This paper proposes an uncertainty and disturbance estimator (UDE)-based controller for nonlinear systems with mismatched uncertainties and disturbances, integrating the UDE-based control and the conventional backstepping scheme. The adoption of the backstepping scheme helps to relax the structural constraint of the UDE-based control. Moreover, the reference model design in the UDE-based control offers a solution to address the “complexity explosion” problem of the backstepping approach. Furthermore, the strict-feedback form condition in the conventional backstepping approach is also relaxed by using the UDE-based control to estimate and compensate “disturbance-like” terms including nonstrict-feedback terms and intermediate system errors. The uniformly ultimate boundedness of the closed-loop system is analyzed. Both numerical and experimental studies are provided.
Issue Section:
Research Papers
References
1.
Youcef-Toumi
, K.
, and Ito
, O.
, 1990
, “A Time Delay Controller for Systems With Unknown Dynamics
,” ASME J. Dyn. Syst. Meas. Control
, 112
(1
), pp. 133
–142
.2.
Park
, J. H.
, and Kim
, Y. M.
, 1999
, “Time-Delay Sliding Mode Control for a Servo
,” ASME J. Dyn. Syst., Meas., Control
, 121
(1
), pp. 143
–148
.3.
Chang
, P.
, Park
, S.-H.
, and Lee
, J.-H.
, 1999
, “A Reduced Order Time-Delay Control for Highly Simplified Brushless Dc
,” ASME J. Dyn. Syst., Meas., Control
, 121
(3
), pp. 556
–560
.4.
Chang
, P. H.
, Park
, B. S.
, and Park
, K. C.
, 1996
, “An Experimental Study on Improving Hybrid Position/Force Control of a Robot Using Time Delay Control
,” Mechatronics
, 6
(8
), pp. 915
–931
.5.
Chang
, P.
, and Lee
, J.
, 1996
, “A Model Reference Observer for Time-Delay Control and Its Application to Robot Trajectory Control
,” IEEE Trans. Control Syst. Technol
, 4
(1
), pp. 2
–10
.6.
Youcef-Toumi
, K.
, and Wu
, S.
, 1992
, “Input-Output Linearization Using Time Delay Control
,” ASME J. Dyn. Syst. Meas. Control
, 114
(1
), pp. 10
–19
.7.
Zhong
, Q.-C.
, and Rees
, D.
, 2004
, “Control of Uncertain LTI Systems Based on an Uncertainty and Disturbance Estimator
,” ASME J. Dyn. Syst. Meas. Control
, 126
(4
), pp. 905
–910
.8.
Zhong
, Q.-C.
, Kuperman
, A.
, and Stobart
, R.
, 2011
, “Design of UDE-Based Controllers From Their Two-Degree-of-Freedom Nature
,” Int. J. Robust Nonlinear Control
, 21
(17
), pp. 1994
–2008
.9.
Shendge
, P.
, and Patre
, B.
, 2007
, “Robust Model Following Load Frequency Sliding Mode Controller Based on UDE and Error Improvement With Higher Order Filter
,” IAENG Int. J. Appl. Math., 37
(1
), pp. 27
–32
.https://www.researchgate.net/profile/Bm_Patre/publication/267180658_Robust_Model_Following_Load_Frequency_Sliding_Mode_Controller_Based_on_DE_and_Error_Improvement_with_Higher_Order_Filter/links/00b495305cb267e52f000000.pdf10.
Chandar
, T. S.
, and Talole
, S. E.
, 2014
, “Improving the Performance of UDE-Based Controller Using a New Filter Design
,” Nonlinear Dyn.
, 77
(3
), pp. 753
–768
.11.
Kuperman
, A.
, 2015
, “Design of α-Filter-Based Ude Controllers Considering Finite Control Bandwidth
,” Nonlinear Dyn.
, 81
(1–2
), pp. 411
–416
.12.
Ren
, B.
, Zhong
, Q.-C.
, and Dai
, J.
, 2017
, “Asymptotic Reference Tracking and Disturbance Rejection of UDE-Based Robust Control
,” IEEE Trans. Ind. Electron
, 64
(4
), pp. 3166
–3176
.13.
Talole
, S.
, and Phadke
, S.
, 2010
, “Robust Input-Output Linearisation Using Uncertainty and Disturbance Estimation
,” Int. J. Control
, 82
(10
), pp. 1794
–1803
.14.
Talole
, S.
, Chandar
, T.
, and Kolhe
, J. P.
, 2011
, “Design and Experimental Validation of Ude Based Controller–Observer Structure for Robust Input–Output Linearisation
,” Int. J. Control
, 84
(5
), pp. 969
–984
.15.
Talole
, S.
, and Phadke
, S.
, 2008
, “Model Following Sliding Mode Control Based on Uncertainty and Disturbance Estimator
,” ASME J. Dyn. Syst. Meas. Control
, 130
(3
), pp. 1
–5
.16.
Castillo
, A.
, Sanz
, R.
, Garcia
, P.
, and Albertos
, P.
, 2017
, “Robust Design of the Uncertainty and Disturbance Estimator
,” IFAC-PapersOnLine
, 50
(1
), pp. 8262
–8267
.17.
Deshpande
, V.
, and Phadke
, S.
, 2012
, “Control of Uncertain Nonlinear Systems Using an Uncertainty and Disturbance Estimator
,” ASME J. Dyn. Syst. Meas. Control
, 134
(2
), p. 024501
.18.
Stobart
, R. K.
, and Zhong
, Q.-C.
, 2011
, “Uncertainty and Disturbance Estimator-Based Control for Uncertain LTI-SISO Systems With State Delays
,” ASME J. Dyn. Syst. Meas. Control
, 133
(2
), pp. 1
–6
.19.
Kuperman
, A.
, and Zhong
, Q.-C.
, 2010
, “Robust Control of Uncertain Nonlinear Systems With State Delays Based on an Uncertainty and Disturbance Estimator
,” Int. J. Robust Nonlinear Control
, 21
(1
), pp. 79
–92
. 20.
Ren
, B.
, Zhong
, Q.-C.
, and Chen
, J.
, 2015
, “Robust Control for a Class of Non-Affine Nonlinear Systems Based on the Uncertainty and Disturbance Estimator
,” IEEE Trans. Ind. Electron
, 62
(9
), pp. 5881
–5888
.21.
Sanz
, R.
, Garcia
, P.
, Zhong
, Q.-C.
, and Albertos
, P.
, 2016
, “Robust Control of Quadrotors Based on an Uncertainty and Disturbance Estimator
,” ASME J. Dyn. Syst. Meas. Control
, 138
(7
), p. 071006
.22.
Chen
, J.
, Ren
, B.
, and Zhong
, Q.-C.
, 2016
, “UDE-Based Trajectory Tracking Control of Piezoelectric Stages
,” IEEE Trans. Ind. Electron
, 63
(10
), pp. 6450
–6459
.23.
Kolhe
, J. P.
, Shaheed
, M.
, Chandar
, T. S.
, and Taloe
, S. E.
, 2013
, “Robust Control of Robot Manipulators Based on Uncertainty and Diturbance Estimation
,” Int. J. Robust Nonlinear Control
, 23
(1
), pp. 104
–122
.24.
Xiao
, L.
, 2014
, “Aeroengine Multivariable Nonlinear Tracking Control Based on Uncertainty and Disturbance Estimator
,” ASME J. Eng. Gas Turbines Power
, 136
(12
), p. 121601
.25.
Ren
, B.
, Wang
, Y.
, and Zhong
, Q.-C.
, 2017
, “UDE-Based Control of Variable-Speed Wind Turbine Systems
,” Int. J. Control
, 90
(1
), pp. 121
–136
.26.
Kuperman
, A.
, and Zhong
, Q.-C.
, 2015
, “UDE-Based Linear Robust Control for a Class of Nonlinear Systems With Application to Wing Rock Motion Stabilization
,” Nonlinear Dyn.
, 81
(1–2
), pp. 789
–799
.27.
Aharon
, I.
, Shmilovitz
, D.
, and Kuperman
, A.
, 2015
, “Robust Output Voltage Control of Multimode Non-Inverting DC–DC Converter
,” Int. J. Control
, 90
(1), pp. 110–120.28.
Wang
, Y.
, Ren
, B.
, and Zhong
, Q.-C.
, 2016
, “Robust Power Flow Control of Grid-Connected Inverters
,” IEEE Trans. Ind. Electron
, 63
(11
), pp. 6887
–6897
.29.
Su
, S.
, and Lin
, Y.
, 2011
, “Robust Output Tracking Control of a Class of Non-Minimum Phase Systems and Application to VTOL Aircraft
,” Int. J. Control
, 84
(11
), pp. 1858
–1872
.30.
Sun
, L.
, Li
, D.
, Zhong
, Q. C.
, and Lee
, K. Y.
, 2016
, “Control of a Class of Industrial Processes With Time Delay Based on a Modified Uncertainty and Disturbance Estimator
,” IEEE Trans. Ind. Electron
, 63
(11
), pp. 7018
–7028
.31.
Krstić
, M.
, Kanellakopoulos
, I.
, and Kokotović
, P. V.
, 1995
, Nonlinear and Adaptive Control Design
, Wiley
, New York
.32.
Ikhouane
, F.
, and Krstić
, M.
, 1998
, “Robustness of the Tuning Functions Adaptive Backstepping Design for Linear Systems
,” IEEE Tran. Autom. Control
, 43
(3
), pp. 431
–437
.33.
Zhou
, J.
, and Wen
, C.
, 2008
, Adaptive Backstepping Control of Uncertain Systems: Nonsmooth Nonlinearities, Interactions or Time-Variations
, Springer
, New York.34.
Swaroop
, D.
, Hedrick
, J. K.
, Yip
, P. P.
, and Gerdes
, J. C.
, 2000
, “Dynamic Surface Control for a Class of Nonlinear Systems
,” IEEE Trans. Autom. Control
, 45
(10
), pp. 1893
–1899
.35.
Yip
, P. P.
, and Hedrick
, J. K.
, 1998
, “Adaptive Dynamic Surface Control: A Simplified Algorithm for Adaptive Backstepping Control of Nonlinear Systems
,” Int. J. Control
, 71
(5
), pp. 959
–979
.36.
Apkarian
, J.
, Karam
, P.
, and Levis
, M.
, 2011
, “Instructor Workbook: Inverted Pendulum Experiment for Matlab/Simulink Users
,” Quanser Inc, Markham, ON, Canada.Copyright © 2018 by ASME
You do not currently have access to this content.
