# Error: ode45 Must return a column vector?

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King Hin Wong on 16 May 2021
Commented: King Hin Wong on 16 May 2021
I'm trying to solve this problem involving a 2DOF system involving springs and dampers, and i've coded all of this below, including the state space matrix, this is urgent as this is due in 2 days, any help would be appreciated :)
function batch_timeresp
% the total time domain response
% System parameters
k3 = 15; k1 = 10.0; k2 = 10.0; m1 = 2.0; m2 = 6.0; L = 1.0; c = 1; ct = 0.5; g = 9.81;kequi=5;
%ball
zeta1 = (c/(2*sqrt(m2*k3)));
%block
zeta2 = (ct/(2*sqrt(m1*kequi)));
%damped natural freq of block
om02=sqrt(kequi/m2);
omd2=om02*(sqrt(1-(zeta2)^2));
%damped natural freq of ball
om01=sqrt(k3/m1);
omd1=om01*(sqrt(1-(zeta1)^2));
T1 = 0.01*((2*pi)/om02);
T2 = 1.50*((2*pi)/om01);
Tpulse = T2-T1;
% Excitation parameters
Ft = 30;
Im = ((Ft*Tpulse)/2);
% State space system matrix and coupling
A=[0,0,1,0;0,0,0,1;-(k1+k2)/(m1+m2),0,-c/(m1+m2),0;0,-k3/(m1*(L^2)),0,-ct/(m1*(L^2))]; %state space matrix
S=[1,0,0,0;0,1,0,0;0,0,1,(m1*L)/(m1+m2);0,0,(m1*L)/(m1*(L^2)),1]; %coupling
Sinv=inv(S);
gmat = [0;0;-g;g/L]; %gravity terms
Fmat=[0;0;Im/(m1+m2);(2*Im*L)/(m1*(L^2))]; %impulse force
% Numerical integration
tspan=linspace(0,5,1e3);
X0=[0;0;0;0];
[T,X]=ode45(@ssmodel,tspan,X0);
% Results
figure
subplot(2,1,1), plot(T,X(:,1)), ylabel('x [m]')
subplot(2,1,2), plot(T,X(:,2)), ylabel('dx/dt [m/s]'), xlabel('time [s]')
function dx=ssmodel(t,x)
% State-space model of 1 DOF system
dx=(A*x+gmat+Fmat).*Sinv;
end
end

Alan Stevens on 16 May 2021
Like this?
% the total time domain response
% System parameters
k3 = 15; k1 = 10.0; k2 = 10.0; m1 = 2.0; m2 = 6.0; L = 1.0; c = 1; ct = 0.5; g = 9.81;kequi=5;
%ball
zeta1 = (c/(2*sqrt(m2*k3)));
%block
zeta2 = (ct/(2*sqrt(m1*kequi)));
%damped natural freq of block
om02=sqrt(kequi/m2);
omd2=om02*(sqrt(1-(zeta2)^2));
%damped natural freq of ball
om01=sqrt(k3/m1);
omd1=om01*(sqrt(1-(zeta1)^2));
T1 = 0.01*((2*pi)/om02);
T2 = 1.50*((2*pi)/om01);
Tpulse = T2-T1;
% Excitation parameters
Ft = 30;
Im = ((Ft*Tpulse)/2);
% State space system matrix and coupling
A=[0,0,1,0;0,0,0,1;-(k1+k2)/(m1+m2),0,-c/(m1+m2),0;0,-k3/(m1*(L^2)),0,-ct/(m1*(L^2))]; %state space matrix
S=[1,0,0,0;0,1,0,0;0,0,1,(m1*L)/(m1+m2);0,0,(m1*L)/(m1*(L^2)),1]; %coupling
Sinv=inv(S);
gmat = [0;0;-g;g/L]; %gravity terms
Fmat=[0;0;Im/(m1+m2);(2*Im*L)/(m1*(L^2))]; %impulse force
% Numerical integration
tspan=linspace(0,5,1e3);
X0=[0;0;0;0];
[T,X]=ode45(@(t,x) ssmodel(t,x,A,gmat,Fmat,Sinv),tspan,X0);
% Results
figure
subplot(2,1,1), plot(T,X(:,1)), ylabel('x [m]')
subplot(2,1,2), plot(T,X(:,2)), ylabel('dx/dt [m/s]'), xlabel('time [s]')
function dx=ssmodel(~,x,A,gmat,Fmat,Sinv)
% State-space model of 1 DOF system
dx=Sinv*(A*x+gmat+Fmat); %%%%%%%%%%%%%%%%%%%%%%
end
King Hin Wong on 16 May 2021
Solved! Thank you so much, have a nice day :)