is there any possibility to linearize nonlinear system and change into state space system

my problem is huge 31dof problem, I figure it out how to solve. But the main problem is linearization so i create fuction which represents the 31 equations of motion and parameters and use simulink to linearize. But its not working i want state space system A,B,C,D from my equations. Is there any method to solve ode and convert into state space. Please help me

Answer 1

[Tim Grunert]

Hey, if you can set up your dynamical equations in explicit form: dx/dt = f(x,u) and y = g(x,u) e.g. using the symbolic math toolbox you can easily linearize your system around a steady state (x0, u0).

As an example your system matrix results from: A = jacobian(f, x) After it you need to replace all remaining x with x0 and u with u0 in A.

For the input matrix likewise shown but with B = jacobian(f,u) For C and D using g instead of f.

We published a small tool to handle nonlinear dynamical systems symbolically in MATLAB. There the feature of linearization is implemented: https://github.com/odesca/ODESCA/releases

[Saad Alshammari]

can you write simple code as example?