Efficient Embedded Model Predictive Vibration Control via Convex Lifting

Martin Gulan (1) , Gergely Takacs (1) , Ngoc Anh Nguyen (2) , Sorin Olaru (3, 2) , Pedro Rodriguez-Ayerbe (2) , Boris Rohal'-Ilkiv (1)

1 Slovak University of Technology in Bratislava
2 L2S - Laboratoire des signaux et systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

This paper presents an efficient real-time implementation of embedded model predictive control, adopted in the context of active vibration control with the objective of minimizing the tip deflection of lightly damped cantilever beams. In particular , we focus on memory and time-efficient explicit solutions to the associated constrained optimal control problem that are easily implementable on low-end embedded hardware. To this end, we exploit the concept of convex lifting and show how it can be used to devise low-complexity, regionless piecewise affine controllers without any loss of optimality and performance. Efficiency of this constructive procedure is quantified via an extensive complexity analysis, evidenced by a successful practical deployment and optimal vibration control performance using a family of 32-bit ARM Cortex-M based microcontroller platforms.

Keywords: explicit solutions; vibration control; convex lifting; embedded systems; Model predictive control

Domains: Engineering Sciences [physics]; Automatic

Martin Gulan, Gergely Takacs, Ngoc Anh Nguyen, Sorin Olaru, Pedro Rodriguez-Ayerbe, et al.. Efficient Embedded Model Predictive Vibration Control via Convex Lifting. IEEE Transactions on Control Systems Technology, In press, PP (99), pp.1-15. ⟨10.1109/TCST.2017.2764019⟩. ⟨hal-01720261⟩