Dynamical System behaving strangely under high frequencies input
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Allan Andre do Nascimento
am 5 Jul. 2016
Kommentiert: Allan Andre do Nascimento
am 5 Jul. 2016
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.
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