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A single-component fractional order element (FOE) is realised and its performance is compared with the conventional FOEs such as cross resistance-capacitance (RC) ladder network and domino ladder network in the analogue domain. The single-component FOE is a capacitive-type probe coated with a porous film of poly-methyl-methacrylate (PMMA) and is dipped in polarisable medium. The fractional exponent of the fabricated single-component FOE and domino ladder can be varied between 0 and 1 whereas that of cross RC ladder realised in this work is 1/2. The performance of fractional order integrator (FOI) using these FOEs is studied in both frequency and time domain by simulation and experimentation. A comparative analysis of the performance of FOI is carried out.
References
-
-
1)
-
K. Biswas ,
S. Sen ,
P.K. Dutta
.
Realization of a constant phase element and its performance study in a differentiator circuit.
IEEE Trans. Circuits Syst. II, Expr. Briefs
,
802 -
806
-
2)
-
K.B. Oldham ,
J. Spanier
.
(1974)
The fractional calculus.
-
3)
-
J. Bisquert ,
A. Compte
.
Theory of the electrochemical impedance of anomalous diffusion.
J. Electroanal. Chem.
,
112 -
120
-
4)
-
C.A. Monje ,
B.M. Vinagre ,
V. Feliu ,
Y.Q. Chen
.
Tuning and auto-tuning of fractional order controllers for industry applications.
Control Eng. Practice
,
798 -
812
-
5)
-
S.C.D. Roy
.
On the realization of a constant-argument immittance or fractional operator.
IEEE Trans. Circuit Theory
,
264 -
274
-
6)
-
R. Deng ,
P. Davies ,
A.K. Bajaj
.
A nonlinear fractional derivative model for large uni-axial deformation behavior of polyurethane foam.
Fract. Calc. Appl. Signals Syst. Signal Process.
,
2728 -
2743
-
7)
-
A. Lasia
.
Electrochemical impedance spectroscopy and its applications.
Mod. Aspects Electrochem.
,
143 -
248
-
8)
-
G.W. Bohannan
.
Analog fractional order controller in temperature and motor control applications.
J. Vib. Control
,
1487 -
1498
-
9)
-
A.G. Radwan ,
A.M. Soliman ,
A.S. Elwakil
.
Design equations for fractional-order sinusoidal oscillators: four practical circuit examples.
Int. J. Circuit Theory Appl.
,
473 -
492
-
10)
-
Chen, Y.Q., Xue, D., Dou, H.: `Fractional calculus and biomimetic control', IEEE Int. Conf. on Robotics and Biomimetics, August 2004, p. 901–906.
-
11)
-
E. Barsoukov ,
J.R. Macdonald
.
(2005)
Impedance spectroscopy: theory, experiment, and application.
-
12)
-
A. Oustaloup ,
J. Sabatier ,
P. Lanusse
.
From fractal robustness to crone control.
Fract. Calc. Appl. Anal.
,
1 ,
1 -
30
-
13)
-
Abbisso, S., Caponetto, R., Diamante, O., Fortunat, L., Porto, D.: `Non integer order integration by using neural networks', IEEE Int. Symp. on Circuits and Systems, 2001, p. 688–691.
-
14)
-
J.A.T. Machado ,
I.S. Jesus
.
Suggestion from the past?.
FCAA J. Fract. Calc. Appl. Anal.
,
4 ,
403 -
407
-
15)
-
J.R. McDonald
.
(1987)
Impedance spectroscopy: emphasizing solid materials and systems.
-
16)
-
Y. Chen ,
K.L. Moore
.
Discretization schemes for fractional differentiators and integrators.
IEEE Trans. Circuits Syst.1: Fundam. Theory Appl.
,
3 ,
363 -
367
-
17)
-
Rodríguez-Castaño, A., Ollero, A., Vinagre, B.M., Chen, Y.Q.: `Fractional controller for guidance of autonomous ground vehicles', Proc. Fifth IFAC Int. Symp. on Intelligent Components and Instruments for Control Applications, (SICICA2003), July 2003.
-
18)
-
C. Ionescu ,
I. Muntean ,
J.A.T. Machado ,
R.D. Keyser ,
M. Abrudean
.
A theoretical study on modeling the respiratory tract with ladder networks by means of intrinsic fractal geometry.
IEEE Trans. Biomed. Eng.
,
246 -
253
-
19)
-
J.C. Wang
.
Realizations of generalized Warburg impedance with rc ladder networks and transmission lines.
J. Electrochem. Soc. Electrochem. Sci. Technol.
,
1915 -
1920
-
20)
-
Sivaramakrishna, M., Das, S., Biswas, K., Goswami, B.: `Characterization of a fractional order element realized by dipping a capacitive type probe in polarizable medium', Symp. on Fractional Signals and Systems Lisbon 09, November 2009.
-
21)
-
A. Charef
.
Analogue realization of fractional order integrator, differentiator and fractional PIλDµ controller.
IEE Proc., Control Theory Appl.
,
6 ,
714 -
720
-
22)
-
H. Zhao ,
J. Yu
.
A simple and efficient design of variable fractional delay FIR filters.
IEEE Trans. Circuits Syst. II
,
157 -
160
-
23)
-
J. Sabatier ,
O.P. Agrawal ,
J.A.T. Machado
.
(2007)
Advances in fractional calculus.
-
24)
-
I.S. Jesus ,
J.A.T. Machado
.
Development of fractional order capacitors based on electrolyte processes.
Nonlinear Dyn.
,
45 -
55
-
25)
-
A. Oustaloup ,
B. Mathieu ,
P. Lanusse
.
The crone control of resonant plants: application to a flexible transmission.
Eur. J. Control
,
2 ,
113 -
121
-
26)
-
C.C. Tseng
.
Design of FIR and IIR fractional order Simpson digital integrators.
Signal Process.
,
5 ,
1045 -
1057
-
27)
-
S. Das
.
(2008)
Functional fractional calculus for system identification and control.
-
28)
-
P. Varshney ,
M. Gupta ,
G.S. Visweswaran
.
New switched capacitor fractional order integrator.
J. Act. Passive Electron. Dev.
,
187 -
197
-
29)
-
M. Sugi ,
Y. Hirano ,
Y. Miura ,
K. Saito
.
Frequency behavior of self-similar ladder circuits.
Colloides and Surfaces A: Physicochem. Eng. Aspects
,
683 -
688
-
30)
-
P. Ostalczyk
.
Fundamental properties of the fractional-order discrete-time integrator.
Signal Process.
,
2367 -
2376
-
31)
-
S. Manabe
.
The non-integer integral and its application to control systems.
ETJ Jpn.
,
83 -
87
-
32)
-
Axtell, M., Bise, M.E.: `Fractional calculus applications in control systems', Proc. IEEE National Aerospace and Electronics Conf., 1990, New York, USA, p. 563–566.
-
33)
-
A. Oustaloup ,
X. Moreau ,
M. Nouillant
.
The CRONE suspension.
Control Eng. Pract.
,
8 ,
1101 -
1108
-
34)
-
I. Podlubny ,
I. Petras ,
B.M. Vinagre ,
P. O'Leary ,
L. Dorcak
.
Analogue realization of fractional-order controllers.
Nonlinear Dyn. Int. J. Nonlinear Dyn. Chaos Eng. Syst.
,
281 -
296
-
35)
-
Petras, I., Grega, S., Dorcak, L.: `Digital fractional order controllers realized by PIC microprocessor: experimental results', Proc. ICCC’2003 Conf., 26–29 May 2003, High Tatras, Slovak Republic, p. 873–876.
-
36)
-
Bohannan, G.W.: `Application of fractional calculus to polarization dynamics in solid dielectrics materials', 2000, PhD, Montana, State University, Bozeman.
-
37)
-
Biswas, K.: `Studies on design, development and performance analysis of capacitive type sensors', February 2007, PhD, Indian Institute of Technology Kharagpur, Department of Electrical Engineering, India.
-
38)
-
Tseng, C.C.: `Closed-form design of variable fractional order integrator using complex cepstrum', IEEE Int. Symp. on Circuits Syst., 27–30 May 2007, p. 3447–3450.
-
39)
-
A. Oustaloup ,
F. Levron ,
B. Mathieu ,
F.M. Nanot
.
Frequency-band complex noninteger differentiator: characterization and synthesis.
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
,
1 ,
25 -
39
-
40)
-
I. Podlubny
.
(1999)
Fractional differential equations.
-
41)
-
G.E. Carlson ,
C.A. Halijak
.
Approximation of fractional capacitors (1/s)1/n by a regular newton process.
IEEE Trans. Circuits Syst.
,
210 -
213
-
42)
-
S. Westerlund
.
Capacitor theory.
IEEE Trans. Dielectr. Electr. Insul.
,
826 -
839
-
43)
-
C. Ionescu ,
J.T. Machado
.
Mechanical properties and impedance model for the branching network of the sapping system in the leaf of hydrangea macrophylla.
Nonlinear Dyn.
,
207 -
216
-
44)
-
K.B. Oldham ,
C.G. Zoski
.
Analogue instrumentation for processing polarographic data.
J. Electroanal. Chem.
,
27 -
51
-
45)
-
M. Moshrefi-Torbati ,
J.K. Hammond
.
Physical and geometrical interpretation of fractional operators.
J. Franklin Inst.
,
6 ,
1077 -
1086
-
46)
-
S. Manabe
.
The non-integer integral and its application to control systems.
J. JIEE (Jpn. Inst. Electr. Eng.)
,
860 ,
589 -
597
-
47)
-
C.C. Tseng
.
Series expansion design of variable fractional order integrator and differentiator using logarithm.
Signal Process.
,
2278 -
2292
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