How can I linearize the simulink built in 'Custom Variable Mass 6DOF ECEF (Quaternion)'?

Hello everyone,

I am trying to simulate the trajectory of a two-stage rocket in Simulink. I am using the 'Custom Variable Mass 6DOF ECEF (Quaternion) Equation of Motion'. I would like to use a PID controller to control the pitch angle of the rocket (note, pitch angle is the output). The issue is that the above Equation of Motion is non-linear. Is there a way to linearize this EOM for the entire trajectory? the system is time dependent ( as the mass, velocity and trajectory changes with time).

link of the EoM:

https://nl.mathworks.com/help/aeroblks/customvariablemass6dofecefquaternion.html

Answer 1

[akshatsood]

Hi @Yama Shewan,

I understand that you want to linearize the Equations of Motion for the entire trajectory of a Two Stage Rocket model in Simulink. You might look into using the "Model Linearizer" App, a powerful tool within Simulink for linear analysis of non-linear systems. You can access the Model Linearizer by navigating to the "Apps" tab within the Simulink toolstrip and finding it under the "Control Systems" section.

Model Linearizer is particularly useful for systems with time-varying dynamics, such as your Two-Stage Rocket model. By using this tool, you can automate the linearization process and analyze the behavior of your non-linear system around specific operating points or along the entire trajectory. For a more detailed understanding of how to use the Model Linearizer for your specific application, I recommend referring to the following documentation:

https://in.mathworks.com/help/slcontrol/ug/modellinearizer-app.html

I hope this helps.

[Yama Shewan]

Dear @ akshatsood ,

Thank you very much for taking the time to assist me. I appreciate your clarification regarding the capabilities of Model Linearizer, especially its applicability to the entire trajectory of systems with time-varying dynamics. I was under the impression that it was primarily designed for specific operating points and limited to LTI systems. Your explanation is very useful to me. I will certainly give it a try and hope it proves beneficial for my work.

Once again thank you for your support.

Best regards,

Yama Shewan