The dissertation is devoted to the solution of the scientific and technical problem of the theory and methods development to analyze dynamic modes of electromechanical systems based on the application of numerical methods and analysis of their influence on the characteristics of electromechanical systems.
The PhD thesis is devoted to the investigaton of the influence of numerical methods of ordinary differential equations solving based on the behavior of a digital model with its adjustment by choosing the appropriate integration step. In real-time digital systems, such as electromechanical systems, the integration step is fixed and predetermined that also has some influence on the behavior of the system. Therefore, from the point of view of the tasks of electric power engineering and electromechanics, it remains expedient to conduct a research of the influence of various approaches and methods on the system, which is modeled and studied as a prototype of real systems for domestic or industrial use.
In the Chapter 1 "Analysis of the state of the problem, formulation of the research problem" the analysis of literary sources connected with the topic of the work is conducted. The theoretical base of numerical methods, their application and implementation are considered. The basic information about the numerical methods usage based on existing research and publications has been analyzed.
Chapter 2, "Analysis of Numerical Methods of Integration as Elements of Digital Systems," presents methods intended for analyzing the behavior of numerical methods, and implementation. In the analysis of numerical methods based on the principle of integration, their advantages, disadvantages, and approaches for their further usage are presented. Their efficiency, stability, and relevance to electromechanics problems are investigated. The explicit Adams formulas are analyzed for the discretization of digital control systems using numerical methods. For this purpose, they are considered as digital filters that are an integral part of a digital system. The analysis of such digital filters was implemented using z-transforms.
During the research conducting, it was found that each numerical method (as a digital filter) causes its own influence on the resulting digital model, that is, the behavior of the model is superimposed on the behavior of the numerical method. The classical method of frequency response was chosen as one way to detect this phenomenon. It was also proposed to use the distribution of zeros/poles of a discrete system on the complex plane for analysis. In fact, the last one was used to obtain an evident result of the superposition of the behavior of numerical methods on the behavior of the model. The emergence of new additional zeros and poles of the discrete system compared to the continuous prototype significantly complicates the resulting digital model of the system. Thus, the studies have shown that it is advisable to use low-order numerical methods to keep the number of zeros/poles.
Chapter 3, "The Method of Zeroes and Poles Matching as a Rational Method for Digital Systems Synthesizing," investigates the effectiveness of the z-transform using, namely, the method of zeroes/poles mapping, to create real-time models. The historical foundations of the method and its basic principles of implementation and application are analyzed. The effectiveness of the implementation of the zero-pole mapping method for the analysis of electromechanical systems is studied. In the Chapter, on the example of modeling dynamic links of the first and second orders, the analysis of the methods applying, advantages and nuances of such application are presented. The Z-transform allows obtaining simple and efficient recurrent modeling formulas based on the pole/zero mapping method.
In Chapter 4, "Experimental Research. Verification of Results" describes the computer models of electrical systems on the basis of which the experimental studies were conducted and the results of the experiment with a microcontroller are presented.
During the research, it was found out that each numerical method (as a digital filter) adds its own influence on the resulting digital model. So, the behavior of the model is supeposed with the behavior of the numerical method. The classical method of frequency response was chosen as one way to detect this phenomenon, and we also proposed to use the distribution of zeros/poles of a discrete system on the complex plane for analysis. In fact, the last method was used as the basis for the visual result of imposing the behavior of numerical methods on the behavior of the model. The appearing of new additional zeros and poles of the discrete system compared to the continuous prototype significantly complicates the resulting digital model of the system. The results obtained in the process of the research will allow us to model the experimental electromechanical systems with higher accuracy
