Output feedback control of constrained descriptor systems: a case study of a hydraulic tank system

Abstract

A novel technique is proposed for output feedback control of constrained linear discrete-time causal descriptor systems. In particular, it is shown how linear state and control constraints can be satisfied by using only output measurements corrupted by unknown but bounded noise. To this end, conditions are established under which a polyhedron contained in the set defined by the state constraints can be made invariant through output feedback. The control input which enforces the constraints can be computed online through the solution of linear programming problems. The proposed technique is then applied to the control of a hydraulic three-tank system. Simulated as well as experimental results illustrate the proposed technique and indicate that it can be potentially used in practical situations.

Dynamic output feedback control of constrained descriptor systems

“…can be checked using the necessary and sufficient condition seen in Araujo et al (2012b) and Dorea (2009). This approach can be justified by the absence, to date, of a method for the computation of an o.f.c.i.…”

“…Two numerical examples, one of which uses the validated model of a three-tank liquid level system (Santos et al, 2009), show the merit of the methodology and its potential use in real-world problems. In the later example discussed, a comparison with static output feedback design using set invariance presented in Araujo et al (2012b) makes it clear that a better performance can be achieved by means of the dynamic output feedback design presented in this work.…”

“…Recently, the set invariance approach has been successfully extended to descriptor systems in the context of both constrained control by means of controlled-invariant polyhedra Araujo et al, 2012b) and state estimation with error limitation by means of conditioned-invariant polyhedra (Araujo et al, , 2012a.…”

“…Descriptor systems have great relevance in theoretical and practical aspects of control fields, as descriptor models give a richer representation of robotic systems, electrical circuits and chemical processes, among other examples (Dai, 1989;Lewis, 1986;Luenberger, 1978;Verghese et al, 1981). Recently, the set invariance approach has been successfully extended to descriptor systems in the context of both constrained control by means of controlled-invariant polyhedra Araujo et al, 2012b) and state estimation with error limitation by means of conditioned-invariant polyhedra (Araujo et al, , 2012a.…”

Static output feedback control design for constrained linear discrete‐time systems using data cluster analysis

“…Such control actions can be computed online, through the solution of several LP problems. This concept has been further extended to linear parameter varying [24] and descriptor systems [25, 26]. An artificial neural network has also been proposed to implement the controller resulting from the solution of the aforementioned LPs [27].…”