Mathematical modeling of mechatronic shuttles as automation objects for multilevel systems of intra-warehouse logistics

Abstract

The subject of the study is the mathematical modeling of mechatronic shuttles of multilevel intra-warehouse logistics systems. The purpose of the article is to ensure energy efficiency and high productivity of multilevel warehouse logistics systems by developing mathematical models of mechatronic electromechanical drives as part of automated autonomous shuttle systems (Pallet Shuttle). To achieve this goal, it is necessary to solve the following tasks: to build a mathematical model of the processes occurring in the transportation shuttle as an electromechanical and mechatronic system; to build a mathematical model of the transportation shuttle as an automation object and to obtain a transfer function of the autonomous shuttle system for automatic control of its speed. Conclusions. The paper develops generalized approaches to the construction of mathematical models of electric drives as automation objects. The developed approach assumes that the linearized mathematical model of an electric drive as an automation object is represented as a linear differential equation with constant coefficients that relate the control and the controlled parameter. The construction of such a differential equation is proposed to be carried out by generalizing the properties inherent in electromechanical systems, and it is assumed that these properties are represented by Lagrange equations of the 2nd kind using electromechanical analogies. As a result of the research, it was shown that the use of this approach leads to a definite equation of the mathematical model of the mechatronic shuttle as an automation object. It is shown that the linearized mathematical model of the shuttle as an automation object should be determined by a differential equation of at least the second order. The research results prove the possibility of improving automation systems in design by taking into account the properties inherent in shuttles as electromechanical and mechatronic systems in more detail. It is shown that the use of this approach leads to a definite equation of the mathematical model of the mechatronic shuttle as an automation object, but it is generally almost impossible to obtain such an equation explicitly. To illustrate the proposed approach, we consider the modeling of a typical mechatronic electric drive of machines used in automated storages and present the results of modeling processes in the electric drive. It is shown that the linearized mathematical model of a mechatronic shuttle as an automation object should be determined by a differential equation of at least the second order. The research results show the possibility of improving automation systems during design due to a more detailed consideration of the properties inherent in shuttles as mechatronic electromechanical systems.