Comparative Analysis and Modification of Imaging Techniques in the Parametric Studies of Control Systems

Abstract

Bauman Moscow State Technical University, Moscow Калининградский государственный технический университет, Калининград The article considers practical application aspects of various imaging techniques for parametric analysis of control systems. It is interpreted as a multivariate analysis aimed at studying the influence of external and internal parameters of the system on the quality of its functioning determined by direct and indirect quality criteria. The ultimate goal is to identify regions in the parameter space to provide an appropriate quality of the system. It is noted that visualization is a very important task-supporting aid for a designer to make decision. Stressed that the problem of parametric studies, in most cases, intersects with the major problem of inconsistency of separate partial criteria, i.e., the problem of multi-criteria optimization (MCO). Therefore, the aim of the article was to solve a joint task of visualization and multi-criteria optimization. The article considers traditional types of visualization in deterministic tasks (a 3-D graphics, plotting contour lines, gradient fields, Andrews curves, parallel coordinates), as well as methods used in statistics (graph matrices, etc.). Testing these methods as applied to the practical task of studying a double-circuit stabilization system allowed formulation of requirements for imaging techniques with multiple criteria. Provides a new perspective on using the traditional means to significantly enhance information capacity of imaging. A generic method of visualization is represented as a three-phase study agreed with the task of finding the compromise solutions. The first phase of the research involved identifying the monotony and contra-monotony domains. The second phase was aimed at identifying a region of compromise, or a weak Pareto optimum. The third phase involved the search for a consistent optimum (strong Pareto optimum). The main object of visualization has become a field of the anti-gradients, which was visualized both through the color-schemes, and through the radial compass-type plots. As a result of building these plots, the criteria have been revealed with anti-gradients in the opposite quadrants, i.e. having opposite trends. The next phase was to assess a degree of the joint effect of parameters on the system behavior. A scatter of gradients for an entire set of varied parameters was visualized, and statistical characteristics of distribution of a set of the anti-gradient vectors were calculated. Losses and winnings when choosing the compromise solutions through visualizations of a series of computational experiments were assessed. The article shows dynamics of changing anti-gradient vectors with variations of parameters. All criteria have been combined in the HivePlots type image. According to the results of a joint analysis of the plots, were determined zones of returned values (inaccessibility values) of criteria for a given structure of control, and a compromise solution in the unified field. Shows the application of the developed approaches to the multi-objective optimization problem when there are more than two criteria, namely, parametric synthesis of a double-circuit motion control system of the aircrafts the quality of which is described by four parameters: overshoot, transition time, rise time, and integral quadratic criterion of the deviation from a terminal trajectory. The developed technique of analysis allows us to identify possible compromise solutions, areas of sensitivity, mutual and dominant influence of parameters, and possible losses in trade-offs. The visual images are the task-supporting aid for a designer to make decision.