Question

slove in Matlab

AP2. A system is modeled by the following differential equation in which X(t) is the output and (() is the input: *+ 2x(t) + 5x(t) = 3u(t), x(0) = 0, X(t) = 2 a. Create a state-space representation of the system. b. Plot the following on the same figure for 0 st s 10 sec : i. the initial condition response (use the initial function) il the unit step response (use the step function) iii. the total (combined) response (use the Isim function) (Hint: create a vector U = ones(1, length()) to simulate a step input for ili.) (include a legend) Reference: Output Reponse x{t) time (s)

Answer 1

Script

clc;close all;clear all;

%state space representation of system

b = [3];%coeffcients of u(t)

a = [1 2 5];%Coefficients of x(t)

[A,B,C,D] = tf2ss(b,a)

%initial condition response

sys=ss(A,B,C,D);x0=[0;2];

figure;[y,t]=initial(sys,x0);plot(t,y,'--r');hold on;

%unit step response

[y,t]=step(sys,t);plot(t,y,'--g');hold on;

%total response

x=(t>=0);

lsim(sys,x,t,x0);hold off;title('Output responses');grid;

legend('Initial response','Step response','Total response')

Output responses - - Initial response -- Step response Total response Amplitude Time (seconds)

Command window:

A =

-2 -5
1 0

B =

1
0

C =

0 3

D = 0