Hello. in order to determine the suitable surface, we must to consider that it is usualy to s= edot + landa*e . my mind is determine the surface based on error(e). we must to consider that the diffrentially order of surface exact one order less.(xdoubledot+xdot+2=0) 

Hi Javad Azizabadi

 thank you for answring, Actually I know that, this what i mean by PD sliding surface, but my question was a bout other type of sliding srface may used auxilary state

Cheers

ok. you are right. it is clear that the surface is invariable time. one of the caual of using pi or i is to reduse the diffrentially order . because the dissrential operator is one of the way to increase the noise. for exp. n= 0.001sin(10000t) ,(n=noise) so wdot= 10cos(10000t). and is t not good. so must of the surface is pd and not  pid. 

The  desired performance during the sliding phase  will decide the selection of sliding surface. Sliding surface may be linear, nonlinear also. Convergence time and steady precision performace will change with the type of sliding surface selection.

Dear Dr. Al-ghanimi,

try and see my site at ResearchGate and download the required papers.

Best Regards,

Hazim

Hazim Hashim Tahir ,Pyare mohan Tiwari    ,Javad Azizabadi, for your answers it waa realy usefull

Thanks, Deepak Fulwani  ,Hazim Hashim Tahir, 

Dear Ali

It's a general question, but you must to know that if you want to have a best result, sign function help you to have a good result  but it has some challenges. you can design higher order SMC or terminal SMC also. if you would like to have any information you also can follow my work.