What are the states in the 4-order state-space model?

Dear All

I do not quite understand the state-scpace model formation and would like to ask for some simple explanation.

Im trying to fit real data with a 4-order state-space model. Number of inputs and outputs are 14 and 3 respectively. Hence, nx=4; Nk=ones(14,1)

(1) Why the resulting model has 4 states, the same as the model order nx?

(2) I guess the x(k) must be 4x1 vector in this case. Hence it seems that the x(k) does not have physical meaning. I would like to make estimation myself, so what (values) shall I use for x(k) to initialize the model:

x(k+1)=Ax(k)+Bu(k)

y(k) = Ax(k)+Du(k)

(3) Please, if possible, give some nice MIMO example or reference to it.

Thank you kindly!

[Azzi Abdelmalek]

what is the exact problem?

[grega]

The exact problem is that I would like to reproduce the sim.m function as described in demo: Control of a MultiInput Single-Output plant (Step-by-step Simulation. The following code is based on the demo example, but I get strange results for our MIMO system. Any strange coding noticed?

[A,B,C,D]=ssdata(MPCobj.Model.Plant);
Tstop=50;                       %Simulation time
x = MPCobj.Model.Nominal.X;
xmpc=mpcstate(MPCobj);          % Initial state of the MPC controller
r= r(1,:);                      % Output reference trajectory

% ---- record
YY=[]; UU=[]; XX=[];

% --- simulation
for t=0:round(Tstop/Ts)-1,
    XX=[XX,x];

      % Define measured disturbance signal
      v = data(t+1,iMD);

      % Plant equations: output update  (note: no feedthrough from MV to Y: D=0)
      y=C*x+D(:,iMD)*v';              % I get pritty wierd results at this line
      YY=[YY,y];

      % Compute MPC law
      u=mpcmove(MPCobj,xmpc,y,r,v);

      % Plant equations: state update
      x=A*x+B(:,iMV)*u+B(:,iMD)*v';%+B(:,3)*d;
      UU=[UU,u];
  end