Digital Realization of $\text{PI}^{\lambda}\mathrm{D}^{\mu}$ Controllers: Performance Evaluation on MCUs and FPGAs

Fractional-Order Proportional-Integral-Derivative controller, also known as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{PI}^{\lambda} \mathrm{D}^{\mu}$</tex>, controllers have attracted great interest in recent years due to their superior performance of many control operations. In this work, we provide a study on <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{PI}^{\lambda} \mathrm{D}^{\mu}$</tex> controllers, with a particular focus on their implementation in a digital environment using microcontroller units (MCUs) and field programmable gate arrays (FPGAs). The study covers mathematical modeling, discretization approaches, and practical implementation. Various performance measures, including resource utilization, power consumption, and through-put, are evaluated for distinct microcontroller unit (MCU) and field-programmable gate array (FPGA) architectures. The results illustrate the compromises between power consumption and computational throughput, offering valuable information on choosing the most suitable hardware platforms for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{PI}^{\lambda} \mathrm{D}^{\mu}$</tex> controller applications.