I want any PAPERS about Multivariable PID controllers, or PART/CHAPTER of a BOOK about this topic. would you help me please?

 

Can you describe the problem you are trying to attack. For 2x2 systems PID control can and has been applied - but is very cumbersome to tune
and thus not recommended. Model Based Control is much easier. For larger and non-square systems there is no way around MBC.

A very simple MBC algo can be found at "www.act-control.com":www.act-control.com under "Tecnology"

 

I won't argue that it is always easier, but MIMO problems have been solved for years with PID-based approaches, even non-square ones. Feed forward, ratio, cascade, split range or parallel output, override control, valve position control, and decoupling and inferential strategies can be deployed to handle many non-square systems and provide some level of constraint control and optimization. MBC may be difficult to deploy in nonlinear systems which require a high degree of turndown. There are systems like boilers where PID-based solutions are widely used, well understood, and quite effective, which is probably one reason why MBC is seldom applied to
them. So while I am actually an advocate of MBC, I will play devil's advocate here and suggest we never say never.

Regards,

Lou Heavner
Emerson Process Management