Piecewise affine convex liftings prove to be versatile tools for the analysis and implementation of piecewise affine control systems. This paper contributes to the theory of convex lifting of polyhedral partitions, by introducing a more efficient approach to the treatment of convexly non-liftable partitions or subpartitions. The main contribution is a new algorithmic procedure to refine polyhedral partitions that do not admit a convex lifting, into convexly liftable ones. This proves the potential computational advantages of a precise, local focus on the problematic regions while preserving the internal boundaries of the original partition to be lifted.Additionally, an algorithm to identify those problematic regions is also introduced and some operations with convexly liftable partitions are discussed.

This paper presents the BicopShield, a novel, opensource educational device developed within the AutomationShield initiative to support hands-on learning in control engineering. It allows students to explore key concepts from control theory, such as system identification and feedback control, through a mechatronic bicopter system. Featuring a low-cost, replicable design with off-the-shelf components and 3D-printed parts, BicopShield is suitable for classroom and take-home applications. The device's application programming interface (API) is available in C/C++ for Arduino IDE, and for MATLAB/Simulink. This paper details the BicopShield's design, API, and sample exercises, demonstrating its use in reinforcing theoretical knowledge through practical application.

This article presents a reference design for the well-known ball-on-beam laboratory experiment, where a spherical ball without direct actuation is only balanced by the inclination of a supporting structure, such as beam, rail or tube. The design introduced here is completely open-source and utilizes only a handful of off-the-shelf components and 3D printing; resulting in an exceptionally low hardware cost. Moreover, the resulting apparatus fits on a standard expansion module format, known as a Shield, which is compatible with a range of microcontroller prototyping boards from the Arduino ecosystem. This affordable, small, reproducible and open design is thus intended to aid control systems or mechatronics education via hands-on student experiments or even conducting research on a budget. In addition to the hardware design with downloadable project files, we also present an application programming interface and the results of a demonstration example here.

This article introduces a prototype reference design for the classical motor speed tracking experiment that is extensively used to teach control engineering and mechatronics concepts all over the globe. The literature is abundant with similar experimental setups combining a direct current motor and an incremental encoder, with the aim of controlling the rotational speed using feedback methods. The didactic device proposed here is special in that it integrates this setup into a miniaturized package at a very low cost, effectively creating take-home experimental systems suitable for remote teaching. In our concept, the motor-encoder coupled with power and measurement electronics is tightly integrated in a so-called shield, which is compatible with a range of microcontroller prototyping boards from the Arduino ecosystem and third-party compatibles. The hardware reference design is offered as an open-source, community driven initiative. In addition to the proposed device we present an application programming interface to abstract fundamental hardware functions and aid the education of higher concepts in control, system identification, signal processing or mechatronics. The programming interface is available in C/C++ for the Arduino IDE, in the MATLAB scripting language and as a Simulink blockset. Demonstration examples for feedback control and system identification are also provided for each environment. The combination of the open-source hardware and programming interface creates a powerful concept that is founded on standardization, meaning that educators may collaborate not only in bettering the existing hardware and software, but also on creating common teaching materials.

This article presents a prototype reference design for a low-cost miniature magnetic levitation experiment. The proposed device is built as an Arduino expansion module, thus may be installed on a broad range of microcontroller prototyping boards. The open-source hardware design uses off-the-shelf and widely available components and 3D printing technology, thus its overall material cost is minimal. This way, the magnetic levitation experiment is transformed into a pocket laboratory that can be borrowed by students for take-home experiments. In addition to the device itself, we present an open-source application programming interface and the outline of classroom examples in modeling, system identification and closed-loop control.

This paper proposes a novel open-source didactic device for control systems engineering education that implements the thermal control of a 3D printer heating block as the underlying dynamic process. The teaching aid is built on a printed circuit board copying the physical outline and the standardized electrical connections of the Arduino Uno microcontroller prototyping board. The educational tool described here can be manufactured for a diminutive cost, thus is accessible to students as a take-home experiment. Moreover, it conforms to the design philosophy of the so-called Arduino Shields, thus, it extends the inherent capabilities of the baseboard and may be combined with other available shields. The proposed hardware is augmented by an application programming interface available in C/C++, MATLAB and Simulink. The paper describes the use of this interface and suggests a sample exercise for the grey-box identification of the differential equation representing the system dynamics which was derived by a first-principles approach. The article also acquaints the reader with sample exercises implementing PID control using the various available programming interfaces.