Networked control systems with delay [Tutorial

Abstract

The issue of time-delay is of primary importance in different areas of modern control systems and instrumentation such as power systems, industrial process control including the steel and oil industry, machining and metallurgical processes, remotely operated robots and control over computer networks (or as it is also known Networked Control Systems) to name a few. A Networked Control System (NCS) is a feedback control system where the feedback loops are closed by means of an electronic network. It is well known that Networked (Control) Systems are not subject to the same design assumptions as non-networked systems, a fact that is mainly due to the inevitable presence of network delays and packet drops. In a typical closed-loop NCS, the state is sampled periodically, transmitted through the network, becomes available to the controller, which after computing the control action, transmits the sampled signal to the event-driven actuator after an uncertain or constant but unknown delay. The plant receives this command via a Zero Order Hold device (ZOH) after a delay τ, which models the sum total of the involved transmission delays. These network-induced delays appear in the information flow between the sensor and the controller (delay τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sc</sub> (k)), as well as between the controller and the actuator (delay τ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ca</sub> (k)), where k denotes the dependence on the k <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> sampling period.