Keywords
magnetic levitation
nonlinear model
structural instability
astatic modal control
state observer
synthesis
research
modeling електромагніт постійного струму
електромагнітна левітація
нелінійна модель
структурна нестійкість
астатичне модальне керування
спостерігач стану
синтез
дослідження
моделювання
How to Cite
Abstract
The work is devoted to an actual problem – the construction of improved systems automatic control (SAC) for the position of electromagnetic levitation systems. A detailed nonlinear mathematical model of a DC electromagnet is obtained, taking into account its structural instability and the unidirectionality of the force, as well as the dependence of the parameters on the working gap. The synthesis problem is formulated in the class of supervisory and software control systems. An astatic modal position controller and a state observer are synthesized to estimate the unmeasured velocity for use in the controller feedback. The synthesized automatic control system is studied by mathematical modeling. It is shown that the process of initial stabilization of the position of a free-falling levitating body is aperiodic. It is confirmed that the system has a 1st order astatism with respect to task and force disturbances and a 2nd order astatism with respect to position disturbances. It is established that the quality indicators of transient processes, as well as the quality factor in terms of speed and frequency of transmission, correspond to those set over the entire operating range of the working gap change. The negative influence of the variable parameters of the object on the quality of the control in the case of a significant increase or decrease of the working gap in relation to the nominal value is revealed. In general, the research results confirm the high quality of the indicators of the functioning of the synthesized automatic control system of the magnetic levitation system. References 19, figures 11, table 3.
References
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