Recently, a robust controller has been proposed to be used in control of plants with large uncertainty in location of one of their poles. By using this controller, not only the phase margin and gain crossover frequency are adjustable for the nominal case but also the phase margin remains constant, notwithstanding the variations in location of the uncertain pole of the plant. In this paper, the tuning rule of the aforementioned controller is extended such that it can be applied in control of plants modeled by fractional order models. Numerical examples are provided to show the effectiveness of the tuned controller.

References

References
1.
Monje
,
C. A.
,
Chen
,
Y. Q.
,
Vinagre
,
B. M.
,
Xue
,
D.
, and
Feliu
,
V.
,
2010
,
Fractional-order Systems and Controls–Fundamentals and Applications (Advanced Industrial Control Series)
,
Springer-Verlag
, London, UK.
2.
Caponetto
,
R.
,
Dongola
,
G.
,
Fortuna
,
L.
, and
Petras
,
I.
,
2010
,
Fractional Order Systems: Modeling and Control Applications
,
World Scientific
, Singapore.
3.
Rekanos
,
I. T.
, and
Yioultsis
,
T. V.
,
2014
, “
Approximation of Grünwald–Letnikov Fractional Derivative for FDTD Modeling of Cole–Cole Media
,”
IEEE Trans. Magn.
,
50
(
2
), pp.
181
184
.10.1109/TMAG.2013.2281998
4.
Mescia
,
L.
,
Bia
,
P.
, and
Caratelli
,
D.
,
2014
, “
Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media
,”
IEEE Trans. Microwave Theory Tech.
,
62
(
9
), pp.
1920
1929
.10.1109/TMTT.2014.2327202
5.
Beaulieu
,
A.
,
Bosse
,
D.
,
Micheau
,
P.
,
Avoine
,
O.
,
Praud
,
J.
, and
Walti
,
H.
,
2012
, “
Measurement of Fractional Order Model Parameters of Respiratory Mechanical Impedance in Total Liquid Ventilation
,”
IEEE Trans. Biomed. Eng.
,
59
(
2
), pp.
323
331
.10.1109/TBME.2011.2169257
6.
Podlubny
,
I.
,
1999
, “
Fractional-Order Systems and PIλDμ-Controllers
,”
IEEE Trans. Autom. Control
,
44
(
1
), pp.
208
214
.10.1109/9.739144
7.
Tavazoei
,
M. S.
, and
Tavakoli-Kakhki
,
M.
,
2014
, “
Compensation by Fractional-Order Phase-Lead/Lag Compensators
,”
IET Control Theory Appl.
,
8
(
5
), pp.
319
329
.10.1049/iet-cta.2013.0138
8.
Oustaloup
,
A.
,
2006
, “
The CRONE Approach: Theoretical Developments and Major Applications
,”
Proceedings of the Second IFAC Workshop on Fractional Differentiation and Its Applications
,
Porto, Portugal
, pp.
39
69
.
9.
Vinagre
,
B. M.
, and
Feliu
,
V.
,
2007
, “
Optimal Fractional Controllers for Rational Order Systems: A Special Case of the Wiener-Hopf Spectral Factorization Method
,”
IEEE Trans. Autom. Control
,
52
(
12
), pp.
2385
2389
.10.1109/TAC.2007.910728
10.
Djennoune
,
S.
, and
Bettayeb
,
M.
,
2013
, “
Optimal Synergetic Control for Fractional-Order Systems
,”
Automatica
,
49
(
7
), pp.
2243
2249
.10.1016/j.automatica.2013.04.007
11.
Yin
,
C.
,
Chen
,
Y.
, and
Zhong
,
S. M.
, 2014, “
Fractional-Order Sliding Mode Based Extremum Seeking Control of a Class of Nonlinear Systems
,” Automatica,
50
(
12
), pp.
3173
3181
.
12.
Pisano
,
A.
,
Rapaić
,
M. R.
,
Jeličić
,
Z. D.
, and
Usai
,
E.
,
2010
, “
Sliding Mode Control Approaches to the Robust Regulation of Linear Multivariable Fractional-Order Dynamics
,”
Int. J. Rob. Nonlinear Control
,
20
(
18
), pp.
2045
2056
.10.1002/rnc.1565
13.
Charef
,
A.
,
Assabaa
,
M.
,
Ladaci
,
S.
, and
Loiseau
,
J. J.
,
2013
, “
Fractional Order Adaptive Controller for Stabilised Systems Via High-Gain Feedback
,”
IET Control Theory Appl.
,
7
(
6
), pp.
822
828
.10.1049/iet-cta.2012.0309
14.
Monje
,
C. A.
,
Vinagre
,
B. M.
,
Feliu
,
V.
, and
Chen
,
Y. Q.
,
2008
, “
Tuning and Auto-Tuning of Fractional Order Controllers for Industry Applications
,”
Control Eng. Pract.
,
16
(
7
), pp.
798
812
.10.1016/j.conengprac.2007.08.006
15.
Yeroglu
,
C.
, and
Tan
,
N.
,
2011
, “
Note on Fractional-Order Proportional-Integral-Differential Controller Design
,”
IET Control Theory Appl.
,
5
(
17
), pp.
1978
1989
.10.1049/iet-cta.2010.0746
16.
Monje
,
C. A.
,
Calderon
,
A. J.
,
Vinagre
,
B. M.
,
Chen
,
Y.
, and
Feliu
,
V.
,
2004
, “
On Fractional PIλ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties
,”
Nonlinear Dyn.
,
38
(
1–4
), pp.
369
381
.10.1007/s11071-004-3767-3
17.
Chen
,
Y.
,
Bhaskaran
,
T.
, and
Xue
,
D.
,
2008
, “
Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers
,”
ASME J. Comput. Nonlinear Dyn.
,
3
(
2
), p.
021403
.10.1115/1.2833934
18.
Chao
,
H.
,
Luo
,
Y.
,
Di
,
L.
, and
Chen
,
Y. Q.
,
2010
, “
Roll-Channel Fractional Order Controller Design for a Small Fixed-Wing Unmanned Aerial Vehicle
,”
Control Eng. Pract.
,
18
(
7
), pp.
761
772
.10.1016/j.conengprac.2010.02.003
19.
Li
,
H.
,
Luo
,
Y.
, and
Chen
,
Y. Q.
,
2010
, “
A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments
,”
Control Syst. Technol., IEEE Trans.
,
18
(
2
), pp.
516
520
.10.1109/TCST.2009.2019120
20.
Tavazoei
,
M. S.
,
Haeri
,
M.
,
Jafari
,
S.
,
Bolouki
,
S.
, and
Siami
,
M.
,
2008
, “
Some Applications of Fractional Calculus in Suppression of Chaotic Oscillations
,”
IEEE Trans. Ind. Electron.
,
55
(
11
), pp.
4094
4101
.10.1109/TIE.2008.925774
21.
Calderon
,
A. J.
,
Vinagre
,
B. M.
, and
Feliu
,
V.
,
2006
, “
Fractional Order Control Strategies for Power Electronic Buck Converters
,”
Signal Process.
,
86
(
10
), pp.
2803
2819
.10.1016/j.sigpro.2006.02.022
22.
Efe
,
M. O.
,
2008
, “
Fractional Fuzzy Adaptive Sliding-Mode Control of a 2-DOF Direct-Drive Robot Arm
,”
IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
,
38
(
6
), pp.
1561
1570
.10.1109/TSMCB.2008.928227
23.
Efe
,
M. O.
,
2011
, “
Fractional Order Systems in Industrial Automation—A Survey
,”
IEEE Trans. Ind. Inf.
,
7
(
4
), pp.
582
591
.10.1109/TII.2011.2166775
24.
Corradini
,
M. L.
,
Giambò
,
R.
, and
Pettinari
,
S.
,
2014
, “
On the Adoption of a Fractional-Order Sliding Surface for the Robust Control of Integer-Order LTI Plants
,”
Automatica
,
51
, pp.
364
371
.
25.
Lan
,
Y. H.
, and
Zhou
,
Y.
,
2013
, “
Non-Fragile Observer-Based Robust Control for a Class of Fractional-Order Nonlinear Systems
,”
Syst. Control Lett.
,
62
(
12
), pp.
1143
1150
.10.1016/j.sysconle.2013.09.007
26.
Luo
,
Y.
,
Chen
,
Y.
,
Ahn
,
H. S.
, and
Pi
,
Y.
,
2010
, “
Fractional Order Robust Control for Cogging Effect Compensation in PMSM Position Servo Systems: Stability Analysis and Experiments
,”
Control Eng. Pract.
,
18
(
9
), pp.
1022
1036
.10.1016/j.conengprac.2010.05.005
27.
Badri
,
V.
, and
Tavazoei
,
M. S.
,
2013
, “
On Tuning Fractional Order [Proportional–Derivative] Controllers for a Class of Fractional Order Systems
,”
Automatica
,
49
(
7
), pp.
2297
2301
.10.1016/j.automatica.2013.04.026
28.
Luo
,
Y.
, and
Chen
,
Y. Q.
,
2009
, “
Fractional Order [Proportional Derivative] Controller for a Class of Fractional Order Systems
,”
Automatica
,
45
(
10
), pp.
2446
2450
.10.1016/j.automatica.2009.06.022
29.
Luo
,
Y.
,
Chen
,
Y. Q.
,
Wang
,
C. Y.
, and
Pi
,
Y. G.
,
2010
, “
Tuning Fractional Order Proportional Integral Controllers for Fractional Order Systems
,”
J. Process Control
,
20
(
7
), pp.
823
831
.10.1016/j.jprocont.2010.04.011
30.
Luo
,
Y.
, and
Chen
,
Y. Q.
,
2012
, “
Stabilizing and Robust Fractional Order PI Controller Synthesis for First Order Plus Time Delay Systems
,”
Automatica
,
48
(
9
), pp.
2159
2167
.10.1016/j.automatica.2012.05.072
31.
Luo
,
Y.
,
Zhang
,
T.
,
Lee
,
B.
,
Kang
,
C.
, and
Chen
,
Y.
,
2014
, “
Fractional-Order Proportional Derivative Controller Synthesis and Implementation for Hard-Disk-Drive Servo System
,”
IEEE Trans. Control Syst. Technol.
,
22
(
1
), pp.
281
289
.10.1109/TCST.2013.2239111
32.
Chen
,
Y. Q.
, and
Moore
,
K. L.
,
2005
, “
Relay Feedback Tuning of Robust PID Controllers With Iso-Damping Property
,”
IEEE Trans. Syst., Man, Cybern.-Part B: Cybern.
,
35
(
1
), pp.
23
31
.10.1109/TSMCB.2004.837950
33.
Barbosa
,
R. S.
,
Tenreiro Machado
,
J. A.
, and
Ferreira
,
I. M.
,
2004
, “
Tuning of PID Controllers Based on Bode's Ideal Transfer Function
,”
Nonlinear Dyn.
,
38
(
1–4
), pp.
305
321
.10.1007/s11071-004-3763-7
34.
Jin
,
Y.
,
Chen
,
Y. Q.
, and
Xue
,
D.
,
2011
, “
Time-Constant Robust Analysis of a Fractional Order [Proportional Derivative] Controller
,”
IET Control Theory Appl.
,
5
(
1
), pp.
164
172
.10.1049/iet-cta.2009.0543
35.
Feliu-Batlle
,
V.
, and
Castillo-García
,
F. J.
,
2014
, “
On the Robust Control of Stable Minimum Phase Plants With Large Uncertainty in a Time Constant, A Fractional-Order Control Approach
,”
Automatica
,
50
(
1
), pp.
218
224
.10.1016/j.automatica.2013.10.002
36.
Petras
,
I.
,
Chen
,
Y. Q.
,
Vinagre
,
B. M.
, and
Podlubny
,
I.
,
2004
, “
Stability of Linear Time Invariant Systems With Interval Fractional Orders and Interval Coefficients
,”
IEEE International Conference on Computational Cybernetics (ICCC)
, pp.
341
346
.
37.
Galvão
,
R. K. H.
,
Hadjiloucas
,
S.
,
Kienitz
,
K. H.
,
Paiva
,
H. M.
, and
Afonso
,
R. J. M.
,
2013
, “
Fractional Order Modeling of Large Three-Dimensional RC Networks
,”
IEEE Trans. Circuits Syst. I: Regular Papers
,
60
(
3
), pp.
624
637
.10.1109/TCSI.2012.2209733
38.
Gabano
,
J. D.
, and
Poinot
,
T.
,
2011
, “
Fractional Modeling and Identification of Thermal Systems
,”
Signal Process.
,
91
(
3
), pp.
531
541
.10.1016/j.sigpro.2010.02.005
39.
Narayanaswamy
,
P. N.
,
Kanthabhabha
,
P.
, and
Hamamci
,
S. E.
,
2010
, “
Fractional Order PIλ Control Strategy for a Liquid Level System
,”
IEEE Second World Congress on Nature and Biologically Inspired Computing (NaBIC)
, pp.
121
126
.10.1109/NABIC.2010.5716345
40.
Bonnet
,
C.
, and
Partington
,
J. R.
,
2000
, “
Coprime Factorizations and Stability of Fractional Differential Systems
,”
Syst. Control Lett.
,
41
(
3
), pp.
167
174
.10.1016/S0167-6911(00)00050-5
41.
Tavazoei
,
M. S.
,
2013
, “
On Type Number Concept in Fractional-Order Systems
,”
Automatica
,
49
(
1
), pp.
301
304
.10.1016/j.automatica.2012.09.022
42.
Mansouri
,
R.
,
Bettayeb
,
M.
,
Djamah
,
T.
, and
Djennoune
,
S.
,
2008
, “
Vector Fitting Fractional System Identification Using Particle Swarm Optimization
,”
Appl. Math. Comput.
,
206
(
2
), pp.
510
520
.10.1016/j.amc.2008.05.146
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