How to update x from ode45 result y? how to see the plot of y from t = 0 to the end of simulation?

%State Space Model of Literature from X.PENG
%Coded by Hng Ming Yang

function dx = system1(t,x)  %#ok<*INUSL>

      %Defining the constants a1:a5 represent product of (volume rate*air pressure*conductivity) 
      a1 = 8.657e3;
      a2 = 2.3324e3;
      a3 = 6.8269e3;
      a4 = 12078;
      a5 = 10681;

      %Defining the heat flux which will varies if different set up
      b1 = 1.9845e3;
      b2 = 1.1276e3;
      b3 = 913.8;
      b4 = 649.8546;
      b5 = 1.4396e3;

      %System Matrix formation
      A = [-484.9/a1 84.6/a1 51.0/a1 152.4/a1 60.9/a1;
          49.1/a2 -120.7/a2 0 0 45.1/a2;
          225.2/a3 0 -485.1/a3 215.6/a3 0;
          64.1/a4 0 390.0/a4 -532.3/a4 48.2/a4;
          10.4/a5 9.6/a5 0 134.2/a5 -226.3/a5];

      %Input Matrix formation
      B = [1/a1 0 0 0 0;
          0 1/a2 0 0 0;
          0 0 1/a3 0 0;
          0 0 0 1/a4 0;
          0 0 0 0 1/a5];

      %Measurement matrix C1:C5 each simulating temperature changes from zone 1
      %to zone 5.
      C1 = [1 0 0 0 0];
      C2 = [0 1 0 0 0];
      C3 = [0 0 1 0 0];
      C4 = [0 0 0 1 0];
      C5 = [0 0 0 0 1];

      %output is Y = CX, in this case D = 0 
      D = 0;

      % Initialising the Original Temperature
      X0 = [32;33;33;36;31];

      global u;

      dx = A*x + B*u;
  end

% and then in another script i run the main file,as follows

setpoint = 25;
global u;
x=[35;34;33;35;34]; %initial value for x
ts=0.01; %Sampling time
t0=0;
TS=600; %Total simulation time

for j=1:TS/ts  
 T=[T t0+(j-1)*ts];
end

for j=1:(TS/ts-1)
    t=T(j);      

      kp = [500 0 0 0 0;
            0 500 0 0 0;
            0 0 500 0 0;
            0 0 0 500 0;
            0 0 0 0 500];

      ki = [10 0 0 0 0;
            0 10 0 0 0;
            0 0 10 0 0;
            0 0 0 10 0;
            0 0 0 0 10];

      integral = 0;

      DeltaE1= setpoint - x(1);
      DeltaE2= setpoint - x(2);
      DeltaE3= setpoint - x(3);
      DeltaE4= setpoint - x(4);
      DeltaE5= setpoint - x(5);

      integral = integral + [DeltaE1;DeltaE2;DeltaE3;DeltaE4;DeltaE5]*ts;

      u = kp*[DeltaE1;DeltaE2;DeltaE3;DeltaE4;DeltaE5] + ki*integral ;

      [t, y] = ode45(@system1, [T(j) T(j+1)], x);
      x(1)=y(length(y(:,1)),:);
      x(2)=y(length(y(:,2)),:);
      x(3)=y(length(y(:,3)),:);
      x(4)=y(length(y(:,4)),:);
      x(5)=y(length(y(:,5)),:);

end

plot(t,y);

% i can't run the file due to wrong updating of x values from y, 
% i can't get a plot that shows y plot from initial to end of simulation, instead the plot always shows me the output of the final "loop", which the time span is a few milliseconds.

Thank you guys, i am sorry for the trouble caused.

Answer 1

[Jordan Ross]

Hi Ming,

There are a few issues with the code that you provided.

1. The value of "T" is undefined on the following line of your script:

>> T = [T t0+(j-1)*ts];

2. When you set the values of "x" in your "for" loop you have an error because you are trying to store a row-vector of length 5 to a scalar. You should instead do the following:

>> numYCols = size(y,2); % get the number of columns of y.
>> x(1:(1:numYCols)) = y(length(y(:,1)),:);

Also note that you are going to have a problem storing values into "x" because you use "x" as an input to the "ode45" function. This function expects "x" to be a column-vector, not a matrix.

For more information about indexing into vectors and matrices please see: http://www.mathworks.com/help/matlab/learn_matlab/array-indexing.html