Output Feedback Invariant Sets with Application to Design of PID Controllers for Constrained Systems
PID Controllers, Linear Systems, Invariant Sets, Reference Tracking, Constrained Control, Data Cluster Analysis.
It is a fact that most industrial systems are subject to constraints or limitations in their states and in the control action. Consequently, an imperative issue to be taken into account in current compensation methods is the direct integration of these constraints in the controllers design. Many research workshave beencarried out in order to develop controllers for such systems, however, few works aimed at the characterization of the problem with constraints in the design of the most common fixed-order controllers in industrial environments, the PID (proportional-integral-derivative) controllers, have been reported. The closest that can be found in terms of incorporating information on processes constraints (in general, of the actuators) to PID design is the implementation of Anti-Windup strategies. Then, in this work, a proposal is first presented for the formulation of discrete-time PI controller with constraints for linear systems, for constant references tracking using set-invariance theory, particularly, the theory of coutput-feedbackcontrolled-invariant polyhedral sets.A methodology for the calculation of an on-line control action for dynamic output feedback is also proposed. Results of numerical experiments are presented, which point towards the applicability of this methodology. In addition, the use of dynamic feedback to expand the condition of invariance by output feedback, the design of PID controllers with constraints using data cluster analysis techniques and the extension of these techniques to linear systems with time-delay are presented as subjects of future research.