Help with Error using ==> plus message

I am getting an Error using ==> plus message when I run the following code:

>> clear
% Continuous-time Model of Mass-Spring-Damper
A=[0 0  0 1 0 0; 0 0 0 0 1 0; 0 0 0 0 0 1; -.1 .1 0 -.05 .05 0; .001 -.201 .2 .0005 -.0305 .03;
    0 2 -2 0 .3 -.3];
B=[ 0 0; 0 0; 0 0; 1 0; -.01 .01; 0 -.1];
G=[ 0; 0; 0; 0; 0; .5]; dt=0.5;  
%Conversion to Discrete-time
ddt = linspace(0,dt,200);
summ = zeros(6); %nx = number of state varicables
for i = 1:200
    summ = summ + expm(A*ddt(i));

Ad = expm(A*dt);
Bd = summ*dt/200*B;  
Gd = summ*dt/200*G;
end
%Simulate Forced Process
NNN=15/dt;  ttt=zeros(1,NNN);  xxx=zeros(6,NNN); 
x0=[1; .1; .5; 0; 0; 0]; xxx(:,1)=x0;
for kk=1:NNN-1
    ttt(kk+1)=dt*kk; uk=0; wk=0;
    xxx(:,kk+1)=Ad*xxx(:,kk) + Bd*uk + Gd*wk;
end
plot(ttt,xxx(1,:),'-k*',ttt,xxx(2,:),'-ko')
legend(' Mass Position',' Mass Velocity')
xlabel('Time (seconds)')
ylabel('State Variables (m or m/s)')
??? Error using ==> plus
Matrix dimensions must agree.

I think it is in my xxx(:,kk+1)=Ad*xxx(:,kk) + Bd*uk + Gd*wk; line of code but I can't figure out why... Any help will be appreciated

Answer 1

[Azzi Abdelmalek]

Just change this part of the code

uk=0;
wk=0;
for kk=1:NNN-1
ttt(kk+1)=dt*kk;
xxx(:,kk+1)=Ad*xxx(:,kk) + uk + Gd*wk;
end

Answer 2

[Walter Roberson]

Examine the expression

Ad*xxx(:,kk) + Bd*uk + Gd*wk

Ad is expm(A*dt). A is 6 x 6, dt is a scalar, so A*dt is 6 x 6 and expm() of a 6 x 6 is in turn 6 x 6.

xxx is 6 x NNN, k is a scalar, so xxx(:,k) is 6 x 1.

6 x 6 matrix-multiply by 6 x 1 gives 6 x 1, so Ad*xxx(:,kk) results in 6 x 1.

Bd is summ*dt/200*B . summ is zeros(6) so it is 6 x 6. dt is a scalar, and 6 x 6 * a scalar is 6 x 6. B is 6 x 2, and 6 x 6 matrix-multiply by 6 x 2 gives 6 x 2.

uk is a scalar. 6 x 2 * a scalar gives 6 x 2, so Bd * uk is 6 x 2. Now uk is 0, so the 6 x 2 matrix will be all 0.

Gd is summ*dt/200*G. As per above, summ*dt/200 is 6 x 6. G is 6 x 1 and 6 x 6 matrix-multiply by 6 x 1 gives 6 x 1.

wk is a scalar. 6 x 1 * a scalar gives 6 x 1, so Gd * wk is 6 x 1. Now wk is 0, so the 6 x 1 matrix will be all 0.

You are thus attempting to add a 6 x 1 matrix together with zeros(6,2) together with zeros(6,1). The result is clearly going to be an error message.

If you are going to set uk and wk to 0, then unless you want the error, you should probably reduce the expression to just xxx(:,kk+1)=Ad*xxx(:,kk) without the Bd and Gd terms.