Abstract

In this study, a novel design method for half-cycle and modified posicast controller structures is proposed for a class of the fractional order systems. In this method, all required design variable values, namely, the input step magnitudes and their application times are obtained as functions of fractional system parameters. Moreover, empirical formulas are obtained for the overshoot values of the compensated system with half-cycle and modified posicast controllers designed utilizing this method. The proposed design methodology has been tested via simulations and ball balancing real-time system. It is observed that the derived formulas are in coherence with outcomes of the simulation and real-time application. Furthermore, the performance of modified posicast controller designed using proposed method is much better than other posicast control method.

References

1.
Smith
,
O. J.
,
1957
, “
Posicast Control of Damped Oscillatory Systems
,”
Proc. IRE
,
45
(
9
), pp.
1249
1255
.10.1109/JRPROC.1957.278530
2.
Tallman
,
G.
, and
Smith
,
O.
,
1958
, “
Analog Study of Dead-Beat Posicast Control
,”
IRE Trans. Autom. Control
,
4
(
1
), pp.
14
21
.10.1109/TAC.1958.1104844
3.
Shields
,
V.
, and
Cook
,
G.
,
1971
, “
Application of an Approximate Time Delay to a Posicast Control System
,”
Int. J. Control
,
14
(
4
), pp.
649
657
.10.1080/00207177108932075
4.
Hamza
,
M.
,
1990
, “
Adaptive Deadbeat Control of Instrument Servos
,”
Trans. Inst. Meas. Control
,
12
(
4
), pp.
219
223
.10.1177/014233129001200408
5.
Hung
,
J. Y.
,
2003
, “
Feedback Control With Posicast
,”
IEEE Trans. Ind. Electron.
,
50
(
1
), pp.
94
99
.10.1109/TIE.2002.804979
6.
Kalantar
,
M.
, and
Mousavi
,
S. M.
,
2010
, “
Posicast Control Within Feedback Structure for a DC–DC Single Ended Primary Inductor Converter in Renewable Energy Applications
,”
Appl. Energy
,
87
(
10
), pp.
3110
3114
.10.1016/j.apenergy.2010.04.012
7.
Singhose
,
W.
,
Porter
,
L.
,
Kenison
,
M.
, and
Kriikku
,
E.
,
2000
, “
Effects of Hoisting on the Input Shaping Control of Gantry Cranes
,”
Control Eng. Pract.
,
8
(
10
), pp.
1159
1165
.10.1016/S0967-0661(00)00054-X
8.
Gürleyük
,
S.
, and
Cinal
,
Ş.
,
2007
, “
Robust Three-Impulse Sequence Input Shaper Design
,”
J. Vib. Control
,
13
(
12
), pp.
1807
1818
.10.1177/1077546307080012
9.
Dhanda
,
A.
,
Vaughan
,
J.
, and
Singhose
,
W.
,
2016
, “
Vibration Reduction Using Near Time-Optimal Commands for Systems With Nonzero Initial Conditions
,”
ASME J. Dyn. Syst., Meas., Control
,
138
(
4
), p.
041006
.10.1115/1.4032064
10.
Newman
,
D.
,
Hong
,
S. W.
, and
Vaughan
,
J. E.
,
2018
, “
The Design of Input Shapers Which Eliminate Nonzero Initial Conditions
,”
ASME J. Dyn. Syst., Meas., Control
,
140
(
10
), p.
101005
.10.1115/1.4039668
11.
Mohamed
,
Z.
, and
Tokhi
,
M. O.
,
2004
, “
Command Shaping Techniques for Vibration Control of a Flexible Robot Manipulator
,”
Mechatronics
,
14
(
1
), pp.
69
90
.10.1016/S0957-4158(03)00013-8
12.
Ghorbani
,
A.
,
Masoudi
,
S.
, and
Shabani
,
A.
,
2012
, “
Application of the Posicast Control Method to Static Shunt Compensators
,”
Turk. J. Electr. Eng. Comput. Sci.
,
20
(
Sup. 1
), pp.
1100
1108
.10.3906/elk-1102-1041
13.
Xu
,
J.
,
Fang
,
H.
,
Zhou
,
T.
,
Chen
,
Y. H.
,
Guo
,
H.
, and
Zeng
,
F.
,
2019
, “
Optimal Robust Position Control With Input Shaping for Flexible Solar Array Drive System: A Fuzzy-Set Theoretic Approach
,”
IEEE Trans. Fuzzy Syst.
,
27
(
9
), pp.
1807
1817
.10.1109/TFUZZ.2019.2892339
14.
Jia
,
S.
, and
Shan
,
J.
,
2019
, “
Vibration Control of Gyroelastic Spacecraft Using Input Shaping and Angular Momentum Devices
,”
Acta Astronaut.
,
159
, pp.
397
409
.10.1016/j.actaastro.2019.03.062
15.
Azarmi
,
R.
,
Tavakoli-Kakhki
,
M.
,
Sedigh
,
A. K.
, and
Fatehi
,
A.
,
2015
, “
Analytical Design of Fractional Order PID Controllers Based on the Fractional Set-Point Weighted Structure: Case Study in Twin Rotor Helicopter
,”
Mechatronics
,
31
, pp.
222
233
.10.1016/j.mechatronics.2015.08.008
16.
Yumuk
,
E.
,
Güzelkaya
,
M.
, and
Eksin
,
İ.
,
2019
, “
Design of an Integer Order Proportional–Integral/Proportional–Integral–Derivative Controller Based on Model Parameters of a Certain Class of Fractional Order Systems
,”
Proc. Inst. Mech. Eng., Part I
,
233
(
3
), pp.
320
334
.10.1177/0959651818792363
17.
Malek
,
H.
,
Luo
,
Y.
, and
Chen
,
Y. Q.
,
2013
, “
Identification and Tuning Fractional Order Proportional Integral Controllers for Time Delayed System With a Fractional Pole
,”
Mechatronics
,
23
(
7
), pp.
746
754
.10.1016/j.mechatronics.2013.02.005
18.
Talmoudi
,
S.
, and
Lahmari
,
M.
,
2018
, “
The Multi-Model Approach for Fractional-Order Systems Modelling
,”
Trans. Inst. Meas. Control
,
40
(
1
), pp.
331
340
.10.1177/0142331216655396
19.
Yumuk
,
E.
,
Güzelkaya
,
M.
, and
Eksin
,
İ.
,
2020
, “
Optimal Fractional-Order Controller Design Using Direct Synthesis Method
,”
IET Control Theory Appl.
,
14
(
18
), pp.
2960
2967
.10.1049/iet-cta.2020.0596
20.
Yumuk
,
E.
,
Güzelkaya
,
M.
, and
Eksin
,
İ.
,
2019
, “
Analytical Fractional PID Controller Design Based on Bode's Ideal Transfer Function Plus Time Delay
,”
ISA Trans.
,
91
, pp.
196
206
.10.1016/j.isatra.2019.01.034
21.
Gonzalez
,
E. A.
,
Hung
,
J. Y.
,
Dorcak
,
L.
,
Terpak
,
J.
, and
Petras
,
I.
,
2013
, “
Posicast Control of a Class of Fractional-Order Processes
,”
Central Eur. J. Phys.
,
11
(
6
), pp.
868
880
.10.2478/s11534-013-0284-3
22.
Valerio
,
D.
, and
da Costa
,
J. S.
,
2011
, “
Introduction to Single-Input, Single-Output Fractional Control
,”
IET Control Theory Appl.
,
5
(
8
), pp.
1033
1057
.10.1049/iet-cta.2010.0332
23.
Dzieliński
,
A.
, and
Sierociuk
,
D.
,
2008
, “
Stability of Discrete Fractional Order State-Space Systems
,”
J. Vib. Control
,
14
(
9–10
), pp.
1543
1556
.10.1177/1077546307087431
24.
Kurucu
,
M. C.
,
Yumuk
,
E.
,
Güzelkaya
,
M.
, and
Eksin
,
İ.
,
2017
, “
Investigation of the Effects of Fractional and Integer Order Fuzzy Logic PID Controllers on System Performances
,” 10th International Conference on Electrical and Electronics Engineering (
ELECO
),
IEEE
,
Bursa, Turkey
, Nov. 30–Dec. 2, pp.
775
779
.https://ieeexplore.ieee.org/document/8266184
25.
Kurucu
,
M. C.
,
Yumuk
,
E.
,
Güzelkaya
,
M.
, and
Eksin
,
İ.
,
2018
, “
Online Tuning of Derivative Order Term in Fractional Controllers
,” Sixth International Conference on Control Engineering Information Technology (
CEIT
),
IEEE
,
Istanbul, Turkey
, Oct. 25–27, pp.
268
272
.10.1109/CEIT.2018.8751806
26.
Monje
,
C. A.
,
Chen
,
Y. Q.
,
Vinagre
,
B. M.
,
Xue
,
D.
, and
Feliu
,
V.
,
2010
,
Fractional-Order Systems and Controls Fundamentals and Applications
,
Springer-Verlag
,
Berlin
.
27.
Tepljakov
,
A.
,
Petlenkov
,
E.
,
Belikov
,
J.
, and
Halas
,
M.
,
2013
, “
Design and Implementation of Fractional-Order PID Controllers for a Fluid Tank System
,”
Proceedings of American Control Conference
,
Washington, DC
,
June 17–19
, pp.
1777
1782
.10.1109/ACC.2013.6580093
28.
Barbosa
,
R. S.
,
Machado
,
J. T.
, 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
29.
Drezner
,
Z.
, and
Drezner
,
T. D.
,
2020
, “
Biologically Inspired Parent Selection in Genetic Algorithms
,”
Ann. Oper. Res.
,
287
(
1
), pp.
161
183
.10.1007/s10479-019-03343-7
30.
Abdelkhalik
,
O.
, and
Darani
,
S.
,
2018
, “
Evolving Hidden Genes in Genetic Algorithms for Systems Architecture Optimization
,”
ASME J. Dyn. Syst., Meas., Control
,
140
(
10
), p. 101015.10.1115/1.4040207
31.
Acrome
,
2014
, “
Ball Balancing Table Courseware…
,” Acrome, Istanbul, Turkey, https://acrome.net/ball-balancing-table-3-2
32.
Tepljakov
,
A.
,
Petlenkov
,
E.
, and
Belikov
,
J.
,
2011
, “
FOMCON: Fractional-Order Modeling and Control Toolbox for MATLAB
,”
18th International Conference on Mixed Design of Integrated Circuits and Systems
,
Gliwice, Poland
,
June 16–18
, pp. 684–689. https://ieeexplore.ieee.org/document/6016009
You do not currently have access to this content.