Models of planar motion of a two-wheeled experimental balancing prototype

The subject of the study is the process of developing motion models on a plane for a two-wheeled experimental balancing prototype (TEBP) considered as a control object. The aim of the study is to develop an approach for constructing mathematical models of the translational and rotational motions of the TEBP, taking into account mechanical and electromechanical processes. A physical model of the TEBP was developed and its nonlinear mathematical description was obtained. The application of analytical linearization made it possible to derive linear approximation models in the form of differential equations with constant coefficients. Using the Laplace transform, transfer functions were obtained, enabling the construction of block diagrams in both time and frequency domains. The motion models of the TEBP are also represented in the state-space form in the controllability canonical form. The simulation results confirm the feasibility of using the developed mathematical descriptions as dynamic models of the control object. The scientific novelty lies in the development of a comprehensive approach to modeling the motions of the TEBP, taking into account the acting forces and moments.