Robustness of the Reduced Automation Dumanic Systems

Abstract

The article is devoted to the influence of various reduction methods of the mathematical models on the robust stability of the automation systems of the technological processes. As is known, these automation systems are designed on the basis of the reduced models. The automation systems of a high order are usually characterized by an increased complexity and high sensitivity to the parameters of deviations from the calculated values. Since the known parameters of the systems are always inexact, a high sensitivity (or low robustness) of the systems lowers sharply the quality of the automated technological processes. Reduction of the dynamic models of the technological processes is frequently applied to eliminate this drawback. The reduction of the models can be carried out by various methods such as elimination of the poorly influencing bonds and small time constants due to removal of the quickly changing variables (cutting of the quick dynamics), etc. The reduced models also allow us to design simpler regulators and more robust automation systems of the lower orders. Besides, a solution to the problem of the automation systems design becomes much easier. However, in a real automation system the cut off quick dynamics influences the properties of the reduced system. Exactly the influence of this cut off quick dynamics on the robust stability of the reduced automation systems is the subject of this work. The robust stability is estimated with the help of V. L. Kharitonov criteria. For solving of the problem the models are reduced by three various methods. The reduced automation systems are created by the analytical design method. The maximal admissible deviations of their parameters for the robust stability are studied with account of the quick dynamics cut off at the stage of designing. It was established, that the cut off quick dynamics rendered an essential influence on the robust stability of the reduced automation systems. The received results can be applied for development of the automation systems for the technological processes in the chemical, power engineering, aviation, machine-building and other sectors.