Two Degree of Freedom Helicopter Model

In 2-DOF helicopter, a coupled 2input-2output system can be achieved due to coupling between the pitch and yaw motor torques. The linear 2-DOF helicopter state-space matrices are

$$\begin{align*} A&=\left[\matrix{ 0 &0 &1 &0\cr 0 &0 &0 &1\cr 0 &0 &-{B_{p}\over J_{eq{\_}p}+m_{heli}{l_{cm}}^{2}} &0\cr 0 &0 &0 &-{B_{y}\over J_{eq{\_}y}+m_{heli}{l_{cm}}^{2}}}\right],\\ B &=\left[ \matrix{ 0 &0\cr 0 &0\cr \dfrac{K_{pp}u_{p}}{J_{eq{\_}p}+m_{heli}{l_{cm}}^{2}} & \dfrac{K_{py}u_{y}}{J_{eq{\_}p}+m_{heli}{l_{cm}}^{2}} \cr \dfrac{K_{yp}u_{p}}{J_{eq{\_}y}+m_{heli}{l_{cm}}^{2}} & \dfrac{K_{yy}u_{y}}{J_{eq{\_}y}+m_{heli}{l_{cm}}^{2}} \cr } \right], \\ C &=\left[\matrix{1 &0 &0 &0\cr 0 &1 &0 &0}\right], D=\left[\matrix{0 &0\cr 0 &0}\right], \end{align*}$$

where $\theta(t)$ is the pitch angle and $\psi(t)$ is the yaw angle. $u_p$ and $u_y$ are the control signals applied to pitch and yaw motors, respectively. The amounts of parameters used in this formula are written in the table below.