Dynamical System behaving strangely under high frequencies input

1 次查看（过去 30 天）

显示更早的评论

Allan Andre do Nascimento 2016-7-5

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/293787-dynamical-system-behaving-strangely-under-high-frequencies-input

评论： Allan Andre do Nascimento 2016-7-5

在 MATLAB Online 中打开

Dear all,

I have been simulating the following dynamical system in matlab:

    w=0.04*(1-cos(8*pi*t)).*(heaviside(t-0.5)-heaviside(t-0.9));
    g=9.81;
    m1 = 290;
    m2 = 59;
    k1 = 16812;
    k2 = 190000;
    b1 = 1000;
    alfa=4.515*(10^13);
    beta=1;
    gama=1.545*(10^9);
    tau=(1/30);
    Ps=10342500;
    A=3.35*(10^(-4));
    dxdt=zeros(6,1);
    dxdt(1) = x(2);
    dxdt(2) = -(k1/m1)*x(1)-(b1/m1)*x(2)+(k1/m1)*x(3)+(b1/m1)*x(4)+(A/m1)*x(5);
    dxdt(3) = x(4);
    dxdt(4) = (k1/m2)*x(1)+(b1/m2)*x(2)-((k1+k2)/m2)*x(3)-(b1/m2)*x(4)-(A/m2)*x(5)+(k2/m2)*w;
    dxdt(5) = -alfa*A*x(2)+alfa*A*x(4)-beta*x(5)+gama*x(6)*sign(Ps-(x(5)*sign(x(6))))*sqrt(abs(Ps-(x(5)*sign(x(6)))));
    dxdt(6) = -(1/tau)*x(6)-(1/tau)*((K(1,1))*x(1)+(K(1,2))*x(2)+(K(1,3))*x(3)+(K(1,4))*x(4)+(K(1,5))*x(5)+(K(1,6))*x(6));

This is a controller for a quarter car vehicle suspension. Its behaviour is fine as long as I keep the input frequency (inside the cos function) low. As I increase the frequency, states behaviour change and it turns out that oscilations never die. I have been thinking for days and I can not find a reason for this to happen. Could someone, please help me to discover what is going on?

Thank you all very much.