An ellipsoidal off-line model predictive control strategy for linear parameter varying systems with applications in chemical processes

• Published in: Systems & control letters Vol. 61; no. 3; pp. 435 - 442
• Main Authors: Bumroongsri, P., Kheawhom, S.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2012; Elsevier
• Subjects: Algorithms; Applied sciences; Computer science; control theory; systems; Continuous stirred tank reactors; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Ellipsoids; Exact sciences and technology; Gain; Linear parameter varying systems; Mathematical models; Modelling and identification; Off-line model predictive control; Optimal control; Predictive control; Scheduling parameter; State feedback; Strategy; Off-line model predictive control; Scheduling parameter; Linear parameter varying systems; Continuous stirred tank reactors; Polytope; State feedback; Linear interpolation; On line; Robust stability; Feedback regulation; Linear parameter varying system; Scheduling; Continuous stirred tank reactor; Real time; Robust control; Model predictive control; Chemical reactor; Indirect method; Off line; Robustness; System identification; Sampling; Ellipsoid
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2012.01.003

In this paper, a novel off-line model predictive control strategy for linear parameter varying systems is presented. The on-line computational burdens are reduced by pre-computing off-line the sequences of state feedback gains corresponding to the sequences of nested ellipsoids. The number of sequences of nested ellipsoids constructed is equal to the number of vertices of the polytope. At each sampling instant, the smallest ellipsoid containing the currently measured state is determined in each sequence of ellipsoids and the scheduling parameter is measured. The real-time state feedback gain is calculated by linear interpolation between the corresponding state feedback gains. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two examples of continuous stirred tank reactors.