Mathematical modeling of automatic control system by numerical integration

Purpose of research. The aim of the work is to study the mathematical model of the automatic control system (ACS), consisting of a regulator and a control object for execution on a microprocessor system with support for a realtime operating system. The structure of the ACS, the coefficients of transfer of the transfer functions of the links, time constants and transport delays are adopted as variable parameters. The output data are presented in the form of transient processes. The task is to compare the analytical and numerical methods for software implementation of the mathematical model of the ACS using a programmable logical controller (PLC) as part of a test bench with a microprocessor electric drive. The objective is to compare analytical and numerical methods for software implementation of a mathematical model of automatic control system using a programmable logic controller (PLC) as part of a test bench with a microprocessor electric drive.

Methods. The methods of system analysis, automatic control theory, numerical methods of differentiation and integration, differential and difference equations were used.

Results. Practical recommendations for choosing a PLC when solving problems of modeling objects and control systems based on the inertia of the links included in the control loop. The relative error (integral, for the ACS as a whole) and the fulfillment of the requirement for the stability of the digital model are used as an evaluation criterion.

Conclusion. The studies have shown that for canonical ACS with 1st and 2nd order objects and transport delay with certain criteria, such as digital model stability and relative error (integral), there is a connection between the speed of the simulated ACS links and the PLC performance. Additional studies are required for practical confirmation of the obtained results.

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