Modeling and control of plate-sphere mechanical system

The sphere and plate system is a type of system generally used in industrial automation applications. The sphere and plate system is used as an experimental system in engineering and especially in the control department. Because the system is so complex, nonlinear, multivariate, and unstable, it is a great opportunity to use it to research, develop, and demonstrate new control strategies. This system also examines the movement or position of a sphere (or a spherical object) on the plate so that it can remain in balance or be brought to the desired position. Although the sphere-plate system seems simple, it is certain that it will encounter complex and great difficulties during its operation. In our study, we obtained the nonlinear equations of the 2-dimensional system we designed with special dimensions from the Euler-Lagrange equation. We then linearized the system equations. Then, we obtained the [k] matrix of the state feedback pole placement control method for the linear state of the system in 2 different ways. Then, we applied and examined the [k] matrix we found to both nonlinear and linear states of the system. We investigated both states of the system before and after the control separately. We obtained different results by comparing the linear and non-linear states of the system and then examined these results. Finally, we show that in both cases it is possible to control the [k] matrix system under certain initial conditions.