Question

can you show how the model would look like on matlab ? please help with this question

For the circuit given below, find the normal form for the inductor current and capacitor voltage. Use Matlab (Create an.m file. Use Isim function) and Simulink (Create a Simulink Model). Plot the responses x1 and x2 over time from the M file and Simulink Model. Do they match? Please explain. Use f(t)-e-cos(2t)u(t) for the input. Assume Zero Initial Conditions. 2Ω I H On word document- Type State Equations with A, B, C, and D matrices, copy and paste m-files and Simulink model. You need to submit word document, m-file, and Simulink mode all together.

Answer 1

Apply mesh equation around loop 1. F = 2i_1 + 2(i_1 - i_2) 4i_1 - 2i_2 = f implies i_1 = f + 2i_2/4 But i_2 = x_1 i_1 = f = 2x_1/4 loop 2 2(i_2 - i_1) + 1 d/dt i_2 = x_2 = 0 But i_2 = x_1 dx_1/dt = -2x_1 + 2i_1 - x_2 = -2x_1 + f/2 + x_1 - x_2 x_1^dot = -x_1 - x_2 + f/2 equation (1) loop 3: x_2 = i_3 middot 1 + i_3 middot 2 = 3 i_3 But - i_3 + i_2 = C dx_2/dt = 1/2 dx_2/dt i_3 = x_1 - 1/2 dx_2/dt x_2 = 3 middot x_1 - 3/2 dx_2/dt 3/2 dx_2/dt = 3x_1 - x_2 x_2^dot = 2x_1 - 2/3 x_2 equation (2) MATLAB code is given below in bold letters. clc: close all: clear all: % define the matrices A = [-1 -1: 2 -2/3]: B = [1/2;0]: C1 = [1 0]: %This corresponds to inductor current C2 = [0 1]: %This corresponds to

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define the matrices
A = [-1 -1; 2 -2/3];
B = [1/2;0];
C1 = [1 0]; %This corresponds to inductor current
C2 = [0 1]; %This corresponds to capacitor voltage
D = 0;

% define the system in state space domain
sys1 = ss(A,B,C1,D);
sys2 = ss(A,B,C2,D);

% define the time vector
t = 0:0.01:10;

% define the input
f = exp(-3*t).*cos(2*t);

% compute the system response
y1 = lsim(sys1,f,t); % inductor current
y2 = lsim(sys2,f,t); % capacitor voltage

% plot the indcutor current and capacitor voltage
figure;
subplot(211);
plot(t,y1,'linewidth',2);grid on; xlabel('time');ylabel('Amplitude');
title('inductor current');

subplot(212);
plot(t,y2,'linewidth',2);grid on; xlabel('time');ylabel('Amplitude');
title('capacitor voltage');