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I've had obtained a mathematical model for the slip controller issue.

As you see I have the diffequation for the slip. and the input that force the system to zero error is provided as well. Now it's time to implement it in simulink or matlab.

I took a look at the example provided on mathwork. Here is a screen shot

The controller is supposed to force \lambda to a certain value. The optimal input is provided as well. So the reference block should be \lambda_desired. That's correct and then it goes to SMC and it gives the input to the system. What is that system? is it the dynamics of the slip? I have only the dynamics in mathematical way and no transfer function. You see that the dynamics of the slip is:

where T is the input . g is constant. R supposed to be observed by a observer. \lambda is slip and J is inertia. \mu is friction and assumed to be constant. \omega is the rotational speed on the wheel. How do I convert this to transfer function. I really need help since I ve done a lot and stuck in this. Please help me with this.

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# MATLAB Simulink: designing a 2nd order sliding controller

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