A unified approach to deal with multivariable constrained process control problems

FABRICIO GARELLI; RICARDO J. MANTZ; HERNÁN DE BATTISTA

Advances in Mechanical Engineering Research.

Nova Science Publishers Inc.

Lugar: New York; Año: 2010; p. 255 - 275

In every real control loop exist physical limits, security bounds or system dynamic behaviorsthat constrain the reachable closed-loop performance. In particular, physical and/or technological limitations of actuators give rise to plant input constraints, whilst safety operationregions or non-minimum phase characteristics generally affect the evolution of the controlledvariables or system outputs. In a multivariable or MIMO (Multiple-Input Multiple-Output)process, the effects of these constraints are worsened because of the presence of directionsassociated to input/output vectors and, even more important, the crossed coupling or interactions between the system variables.This chapter deals with some relevant practical problems of multivariable process control,which are consequence of crossed interactions, control directionality and input or outputconstraints. To this end, recently proposed control strategies are unified in a generalizedframework to deal with both input and output constraints. The resulting control strategy,which is herein called sliding mode reference conditioning (SMRC) technique, makes use ofvariable structure control (VSC) and sliding modes (SM) related concepts in order to preventthe process from violating its restrictions while minimizing their undesired effects. Slidingregimes are just transiently employed by SMRC over bounding surfaces corresponding to theunavoidable process constraints, and they are confined to an auxiliary reference conditioningloop in the low-power side of the system. This way of operation permits accomplishingdistinctive properties and design methodologies with respect to the conventional applicationsof VSC and SM.The chapter is outlined as follows. Firstly, the basic ideas behind SMRC are introducedfor systems involving biproper transfer function descriptions, such as proportional orproportional-integral industrial controllers. Then, the methodology analysis and design isextended to deal with strictly-proper systems. This general analysis is performed independentlyof the type of constraint. From then on, some applications or case studies of practicalinterest in multivariable control are discussed and results are presented: (i) the preservationof control directionality and full dynamic decoupling even in the presence of actuator saturation,(ii) the limitation of remaining coupling in partial decoupled non-minimum phaseprocesses, and (iii) a way of delimiting the crossed interactions in industrial decentralizedor multi-loop control of multivariable processes.