This paper presents the concept of convex lifting which will be proven to enable significant implementation benefits for the class of piecewise affine controllers. Accordingly, two different algorithms to construct a convex lifting for a given polyhedral/polytopic partition will be presented. These two algorithms rely on either the vertex or the halfspace representation of the related polyhedra. Also, we introduce an algorithm to refine a polyhedral partition, which does not admit a convex lifting, into a convexly liftable one. Furthermore, two different schemes will be put forward to considerably reduce both the memory footprint and the online evaluation effort, which play a key role in implementation of piecewise affine controllers. Finally, these results will be illustrated via numerical examples and a complexity analysis.

Digital twin (DT) is an emerging key technology that enables sophisticated interaction between physical objects and their virtual replicas, with applications in almost all engineering fields. Although it has recently gained significant attraction in both industry and academia, so far it has no unanimously adopted and established definition. One may therefore come across many definitions of what DT is and how to create it. DT can be designed for an existing process and help us to improve it. Another possible approach is to create the DT for a brand new device. In this case, it can reveal how the system would behave in given conditions or when controlled. One of purposes of a DT is to support the commissioning of devices. So far, recognized and used techniques to make the commissioning more effective are virtual commissioning and hybrid commissioning. In this article, we present a concept of hybrid virtual commissioning. This concept aims to point out the possibility to use real devices already at the stage of virtual commissioning. It is introduced in a practical case study of a robotic manipulator with machine vision controlled with a programmable logic controller in a pick-and-place application. This study presents the benefits that stem from the proposed approach and also details when it is convenient to use it.

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 of the associated constrained optimal control problems 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. The 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.

This article presents an open-source device illustrating the well-known magnetic levitation experiment. The uniqueness of this particular device lies in its exceptionally small dimensions, affordability and availability, which makes it a perfect design for take-home experiments for education but it can also serve as a referential design for testing various control algorithms in research. In addition, this paper provides a comprehensive hardware design for reproducibility along with the detailed derivation of the mathematical model, system identification and validation. Moreover, the introduced hardware comes with an easy-to-use open-source application programming interface in C/C++ for the Arduino IDE, Simulink and CircuitPython. REXYGEN, another environment similar to Simulink, had also been used to demonstrate the capabilities of the MagnetoShield.