For programming the AR tools, interactive objects and creating the markers, the method of fiber spaces (k-space) for modeling of ultrasonic wave propagation in an inhomogeneous medium using coarse grids, with maintaining the required accuracy was used. The algorithm and tools of augmented reality were introduced into the adaptive control system of the pulp gas phase in the iron ore flotation process using a control action on the basis of high-energy ultrasound dynamic effects generated by ultrasonic phased arrays. The tools of augmented reality based on k-space methods allow to facilitate wider adoption of ultrasound technology and visualize the ultra-sound propagation in heterogeneous media by providing a specific correspondence between the ultrasound data acquired in real- time and a sufficiently detailed augmented 3D scene. The tools of augmented reality allow seeing the field of ultrasound propagation, its characteristics, as well as the effect of the dynamic effects of ultrasound on the change in the gas phase during the flotation process.

As a result of the identification based on the Hammerstein model of objects of the first stage of iron ore magnetic separation, the adequacy of the model is obtained. All results of the testing of the developed identification algorithms show that the subsystem of identification of the automated process control systems of processing plants based on the Hammerstein hybrid model allows to carry out satisfactory identification of objects and, as a consequence, to improve the quality of technological processes. The study of the influence of the coefficient of various typical links on the results of identification using orthogonal parallel and parallel-recursive Hammerstein models showed that these models allow considering the differences in the properties of identifiable objects adequately.