How can I find the transfer function of this system and calculate the unit step response?

x1_dot=v1; v1_dot=(1/M1)*(-F-Ks1*(x1-x2)^3-Kd1*(v1-v2)); x2_dot=v2; v2_dot=(1/M2)*(Ks1*(x1-x2)^3+Kd1*(v1-v2)-Ks2*x2^3-Kd2*v2) y=x1-x2;

x1,v1,x2,v2 are the states and y is the output. F is the input. Ks1, Kd1, Ks2, Kd2 are constants. Since there is the expression (x1-x2)^3 in the equations I don't know how to find the transfer function to calculate the unit step response.

Answer 1

[Arkadiy Turevskiy]

Transfer function is a concept that applies to LTI ( linear time-invariant) systems.As you point out in your question, your system is non-linear. The easiest way to simulate such a nonlinear system is using Simulink. Using basic blocks such as Sum, Integrator, and Gain you can construct and simulate your model .

You can also linearize your nonlinear model using Simulink Control Design as explained on the linearization page. This will provide a transfer function at a specific operating point you choose.