Моделі плоского руху двоколісного експериментального балансуючого зразка

• Datum: 2023
• Hauptverfasser: Kulik, Anatoliy, Dergachov, Konstantin, Pasichnik, Sergey
• Format: Artikel
• Sprache: Ukrainian
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2023
• Schlagworte: двоколісний експериментальний балансуючий зразок (ДЕБЗ); електропривод; об’єкт управління; математичні моделі; передавальна функція; простір станів
• Online Zugang: https://jais.net.ua/index.php/files/article/view/5
• Назва журналу: Problems of Control and Informatics

The subject is the process of holding-balance two-wheeled experimental sample (HTES) planar motion models formation. The goal is to develop an approach to the formation of flat motion models of the HTES as an automatic controlled object. The problems: to form a physical model of a holding-balance two-wheeled experimental sample; to develop a nonlinear mathematical description of the forward and angular HTES motion on the plane using the Lagrangian formalism; to make a description of the controlled object in the frequency domain using Laplace transforms; to obtain a linearized mathematical description of the automa­tic controlled object in the state space; to form graphic models of the HTES as a control object using structural diagrams in the time and frequency domains; to form the conditions for using mathematical descriptions as mathematical models of the automatic control object. The methods applied are: Lagrange method, analytical linearization, state space, Laplace transformation. The following results were obtained: dynamic models of mechanical and electromechanical processes of forward and angular HTES movements on a plane were formed. Using the Lagrangian approach, a nonlinear mathematical model of the holding-balance two-wheeled experimental sample movement was developed. Using the method of analytical linearization, a mathematical model of linear approximation in the form of differential equations with constant coefficients was obtained. The mathematical models of local movements in the frequency domain in the form of transfer functions have been formed. A structural diagram of the transformation processes in holding-balance two-wheeled experimental sample has been created. The possibility of constructing mathematical models in the space of states in both vector-matrix form and structural diagrams form for solving specific problems of analysis and synthesis is shown. Conclusions. The scientific novelty consists in the formation of an approach to obtaining models of translational and angular movements of holding-balance two-wheeled experimental sample on a plane, which differs from the known ones in the completeness of accounting for acting forces and moments.