An analog fractional order PI λ controller, using a circuit element with fractional order impedance, a Fractor (patent pending), is demonstrated in both a simple temperature control application and a more complex motor controller. The performance improvement over a standard PI controller was notable in both reduction of overshoot and decreased time to stable temperature, while retaining long term stability. In the motor controller, set point accuracy was considerably improved over conventional control. The modification of the standard controller to a fractional order controller was as simple as replacing the integrator capacitor with a Fractor. Mixing (i.e., hybridization) of digital and analog control was demonstrated.

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Here, we propose the fabrication of a solid state fractional capacitor for which constant phase (CP) angles were attained in different frequency zones: 110 Hz–1.1 kHz, 10 kHz–118 kHz, and 230 kHz–20 MHz. The configuration makes use of epoxy resin as the matrix in which multi-walled carbon nanotubes (MWCNTs) are dispersed. Adhesive nature of the epoxy resin is utilized for binding the electrodes, which avoids the extra step for packaging. The fractional capacitive behavior is contributed by the distribution of time constants for the electron to travel from one electrode to the other. The distributive nature of the time constant is ensured by inserting a middle plate which is coated with a porous film of polymethyl-methacrylate in between the two electrodes. The phase angle trend for the configuration is studied in detail, and it is observed that as the % of carbon nanotubes (CNTs) loading increases, the CP angle increases from −85° to −45° in the frequency zones above 100 Hz. The developed device is compact and it can be easily integrated with the electronic circuits.

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