Is you know the Fixed construction of PID controller could not be covered the wide range of operating points. So, slide modes controller could be achieved the targets goal
I would like to give a comparaison between Sliding mode control and linear control.
Linear P control can be transformed to SMC sign function
PD control ==> Twisting or suboptimal
Linear Backstepping ==> Higher Order Sliging Mode
Now
PI controller ==> Supertwisting Controller
PID ==> ???
Recently researchers (including me) are working on generalising Supertwisting to Higher Order. So you can have robust version of PID by using the Higher Order Supertwisting.
Plz refer to the work of Fridmann in CDC 15 (published since one month). He call the proposed controller : continuous twisting controller, in reality it's second order supertwisting.
You can also refer to my proposed Higher order supetwisting (under review) for arbitrary order.