What is the script code of the PI controller with saturation and rate limiter in the ode form?

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I want to implement below box in the script form. How to do it? I converted the PI block in ode as
du/dt = Wt_rated - wt;
B_ref = Kp *(Wt_rated - wt) + Ki *u
where wt is coming from another ode equation
dwt/dt= (Pt - Pg)/wt;
But I don't able to code saturation and rate limiter block.
Also how to code hysteresis comparator?

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