Control of Flexible Structures Using Model Predictive Control and Gaussian Processes

There is a recognised need to address issues of vibration control by making use of recent developments in data-driven modelling. The present study considers the difficulties imposed by the limitations of the actuator in the range of active vibration control. The paper proposes and examines a data-based Gaussian process (GP) model of a proof mass actuator in a flexible structural framework, aiming to improve control performance. This requires incorporating an inverse GP of static nonlinearity within the Wiener-Hammerstein model. The model starts with designing model predictive control (MPC) for a cantilever beam, in which the aim is to identify the optimal control force. Utilising the GP is the second step towards quantifying the uncertainty and limitation of the proof mass actuator by designing an inverse GP for the static nonlinearity. This quantification forwards to an MPC controller using a steady-state target optimisation tracking approach, in which this controller provides the optimal voltage required to eliminate vibration within the controller's limitations. The numerical outcome shows that the proposed scheme was capable of supplying the necessary voltage, which eliminated the structure's vibration within an actuator's limits. The results of this work encourage additional research into the developed strategy, particularly in the context of experimental real-time implementation.