Analog Fractional Order Controller in Temperature and Motor Control Applications

Abstract

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.

Kalman filter Observer for SoC prediction of Lithium cells

“…The main role of observers is determining the unknown variables related to the state vector and reducing the use of expensive sensors [40]. This area has been attractive by many researches [41,42] and many kind of observer strategies have been evolved especially for several classes of chemical systems to estimate their internal states [43,44].…”

A review and evaluation of numerical tools for fractional calculus and fractional order controls

“…Besides the fundamental mathematical study, more and more researchers from different academic disciplines begin to utilize it in a varieties of subjectassociated research, such as in biology and biomedical [4,5], sociology [6,7], economics [8,9], and control engineering [10,11,12], etc. Along with the rapid development of theoretical study, the numerical methods and practical implementation also made considerable progress [13,14,15]. Sharp tools are prerequisite to a successful job.…”

An ultra-broadband single-component fractional-order capacitor using MoS2-ferroelectric polymer composite

“…Even though the CPA of the FOCs fabricated using polymer composites is tunable, their CPZ has been limited to 2.5 decades, between 50 kHz and 10 MHz. It is clear that these FOCs are not suitable for many electronic systems, which work at low frequencies, such as fractional controllers 7 and neural networks. 2,31,32 To alleviate this problem, in this work, an FOC is fabricated using PDVF polymer composites embedding molybdenum disulfide (MoS 2 ) nanosheets [see Fig.…”

“…[1][2][3][4][5][6][7][8][9][10][11] Thanks to the additional parameter, namely, the fractional order (see supplementary material Sec. S1 and Fig.…”

“…25,26 Another example is the use of an FOC in a temperature controller instead of a conventional controller: The FOC reduces drastically both the overshoot amplitude and the time required to stabilize the temperature. 7 One method of realizing an FOC in an electrical circuit is to represent it in terms of a chain network of resistors and capacitors (RC). The resulting circuit's overall impedance yields a transfer function with a non-integer order.…”