How to get sensitivity matrix of a system from a full non-linear model?

Hi!

I am doing a simple turbojet engine model( steady state) model for on-design and off-design performance simulations. I have written the full code in matlab and now am porting it to simulink. I have evaluated the partial derivatives of the major performance parameters like thrust with respect to input parameters like calorific value of fuel. Now I need to do the same with Simulink! I have made the model of the engine. Are there any ways in simulink where I can specify two input parameters and two output parameters and ask the system to evaluate the partial derivatives of the 2 outputs wrt the 2 inputs? The output should be the 2x2 matrix.

Thank you for your time!

Answer 1

[Arkadiy Turevskiy]

Simulink Control Design lets you linearize the nonlinear model to get a MIMO transfer function describing dynamics between your inputs and outputs. You could then just evaluate this transfer function at DC to get your sensitivities.

Note that it will be important to figure out/specify the operating point around which you want to linearize, i.e., is your engine rotor speed 1,000 rpm or 6,000 rpm? Depending on that, sensitivities could vary quite a bit.

[Balaji]

My model, as of now is time independent. It is a set of algebraic equations with lot of iterations while loops inside for map lookups. Will the linearization approach work on algebraic sets with while loops inside?

Thank you for your time.

[Arkadiy Turevskiy]

It might, hard to say without trying.