Modelling of a revolving body in a black box model

I need to create a model of a camera gimbal. I didn't build it and can't look inside of it, so I need to treat it like a black box. The models created by the System Identification Toolbox work like a charme, but have one big Problem:

The scale of the gimbal goes from -180° to 180°. So if I want to move from Position 150° to -150°, it needs to cover a distance of 60°. But my model in Simulink moves the other way around and covers the 300° in the other direction. It doesn't "understand" that it's moving in a circle, that -180° = 180° and takes the longer route.

I thought of manipulating the state space model inside (something like if azimuth < 0 then azimuth = azimuth + 360). But only the input and the output have a "real" meaning and the states of the state space model are only relevant for computation and have no physical meaning (remember: black box model). So I don't know how to manipulate the states.

My Question: Is there an option in the System Identification Toolbox which makes it possible for the model to think in circles and not in scales? (stupid phrasing, but I hope you unterstand what I mean)