Abstract
This paper deals with the parameter identification problem for nonlinear mechanical systems based on state estimation. Here, the concept of Sliding Mode Observer for finite time state estimation and the Least-Square Method for parameter identification have been combined; thus, guaranteeing that the estimated state converges to the real one in a finite time. The asymptotic parameter identification is performed by applying the Least-Square approach, minimizing the so-called joint uncertainty; in this process, a specific persistent excitation condition is introduced to guarantee the effectiveness of the proposed identification algorithm. With the proposed approach and some considerations, the algorithm is capable of estimating friction coefficients and inertia moments, within a narrow time-window. Finally, the performance of the identification algorithm designed in this paper is tested on a real-time underactuated system, specifically the double pendulum on a cart platform. Furthermore, a successful benchmarking between the algorithm herein and the traditional least-square method is reported.
Issue Section:
Research Papers
References
1.
Jamshidifar
,
H.
,
Askari
,
H.
, and
Fidan
,
B.
, 2018
, “
Parameter Identification and Adaptive Control of Carbon Nanotube Resonators
,” Asian J. Control.
,
20
(4
), pp. 1329
–1338
.10.1002/asjc.14232.
Pohl
,
K.
, 2010
, Requirements Engineering: Fundamentals, Principles, and Techniques
,
Springer Publishing Company
, Berlin
.3.
Spong
,
M. W.
, and
Vidyasagar
,
M.
, 2008
, Robot Dynamics and Control
,
Wiley
, Hoboken, NJ
.4.
Utkin
,
V.
,
Guldner
,
J.
, and
Shi
,
J.
, 2017
, Sliding Mode Control in Electro-Mechanical Systems
,
CRC Press
, West Sussex, UK
.5.
Ma
,
Z.-S.
,
Li
,
L.
, and
Ding
,
Q.
, 2020
, “
Multivariate Recursive Bayesian Linear Regression and Its Applications to Output-Only Identification of Time-Varying Mechanical Systems
,” J. Vib. Control
, epub.10.1177/10775463209417036.
Al-Bender
,
F.
,
Lampaert
,
V.
, and
Swevers
,
J.
, 2005
, “
The Generalized Maxwell-Slip Model: A Novel Model for Friction Simulation and Compensation
,” IEEE Trans. Autom. Control
,
50
(11
), pp. 1883
–1887
.10.1109/TAC.2005.8586767.
Do
,
T.
,
Tjahjowidodo
,
T.
,
Lau
,
M.
, and
Phee
,
S.
, 2015
, “
Nonlinear Friction Modelling and Compensation Control of Hysteresis Phenomena for a Pair of Tendon-Sheath Actuated Surgical Robots
,” Mech. Syst. Signal Process.
,
60–61
, pp. 770
–784
.10.1016/j.ymssp.2015.01.0018.
D. D
,
R.
, and
S. D
,
F.
, 2005
, “
Maxwell Slip Model Based Identification and Control of Systems With Friction
,” 44th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC'05
), Seville, Spain, Dec. 15, pp. 4578
–4583
.10.1109/CDC.2005.15828849.
Ruderman
,
M.
, and
Bertram
,
T.
, 2011
, “
Modified Maxwell-Slip Model of Presliding Friction
,” IFAC Proc. Vols.
,
44
(1
), pp. 10764
–10769
.10.3182/20110828-6-IT-1002.0030910.
Choi
,
J.-W.
,
Lee
,
S.-C.
, and
Kim
,
H.-G.
, 2006
, “
Inertia Identification Algorithm for High-Performance Speed Control of Electric Motors
,” IEE Proc. Electric Power Appl.
,
153
(3
), pp. 379
–386
.10.1049/ip-epa:2005036011.
Wu
,
J.
,
Wang
,
J.
, and
You
,
Z.
, 2010
, “
An Overview of Dynamic Parameter Identification of Robots
,” Rob. Comput.-Integr. Manuf.
,
26
(5
), pp. 414
–419
.10.1016/j.rcim.2010.03.01312.
Bitmead
,
R.
, 1984
, “
Persistence of Excitation Conditions and the Convergence of Adaptive Schemes
,” IEEE Trans. Inf. Theory
,
30
(2
), pp. 183
–191
.10.1109/TIT.1984.105689813.
Ljung
,
L.
, 1998
, “
System Identification
,” In Signal Analysis and Prediction
,
Springer
, New York
, pp. 163
–173
.14.
Poznyak
,
A. S.
, 2009
, “
Advanced Mathematical Tools for Automatic Control Engineers
,” Stoc. Tech.
,
2
, pp. 393
–399
.15.
Chen
,
B.
,
Zhu
,
Y.
,
Hu
,
J.
, and
Principe
,
J. C.
, 2013
, System Parameter Identification: Information Criteria Algorithms
, Newnes
, FL
.16.
Zhang
,
X.
,
Ding
,
F.
,
Alsaadi
,
F. E.
, and
Hayat
,
T.
, 2017
, “
Recursive Parameter Identification of the Dynamical Models for Bilinear State Space Systems
,” Nonlinear Dyn.
,
89
(4
), pp. 2415
–2429
.10.1007/s11071-017-3594-y17.
Janot
,
A.
,
Vandanjon
,
P. O.
, and
Gautier
,
M.
, 2014
, “
An Instrumental Variable Approach for Rigid Industrial Robots Identification
,” Control Eng. Pract.
,
25
, pp. 85
–101
.10.1016/j.conengprac.2013.12.00918.
Poznyak
,
A.
, 1980
, “
Estimating the Parameters of Autoregression Processes by the Method of Least Squares
,” Int. J. Syst. Sci.
,
11
(5
), pp. 577
–588
.10.1080/0020772800896703819.
Åström
,
K. J.
, and
Wittenmark
,
B.
, 1989
, Adaptive Control
,
Addison-Wesley
, New York
.20.
Narendra
,
K. S.
, and
Annaswamy
,
A. M.
, 2005
, Stable Adaptive Systems
,
Dover Publications
, Mineola, NY
.21.
Edwards
,
C.
,
Fossas Colet
,
E.
, and
Fridman
,
L.
, 2006
, Advances in Variable Structure and Sliding Mode Control
,
Springer Verlag
, Berlin
.22.
Sessa
,
S.
,
Vaiana
,
N.
,
Paradiso
,
M.
, and
Rosati
,
L.
, 2020
, “
An Inverse Identification Strategy for the Mechanical Parameters of a Phenomenological Hysteretic Constitutive Model
,” Mech. Syst. Signal Process.
,
139
, p. 106622
.10.1016/j.ymssp.2020.10662223.
Vaiana
,
N.
,
Sessa
,
S.
, and
Rosati
,
L.
, 2021
, “
A Generalized Class of Uniaxial Rate-Independent Models for Simulating Asymmetric Mechanical Hysteresis Phenomena
,” Mech. Syst. Signal Process.
,
146
, p. 106984
.10.1016/j.ymssp.2020.10698424.
Li
,
M.
,
Wu
,
H.
,
Wang
,
Y.
,
Handroos
,
H.
, and
Carbone
,
G.
, 2017
, “
Modified Levenberg–Marquardt Algorithm for Backpropagation Neural Network Training in Dynamic Model Identification of Mechanical Systems
,” ASME J. Dyn. Syst., Meas., Control
,
139
(3
), p. 031012
.10.1115/1.403501025.
Elinger
,
J.
, and
Rogers
,
J.
, 2018
, “
Information Theoretic Causality Measures for System Identification of Mechanical Systems
,” ASME J. Comput. Nonlinear Dyn.
,
13
(7
), p. 071005
.10.1115/1.404025326.
Pappalardo
,
C. M.
, and
Guida
,
D.
, 2018
, “
A Time-Domain System Identification Numerical Procedure for Obtaining Linear Dynamical Models of Multibody Mechanical Systems
,” Arch. Appl. Mech.
,
88
(8
), pp. 1325
–1347
.10.1007/s00419-018-1374-x27.
Nechak
,
L.
, 2020
, “
Nonlinear State Observer for Estimating and Controlling of Friction-Induced Vibrations
,” Mech. Syst. Signal Process.
,
139
, p. 106588
.10.1016/j.ymssp.2019.10658828.
Sun
,
L.
, and
Liu
,
Y.
, 2020
, “
Extended State Observer Augmented Finite-Time Trajectory Tracking Control of Uncertain Mechanical Systems
,” Mech. Syst. Signal Process.
,
139
, p. 106374
.10.1016/j.ymssp.2019.10637429.
Majumder
,
K.
, and
Patre
,
B.
, 2019
, “
Adaptive Sliding Mode Control for Asymptotic Stabilization of Underactuated Mechanical Systems Via Higher-Order Nonlinear Disturbance Observer
,” J. Vib. Control
,
25
(17
), pp. 2340
–2350
.10.1177/107754631985319930.
Ordaz
,
P.
,
Rodríguez-Guerrero
,
L.
,
Santos
,
O.
,
Cuvas
,
C.
,
Romero
,
H.
,
Ordaz-Oliver
,
M.
, and
López-Pérez
,
P.
, 2020
, “
Parameter Estimation of a Second Order System Via Nonlinear Identification Algorithm
,” IOP Conference Series: Materials Science and Engineering
, Vol.
844
,
IOP Publishing
, Cartagena de Indias, Colombia
, p. 012038
.31.
Davila
,
J.
,
Fridman
,
L.
, and
Poznyak
,
A.
, 2006
, “
Observation and Identification of Mechanical Systems Via Second Order Sliding Modes
,” Int. J. Control
,
79
(10
), pp. 1251
–1262
.10.1080/0020717060080163532.
Gao
,
G.
,
Sun
,
G.
,
Na
,
J.
,
Guo
,
Y.
, and
Wu
,
X.
, 2018
, “
Structural Parameter Identification for 6 Dof Industrial Robots
,” Mech. Syst. Signal Process.
,
113
, pp. 145
–155
.10.1016/j.ymssp.2017.08.01133.
Garćıa-Alarćon
,
O.
,
Puga-Guzman
,
S.
, and
Moreno-Valenzuela
,
J.
, 2012
, “
On Parameter Identification of the Furuta Pendulum
,” Procedia Eng.
,
35
, pp. 77
–84
.10.1016/j.proeng.2012.04.16734.
Jin
,
J.
, and
Gans
,
N.
, 2015
, “
Parameter Identification for Industrial Robots With a Fast and Robust Trajectory Design Approach
,” Rob. Comput.-Integr. Manuf.
,
31
, pp. 21
–29
.10.1016/j.rcim.2014.06.00435.
Khosla
,
P. K.
, and
Kanade
,
T.
, 1985
, “
Parameter Identification of Robot Dynamics
,” 24th IEEE Conference on Decision and Control
, Vol.
24
,
IEEE
, Fort Lauderdale, FL
, Dec. 11–13, pp. 1754
–1760
.10.1109/CDC.1985.26883836.
De Silva
,
C. W.
, 2015
, Sensors and Actuators: Engineering System Instrumentation
,
CRC Press
, Boca Raton, FL
.37.
Liu
,
G.
, 2002
, “
On Velocity Estimation Using Position Measurements
,” Proceedings of American Control Conference
, Vol.
2
,
IEEE
, Anchorage, AK
, May 8–10, pp. 1115
–1120
.10.1109/ACC.2002.102316838.
Merry
,
R.
,
Van de Molengraft
,
M.
, and
Steinbuch
,
M.
, 2010
, “
Velocity and Acceleration Estimation for Optical Incremental Encoders
,” Mechatronics
,
20
(1
), pp. 20
–26
.10.1016/j.mechatronics.2009.06.01039.
Proca
,
A. B.
, and
Keyhani
,
A.
, 2007
, “
Sliding-Mode Flux Observer With Online Rotor Parameter Estimation for Induction Motors
,” IEEE Trans. Ind. Elect.
,
54
(2
), pp. 716
–723
.10.1109/TIE.2007.89178640.
Shtessel
,
Y.
,
Edwards
,
C.
,
Fridman
,
L.
, and
Levant
,
A.
, 2014
, Sliding Mode Control and Observation
, Vol.
10
,
Springer
, New York
.41.
Zhang
,
X.
, and
Li
,
Z.
, 2016
, “
Sliding-Mode Observer-Based Mechanical Parameter Estimation for Permanent Magnet Synchronous Motor
,” IEEE Trans. Power Electron.
,
31
(8
), pp. 5732
–5745
.10.1109/TPEL.2015.249518342.
Shtessel
,
Y. B.
, and
Poznyak
,
A. S.
, 2005
, “
Parameter Identification of Affine Time Varying Systems Using Traditional and High Order Sliding Modes
,” Proceedings of the American Control Conference
,
IEEE
, Portland, OR
, June 8–10, pp. 2433
–2438
.10.1109/ACC.2005.147033143.
Ordaz
,
P.
, and
Poznyak
,
A.
, 2015
, “
Kl-Gain Adaptation for Attractive Ellipsoid Method
,” IMA J. Math. Control Inf.
,
32
(3
), pp. 447
–469
.10.1093/imamci/dnt04644.
Khalil
,
H. K.
, and
Grizzle
,
J. W.
, 2002
, Nonlinear Systems
, Vol.
3
,
Prentice Hall
,
Upper Saddle River, NJ
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