# Practical Design of RC Approximants of Constant Phase Elements and Their Implementation in Fractional-Order PID Regulators Using CMOS Voltage Differencing Current Conveyors

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## Abstract

This paper brings a practical and straightforward view on the design of circuit elements described by fractional-order dynamics known as the constant phase element (CPE) and their implementation in a novel structure of a PI^{α}D^{β} (or PI^{λ}D^{μ} in some literature) regulator based on fabricated CMOS voltage differencing current conveyors. Comparison of presented topology with known solutions indicates significant improvements regarding overall simplification, simpler electronic controllability of time constants, and having all passive elements in grounded form. Step-by-step design of the CPE as well as the PI^{α}D^{β} regulator is supported by experiments with active devices fabricated using the C07 I2T100 0.7 μm CMOS process (ON Semiconductor). Laboratory tests in frequency and time domain confirm the correct operation of the designed application and the accuracy of the derived results in comparison with the theoretical expectations.

## Keywords

Constant phase element (CPE) Differentiator Fractional-order circuit Integrator Proportional branch Proportional integrational and differential controller (PID) Voltage differencing current conveyor (VDCC)## Notes

### Acknowledgements

Research described in this paper was financed by Czech Science Foundation under Grant No. 16-06175S and the National Sustainability Program under Grant LO1401. For the research, infrastructure of the SIX Research Center was used. This article is based upon work from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).

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