You will have to do it in the same way as you would have done it if it weren't a disturbance input i.e. you will have to consider the disturbance as the primary input and then perform an nlarx on it.

Dear Anirudh,

According to the description of your system that you give, you can do the following assumptions:

-consider Disturbance as an input or an unknown input.

-In This case the system becomes multivariable you'll have to use a nonlinear multivariable identification method. Here are links and some items attached dealing with different cases of system identification.

- Identify Nonlinear Black-Box Models Using System Identification App ...

https://www.mathworks.com/.../identify-nonlinear-bla...

- Observer/Kalman Filter Identification

www.dartmouth.edu/~mqphan/sidhlights.html

Best regards

Thank you very much Sir.

Please refer to these articles:

https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller

https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance

https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design

Article From PID to Nonlinear State Error Feedback Controller

Article Improved Sliding Mode Nonlinear Extended State Observer base...

Article On the Improved Nonlinear Tracking Differentiator based Nonl...