AN ASSESSMENT METHOD FOR THE CONTROL SYSTEMS QUALITY

Abstract

Abstract. Possibilities and methods of applying the concept of uncertainty in order to assess the quality of control are investigated. An analysis of the approaches currently used for uncertainty assessment is carried out. The use of the informational approach for this purpose is substantiated. It is proposed to use informational uncertainty as a criterion for the quality of control tools. For this, the amount of negative information (misinformation) caused by the imperfection of management methods and devices is calculated. The method of estimating the amount of misinformation is based on Bongard's concept of uncertainty. Misinformation is considered as Bongard's negative useful information. The amount of misinformation is the difference between the Shannon entropy and the Bongard’s uncertainty and is used as a criterion for absolute information uncertainty. The criterion of relative information uncertainty is also proposed as the ratio of the amount of misinformation introduced by the control tool to the maximum possible value of misinformation. The maximum value is the amount of misinformation at zero Shannon entropy. Mathematical expressions for calculating the absolute and relative uncertainty of control systems are given. Formulas for calculating deterministic analogs of Shannon's entropy and Bongard's uncertainty are proposed to assess the quality of control tools that are investigated by non-statistical methods. Appropriate expressions for calculating criteria of absolute and relative uncertainty based on transient processes of control systems are derived. The practical use of the proposed method is shown. To demonstrate the use of the criterion of information uncertainty, simulation of the PID controller was carried out using Scilab/Xcos tools. The vectors of input and output values ​​obtained as a result of modeling were processed using the formulas introduced in this article. The criterion of relative information uncertainty was applied to compare the quality of PID controllers that were discretized by different methods.

Keywords

• control system
• criterion
• quality of control
• uncertainty measure
• entropy
• bongard's uncertainty
• misinformation
• information saturation
• scilab/xcos