Σθεναρός έλεγχος δικτυωμένων συστημάτων

Abstract

This research work is concerned with robustness issues arising in Νetworked Cοntrοlled Systems - (ΝCS), where the main sources of uncertainty are the time-varying network-induced delays. In this framework the presented results concern robust stability analysis and synthesis of robust controllers. The NCS studied consist of a Linear Time Invariant continuous time plant and a discrete time controller. This configuration includes a time driven (periodic) sampler (taking samples from the sensors with constant sampling period h) and an event–driven controller which transmits the control command via the network to the event–driven actuator. Two modeling approaches for Networked Controlled Systems (NCS) with uncertainly varying bounded transmission delays and static discrete--time control laws are presented. Different models are offered for each case, all linked to the objective of designing robust discrete-time controllers. It is analytically shown how the careful mixing of asynchronous (event--driven) and synchronized (clocked) signals can lead to discrete time uncertain (possibly switched) systems, where results form robust control analysis and synthesis can be applied. After showing the implications of these modelling results for control synthesis purposes, sufficient conditions for the robust stability are given for each approach and a comparison of the conservatism of results is discussed The first group of robust stability results (one for each of the two discrete-time NCS models) is based on a singular value formulation, which although conservative, is extremely simple and has low computational cost The second one is derived and expressed via Linear Matrix Inequalities (LMI) and yields less conservative results at the expense of higher computational cost. Regarding the synthesis of Robust controllers, the following four methodologies were developed: 1. Synthesis of Robust Static State feedback 2. Synthesis of Robust Static State feedback via the “Guaranteed Cost Formulation” which combines stability and performance design objectives 3. Synthesis of Constrained Robust feedback controller (with a Piecewise Affine Structure) which respects the constraints on the control effort and the state (or output). 4. The previous result (Constrained Robust feedback controller) is then generalized for set-point tracking and for various types of network-induced delays (small, large and switching delays)