Control of Flexible Structures Using Model Predictive Control and Gaussian Processes

There is a recognized need to tackle issues of vibration control making use of recent developments of data-driven modelling. In structural dynamics, data driven modelling has been extensively investigated, including with probabilistic approaches to quantify the uncertainty in dynamic systems. However, uncertainty within structural control systems is still an issue, which has become even more problematic, as interest in flexible structures has grown. It is desirable that structural control systems also implement some of these approaches, in order to improve control performance and gain more insight when an informative controller, such as model predictive control (MPC), is in the loop. This work addresses the difficulties imposed by the limitations of the actuator and its dynamics in the range of active vibration control. This paper proposes and examines a data-based Gaussian process NARX model of a proof mass actuator, in a flexible-structure framework, aiming to improve the control performance. This work requires incorporating the identified best nonlinear dynamic model of the actuator, based on data driven modelling, into the control strategy. The proposed method compromises a combination of GP-NARX and MPC to achieve desirable vibration performance. As part of MPC, restrictions on what control actions are permissible can be explicitly considered when determining the best control action. A simulated simply supported beam and nonlinear analysis of the proof mass actuator is shown as a case study for the proposed method. The efficacy of the devised methodology is firstly compared against the standard approximation of the dynamic of the proof mass actuator in a linear benchmark application, where the dynamic of the actuator is assumed linear. Then, the control method is tested on a more complex problem where the actuator dynamic model is assumed to be both uncertain and nonlinear. The outcome of this work encourages further investigation of the developed strategy, especially in real time experimental implementation.