How do i resolve this problem ??????

this is state space model of dynamical system. in this problem, v is input of system. i'd like to put a function ( i made a function v below ) on v what should i do?

function xdot=example(t,x,v)

    xdot=zeros(2,1);
    xdot(1)=x(2);
    xdot(2)=(v-4*x(1)-7*x(2))/5;

end

//////////////////////////////////////////////////////

tspan=0:0.01:20;

 k=0;
    for time=0:0.01:20;
        k=k+1;
        if time<1
            v(k)=10*time;

        elseif time<=4
            v(k)=10;

        elseif time<=5
            v(k)=-10*(time-4)+10;

        else
            v(k)=0;

        end
    end

[t,x]=ode45(@example,tspan,[0 9],[],v);

Answer 1

[Torsten]

function main
tspan = [0 1];
[t1,x1]=ode45(@(t,x)example(t,x,1),tspan,[0 9]);
tspan = [1 4];
[t2,x2]=ode45(@(t,x)example(t,x,2),tspan,[x1(end,1) x1(end,2)]);
tspan = [4 5];
[t3,x3]=ode45(@(t,x)example(t,x,3),tspan,[x2(end,1) x2(end,2)]);
tspan = [5 20];
[t4,x4]=ode45(@(t,x)example(t,x,4),tspan,[x3(end,1) x3(end,2)]);

function xdot=example(t,x,flag)
if flag==1
  v = 10*t;
elseif flag==2
  v = 10;
elseif flag==3
  v = -10*(t-4)+10;
elseif flag==4
  v = 0;
end
xdot=zeros(2,1);
xdot(1)=x(2);
xdot(2)=(v-4*x(1)-7*x(2))/5;
end

Best wishes

Torsten.

[cha seung woo]

TO begin with, thank you very much . it's very helpful for me. but do u know another method by using matrix or extra . here is my second code .

function v=v1(time)

    k=0;

    for time=0:0.01:20;
        k=k+1;
        if time<1
            v(k)=10*time;

        elseif time<=4
            v(k)=10;

        elseif time<=5
            v(k)=-10*(time-4)+10;

        else
            v(k)=0;

        end
    end
end

function xdot=example(t,x,time,v1)

    xdot=zeros(2,1);

    v1=interp1(time,v1,t);

    xdot(1)=x(2);
    xdot(2)=(v1-4*x(1)-7*x(2))/5;

end

////////////////////////////////////////

tspan=0:0.01:20;
time=0:0.01:20;
[t,x]=ode45(@example,tspan,[0 9],[],time,v1);
plot(t,x(:,1)'--')

[Torsten]

No.

It's better to restart ODE45 each time there is a discontinuity in the first derivative of v.

You could alternatively try

function main
tspan = [0 9];
[t,x]=ode45(@example,tspan,[0 9]);

function xdot=example(t,x)
if t<1 
  v = 10*t;
elseif t>=1 && t<4
  v = 10;
elseif t>=4 && t<5
  v = -10*(t-4)+10;
else
  v = 0;
end
xdot=zeros(2,1);
xdot(1)=x(2);
xdot(2)=(v-4*x(1)-7*x(2))/5;
end

but my guess is that the solver will behave much worse than in my previous suggestion.

Best wishes

Torsten.

[cha seung woo]

thank you very much !!, i will ask you something later , too . good bye