Mathematical modeling of robust automatic control system of magnetic levitation with uncertain parameters

Abstract

The topic of the research is the development of automated control systems for real processes, which must satisfy various requirements, for example, resistance to unmodeled dynamics (robust stability), as well as meet the required quality of transient processes that arise in the case of external disturbances of various natures. In this regard, there is a need to create appropriate mathematical models for the control of non-stationary objects, the model of which includes uncertain parameters. The problem of developing and studying a mathematical model for controlling the process of electrodynamic magnetic levitation, the main problem of which is dynamic stability, is considered. It is noted that systems using the effect of magnetic levitation are widely used, for example, in shipbuilding, in elements of ship mechanisms, instrument making, as well as in the transportation of various cargoes. The relevance of the work related to the need to develop such automatic control systems that can suppress the emerging oscillatory motion of levitating bodies is substantiated. The initial mathematical model of the magnetic levitation control process, which has uncertain coefficients in differential equations and is nonlinear, is considered. To “hang” at a given (working) point of a levitating body, it is enough to create a mathematical control model in the vicinity of this point based on the linearization of the original mathematical model. A PID-based controller and feedback are added to the resulting model. The four controller coefficients are adjusted using special algorithms, taking into account the requirements for the robustness of the control system. Numerical experiments are carried out to analyze the behavior of the control system depending on the magnitude of the parameter uncertainty. Based on the analysis performed, a conclusion about the robustness of the developed control system for the object under consideration is made. The results of the study are presented in graphical form. The MATLAB system is used as a toolkit.