I am trying to linearize the non-linear state space model of:
$\dot{x_1} = \frac{1}{C_p}(i_{pv} - x_2u)$
$\dot{x_2} = \frac{1}{L}(R_o(i_o - x_2) - R_Lx_2 - x_3 + (V_D + x_1 - R_mx_2)u) - \frac{V_D}{L}$
$\dot{x_3} = \frac{1}{C_o}(x_2 - i_o)$
So I take all the partials with respect to each state, I end up with:
$A = \begin{bmatrix} \frac{\partial \dot{x_1}}{\partial x_1} & \frac{\partial \dot{x_1}}{\partial x_2} & \frac{\partial \dot{x_1}}{\partial x_3} \\ \frac{\partial \dot{x_2}}{\partial x_1} & \frac{\partial \dot{x_2}}{\partial x_2} & \frac{\partial \dot{x_2}}{\partial x_3} \\ \frac{\partial \dot{x_3}}{\partial x_1} & \frac{\partial \dot{x_3}}{\partial x_2} & \frac{\partial \dot{x_3}}{\partial x_3} \end{bmatrix} = \begin{bmatrix} 0& -\frac{1}{C_{p}}u^*& 0\\ \frac{1}{L}u^* & \frac{1}{L}(-R_o - R_L - R_mu^*) & -\frac{1}{L} \\ 0 & \frac{1}{C_o} & 0 \end{bmatrix} $
and
$B = \begin{bmatrix} \frac{\partial \dot{x_1}}{\partial u} \\ \frac{\partial \dot{x_2}}{\partial u} \\ \frac{\partial \dot{x_3}}{\partial u} \end{bmatrix} = \begin{bmatrix} -\frac{1}{C_p}x_2^* \\ \frac{1}{L}(V_d + x_1^* - R_mx_2^*) \\ 0 \end{bmatrix}$
$\dot{x} = Ax + Bu$
Where the terms with the stars are the operating points. What I did to test this was simulate the non-linear system using a constant input, copied the steady-state values and used these values as my linearized system operating points and applied the same constant input to the system.
But when I simulate the linearized system, it doesn't even look stable. All states are oscillating, and x1 seems to be non-converging.
What am I doing wrong?