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

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?