Development of an adaptive predictive control system for a vibrating feeder with an unbalanced drive based on the Hammerstein model

This article discusses the development of an adaptive control system based on a model predictive controller (MPC) for a vibration feeder with an unbalanced drive. A distinctive feature of such mechanical systems is the significant nonlinearity of their dynamic characteristics, caused by the design of the unbalanced vibration exciter and the dependence of amplitude-frequency properties on variable operating conditions-feeder load, properties of the transported material, and temperature effects. To adequately describe these phenomena, the Hammerstein model, which combines a static nonlinear component and a linear dynamic part, was selected as the mathematical model of the controlled object. This approach maintains the computational efficiency characteristic of linear MPC while accounting for the nonlinear effects inherent in real vibrating systems. The structure of the predictive controller is presented: formulation of the optimization problem with a prediction horizon, derivation of the cost function, and consideration of constraints on control actions and output variables. Special attention is given to adaptation algorithms and mechanisms for real-time updating of model parameters as operating conditions change, ensuring stability and high-quality control throughout the entire process cycle.

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