how to solve the equation: xdot=AX+Bu; where u=sin(2t)

This is my system. I want to solve it using ode45.

I have solved this using ode45 but by keeping sin(2t)=0. the following is the code.

What changes i need to do to the following to solve my actual system.

function [y]= smc3()

clc

a=[0 1;-3 -4];

b=[0 1];

c=[1 0];

ic=[1 -2];

i=zeros(1,2);

[t y]=ode45(@smc4,[0 8],ic);

function [di]= smc4(~,i)

di = zeros(2,1); % a column vector

di(1) = a(1,1)*i(1)+a(1,2)*i(2)-b(1);

di(2) = a(2,1)*i(1)+a(2,2)*i(2)-b(2);

end

id=y(:,1);

iq=y(:,2);

plot(t,y(:,1),t,y(:,2));

end

Thanks in advance !!!!!

[Ebraheem Menda]

Is there any other function to solve this If not possible with ode45.

Answer 1

[David Goodmanson]

Hi Ebraheem,

ode45 is fine with explicit time dependence in the calculation of xdot:

[t, x] = ode45(@smc5,[0, 10],[1, -2])
plot(t,x)
grid on

function xdot = smc5(t,x)
  xdot = [0 1;-3 -4]*x + [0; 1]*sin(2*t);
end

[Ebraheem Menda]

Thank you verymuch Mr.David.You have shown me the simple way to write the code for my problem.

i will again comeback with few more questions.

Thank You.