How can I linearize "signum" function using "Linear Analysis Toobox" ?

image of the SIMULINK Model is given below ...

Regards

Habib

Answer 1

[Matt J]

It's already linearized isn't it? I assume you mean you want to linearize it for small variations around some nominal point. Since signum is already locally linear (in fact locally constant), I don't see what there is to modify.

[Habib RK]

Yes, It is Linear when the system goes to a steady state, but I need a linear model of this system, when it(system) is feed with a unit Step input, that would make a signum function a highly non-linear ...

When I ask SIMULINK to linearize between input and output points, it produces this error

"The Simulink model could not be linearized because the blocks listed below have individual linearizations with A, B, C, or D matrices which are not finite. Either linearize at another operating point or remove the blocks."

Regards

Habib

[Matt J]

I assume that's because you're trying to linearize the signum block at 0, where it is discontinuous. You cannot linearize discontinuities, I don't imagine, nor any other operating point that isn't at least once continuously differentiable.

You could possibly replace the pure signum with use a continuous approximation to the signum (e.g., f(x) = arctan(x)) and linearize that.

[Habib RK]

Thanks mate, for the arctan() approximation, I guess that would work...

Regards

Habib

[Matt J]

A sigmoid would probably be even better.