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

2015 11 11
1 个回答
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更新时间：2015 11 11
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0 个投票

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);

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 采纳的回答

Torsten
Torsten 2015-11-11
编辑：Torsten 2015-11-11

0 个投票

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.

3 个评论
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cha seung woo
cha seung woo 2015-11-11
编辑：cha seung woo 2015-11-11
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
Torsten 2015-11-11
编辑：Torsten 2015-11-11
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
cha seung woo 2015-11-11
编辑：cha seung woo 2015-11-11
thank you very much !!, i will ask you something later , too . good bye

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