('Enter L: ');
C = input('Enter C: ');
T0 = input('Enter T0: ');
Tf = input('Enter Tf: ');
DeltaT = input('Enter DeltaT: ');
f = input('Enter f: ');

% Compute alpha and beta,w
alpha = R/(2*L);
beta = 1/(L*C);
w = 2*pi*f;
% now define symbolic variable s
syms s;

% define Q(s), charge on the capacitor
Q = s/(L*(s^2+w^2)*(s^2+2*alpha*s+beta));

% obtain the inverse laplace transform of Q(s)
q = ilaplace(Q);

% define time vector
t = T0:DeltaT:Tf;

% substitute time in q(t)
q_t = subs(q);

% now plot the capacitor charge as a function of time
figure;
plot(t,q_t,'linewidth',2);title('charge on capacitor');
grid on;

RESULT:

Enter R: 20
Enter L: 80e-3
Enter C: 20e-6
Enter T0: 0
Enter Tf: 1
Enter DeltaT: 1e-3
Enter f: 20

01 0.2 0.3 04 0.5 06 0.7 08 0. 9 1