Algebraic Design of Multi-rate Control Systems for Environments with Limited Random Delays

Nowadays, in industrial control applications, is rather usual to sample and update different variables at different rates, although it is common to consider all these activities equally and regularly spaced on time. These applications can be found, for example, on real-time operating systems by decomposing them into several tasks in such a way that pre-emption and blocking may appear due to task priorities and resource sharing, or in networked control systems, where due to the existence of large distances and space limitations, several devices (controller, process and others) share a common communication bus. In both cases, these facts could imply the presence of limited random delays, leading to a non-regular non-periodic behavior and, as a result, the control performance can be degraded. In order to undertake this problem, a solution based on a modeling methodology for non-uniform sampled-data systems can be utilized. This technique permits the consideration of any cyclic sampling pattern. However, it can be adapted to deal with limited random delays, and later on, a multi-rate controller based on this model can be designed. In this way, if the considered non-conventional control system is implemented, a clear performance improvement can be observed