On networked control system stabilisation under variable sampling using a reset integrator

ESTEBAN N. OSELLA; JULIO BRASLAVSKY

2013-01-15/2013-03-01

Informática (software)

Energia-Varios

The material in this report summarises the main results of the activities during the visit of Esteban Osella, which took place along 6 weeks between January/February 2013. Esteban Osella was under the supervision of Dr. Julio Braslavsky at CSIRO, and Dr. Maria M. Seron at University of Newcastle, Australia, where other studies related with Networked Control Systems and Fault Tolerant Control were performed. During this visit to CSIRO, we studied the problem of providing stability conditions for a continuous-time plant controlled using a Networked Control System (NCS). The NCS is a scheme in which the controller interacts with the plant using a shared resources network. Since constant sampling may not be possible, the stability of the system must hold irrespective of the way in which the time between samples change. In some of our previous works, we considered that it was the controller itself the one that, in advance, decided when it will take the next sample and control action, controlling not only the process but also the communication data rate. For such a case, the previous knowledge has two main consequences. On one side, it simplifies the stability analysis. On the other, it reduces the applicability of the obtained solution. In the present work we are to relax the conditions of the considered problem by assuming not only that the sampling instants are non-necessarily uniform, but also, the controller has no information regarding when the next sampling and control action will occur. Thus, the control action may have to be dynamically adjusted. Such time-varying corrections motivate the definition of a generalised sample and hold function is required. With the aim to extend previous work based on the observability gramian, the main objective during this visit was to obtain more general stability conditions for the case where state and output feedback stabilisation control is applied using a NCS where the next sampling instant is unknown. This report presents the basic results, establishing conditions for feedback stabilisation using time-varying state feedback and a resetting integrator. Potential extensions to state estimation are outlined and remain as a topic for further study.