MPC Implementation for Vibration Control

Abstract

This chapter is devoted to the implementation of model predictive control (MPC) algorithms in active vibration control (AVC) applications. Even though the main area of interest is AVC, the software implementation tasks presented here are valid for any other engineering application of MPC, thus the material may be recommended to anyone interested in practical issues with MPC software deployment. Three different MPC strategies are discussed, each having its own advantages and disadvantages: the well known infinite horizon cost dual-mode quadratic programming based MPC (QPMPC), optimal and suboptimal explicit pre-computed multi-parametric programming based MPC (MPMPC) and the efficient but suboptimal Newton–Raphson MPC (NRMPC). The offline portion of the algorithms is implemented in the Matlab m-file scripting language, while the real-time controllers are realized in Simulink and subsequently transferred to the xPC Target rapid control software prototyping platform. The practical approach utilized here is focused at simplicity. An off-the shelf quadratic solver called qpOASES is used for the online implementation of QPMPC, while the MPMPC algorithm is implemented using the MPT Toolbox. As the implementation of NRMPC to physical systems is unique to this book, the most attention is devoted to the code developed for the use of Newton–Raphson MPC in the vibration damping of lightly damped structures.