Subspace predictive control of flexible structures actuated by piezoelectric elements

In this paper we consider data-driven control of vibrations in a flexible structure equipped with piezoelectric transducers. The control algorithm uses elements from the fairly recent data-enabled predictive control framework. In particular, we will develop a real-time implementation of the subspace predictive control algorithm. This algorithm first solves a linear least-squares problem to recursively estimate the observer Markov parameters of the system. With those parameters a predictor is constructed which is used to solve a predictive control problem subject to constraints. The feasibility of the approach is highlighted by applying it to an experimental setup using an efficient implementation. First, this demonstrates that computations can be performed in real-time for a realistic situation. Second, we show how the scheme rapidly adapts when a sudden significant change in structural dynamics is introduced by changing one of the structural parameters.