When I use ode45 to solve a state space equation, the solution will be diverge. Interestingly, if I set the ma (which I've overstriked) to zero, the result will be converge.

clear
clc
xm_init = [0.09 0 0 0 0 0];
[t, xm] = ode45(@simplified_model, [0,200], xm_init);
plot(t,xm(:,1))

function dxm = simplified_model(t,xm)
kt = 1.8406e9;
kp = 1.3386e10;
ct = 5.2321e7;
cp = 2.35951e7;
It = 2.0444e9;
Ip = 3e9;
g = 9.8;
ma = 20000;
ka = 5000;
ca = 9000;
mt = 347460;
mp = 5452000;
Rt = 40;
Rp = 0.28;
Ra = 90;
M = [Ip 0  0
    0  It 0
    0  0  ma];
K = [kp+kt+mp*g*Rp             -kt                    0
    -kt      -mt*g*Rt+kt+ka*Ra*Ra+ma*g*Ra  -ka*Ra-ma*g
    0                    -ka*Ra-ma*g           ka];
C = [cp+ct      -ct         0
    -ct   ct+ca*Ra*Ra  -ct*Ra 
    0       -ct*Ra       ca];
Am = zeros(6,6);
Am(1:3,4:6) =...
    [1 0 0
    0 1 0
    0 0 1];
Am(4:6,1:3) =-M\K;
Am(4:6,4:6) =-M\C;
xm = [xm(1) xm(2) xm(3) xm(4) xm(5) xm(6)]';
dxm = Am*xm;
end

Answer 1

[David Goodmanson]

Hi Z^2,

It's not easy to say for sure without seeing the actual model, but I think there is a decent chance that your C matrix should not be

C = [cp+ct      -ct         0
    -ct   ct+ca*Ra*Ra  -ct*Ra 
    0       -ct*Ra       ca];

but rather

C = [cp+ct      -ct         0
    -ct   ct+ca*Ra*Ra  -ca*Ra 
    0       -ca*Ra       ca];

i.e. the (2,3) and (3,2) elements go from ct to ca. That change produces the following plot:

[宗祥]

Hi David

You're right! The problem is with my model, not with ode45!

Thank you very much for your help!