This bachelor thesis focuses on the hardware modernization of a ball on plate (BoP) laboratory platform, the design of a digital twin (DT) methodology, the implementation of selected control algorithms, and the development of a computer vision algorithm. The BoP system was identified as two subsystems: the servomotor subsystem parameters were identified using measured data from the physical laboratory model and a chosen linear structure, while the BoP dynamics subsystem, represented by a mathematical model in the form of a nonlinear differential equation, had its coefficient of restitution further identified. By applying the proposed identification methodology, a grey-box BoP model was obtained, which serves as a digital twin for the laboratory BoP model. Based on the resulting BoP model, which represents a DT for the laboratory model, control algorithms were designed based on the linearized model. The proposed PID and optimal state-space control algorithms (LQI/MPC) were verified through simulations in control structures, and the obtained control results using the DT for various objectives were compared with control results obtained using the physical BoP laboratory model. Furthermore, the thesis addresses software tasks within the international collaboration with the ALICE experiment at CERN, specifically the modernization of the AGRANA monitoring application and the design of the DARMA4 information system.