can't get same results Matlab generates - c++

Question

Take a look at the following transfer function:
With Matlab Simulink:
The result is
In State-space representation, the system can be modeled as follows:
In Matlab, we can model the system in the state-space representation:
which yields the following plot:
which is exactly the result generated by using transfer function. I'm trying to generate same results with odeint but failed. This is the code
#include <iostream>
#include <Eigen/Dense>
#include <boost/numeric/odeint.hpp>
#include <iomanip>
#include <fstream>
using namespace std;
using namespace boost::numeric::odeint;
typedef std::vector< double > state_type;
void equations(const state_type &y, state_type &dy, double x)
{
Eigen::MatrixXd A(3, 3), B(3,1);
/*
x = y[0]
dx = y[1] = dy[0]
ddx = y[2] = dy[1]
dddx = dy[2]
*/
const double r(1);
A << 0, 1, 0,
0, 0, 1,
-24, -26, -9;
B << 0, 0, 1;
//#####################( ODE Equations )################################
Eigen::MatrixXd X(3, 1), dX(3,1);
X << y[0], y[1], y[2];
dX = A*X + B*r;
dy[0] = dX(0,0);
dy[1] = dX(1,0);
dy[2] = dX(2,0);
}
int main(int argc, char **argv)
{
const double dt = 0.01;
runge_kutta_dopri5 < state_type > stepper;
state_type y(3);
// initial values
y[0] = 0.0; // x1
y[1] = 0.0; // x2
y[2] = 0.0; // x3
ofstream data("file.txt");
for (double t(0.0); t <= 5.0; t += dt){
data << t << " " << 2*y[0] << " " << 7*y[1] << " " << 1*y[2] << std::endl;
stepper.do_step(equations, y, t, dt);
}
return 0;
}
And this is the result for all state vector
None of the preceding variables match the results generated by Matlab. Any suggestions to fix this code?

Answer 1

Look at the expression you have for y. When you multiply a 1x3 matrix with a 3x1 matrix, the result should be a 1x1 matrix, where the value of the single element is the dot product of the two matrices. What you're currently doing is element-wise multiplication when you write to data instead of calculating the dot product.