In this paper, a state and extended disturbance observer (DO) is designed for mismatched uncertain systems. Apart from system states and disturbances, the proposed observer estimates the derivatives of the disturbances and thereby improves the accuracy of estimation of disturbances as well as the states. No knowledge of bounds of disturbances or their derivatives is assumed. An observer–controller combination for a sliding mode controller that requires the estimates of the derivatives of disturbances is described, and the ultimate boundedness of the overall system is proved. The proposed observer is illustrated by simulation of a numerical example and a rotary hydraulic actuator. The proposed observer–controller combination is validated on a serial flexible joint manipulator in laboratory.
Issue Section:
Technical Brief
References
1.
Drazenovich
, B.
, 1969
, “The Invariance Conditions in Variable Structure Systems
,” Automatica
, 5
(3
), pp. 287
–295
.10.1016/0005-1098(69)90071-52.
Yang
, J.
, Li
, S.
, and Yu
, X.
, 2013
, “Sliding-Mode Control for Systems With Mismatched Uncertainties Via a Disturbance Observer
,” IEEE Trans. Ind. Electron.
, 60
(1
), pp. 160
–169
.10.1109/TIE.2012.21838413.
Ginoya
, D.
, Shendge
, P. D.
, and Phadke
, S. B.
, 2014
, “Sliding Mode Control for Mismatched Uncertain Systems Using an Extended Disturbance Observer
,” IEEE Trans. Ind. Electron.
, 61
(4
), pp. 1983
–1992
.10.1109/TIE.2013.22715974.
Olfati-Saber
, R.
, 2002
, “Normal Forms for Underactuated Mechanical Systems With Symmetry
,” IEEE Trans. Autom. Control
, 47
(2
), pp. 305
–308
.10.1109/9.9833655.
Chen
, Y.-F.
, and Huang
, A.-C.
, 2012
, “Controller Design for a Class of Underactuated Mechanical Systems
,” IET Control Theory Appl.
, 6
(1
), pp. 103
–110
.10.1049/iet-cta.2010.06676.
Wen
, C. C.
, and Cheng
, C. C.
, 2008
, “Design of Sliding Surface for Mismatched Uncertain Systems to Achieve Asymptotical Stability
,” J. Franklin Inst.
, 345
(8
), pp. 926
–941
.10.1016/j.jfranklin.2008.06.0037.
Swaroop
, D.
, Hedrick
, J.
, Yip
, P.
, and Gerdes
, J.
, 2000
, “Dynamic Surface Control for a Class of Nonlinear Systems
,” IEEE Trans. Autom. Control
, 45
(10
), pp. 1893
–1899
.10.1109/TAC.2000.8809948.
Liang
, Y.-W.
, Ting
, L.-W.
, and Lin
, L.-G.
, 2012
, “Study of Reliable Control Via an Integral-Type Sliding Mode Control Scheme
,” IEEE Trans. Ind. Electron.
, 59
(8
), pp. 3062
–3068
.10.1109/TIE.2011.21622119.
Choi
, H.
, 2007
, “LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems
,” IEEE Trans. Autom. Control
, 52
(4
), pp. 736
–742
.10.1109/TAC.2007.89454310.
Cao
, Y.
, and Chen
, X.
, 2014
, “Disturbance-Observer-Based Sliding-Mode Control for a 3-DOF Nanopositioning Stage
,” IEEE/ASME Trans. Mechatronics
, 19
(3
), pp. 924
–931
.10.1109/TMECH.2013.226280211.
Liu
, J.
, Laghrouche
, S.
, and Wack
, M.
, 2014
, “Observer-Based Higher Order Sliding Mode Control of Power Factor in Three-Phase AC/DC Converter for Hybrid Electric Vehicle Applications
,” Int. J. Control
, 87
(6
), pp. 1117
–1130
.10.1080/00207179.2013.86860912.
Cui
, R.
, Ren
, B.
, and Ge
, S.
, 2012
, “Synchronised Tracking Control of Multi-Agent System With High Order Dynamics
,” IET Control Theory Appl.
, 6
(5
), pp. 603
–614
.10.1049/iet-cta.2011.001113.
Guan
, Y.
, and Saif
, M.
, 1991
, “A Novel Approach to the Design of Unknown Input Observers
,” IEEE Trans. Autom. Control
, 36
(5
), pp. 632
–635
.10.1109/9.7637214.
Chen
, W. H.
, 2003
, “Nonlinear Disturbance Observer-Enhanced Dynamic Inversion Control of Missiles
,” J. Guid., Control, Dyn.
, 26
(1
), pp. 161
–166
.10.2514/2.502715.
Deshpande
, V. S.
, and Phadke
, S. B.
, 2012
, “Control of Uncertain Nonlinear Systems Using an Uncertainty and Disturbance Estimator
,” ASME J. Dyn. Syst., Meas., Control
, 134
(2
), p. 024501
.10.1115/1.400504216.
Jiang
, L.
, and Wu
, Q.
, 2002
, “Nonlinear Adaptive Control Via Sliding-Mode State and Perturbation Observer
,” IEE Proc. Control Theory Appl.
, 149
(4
), pp. 269
–277
.10.1049/ip-cta:2002047017.
Han
, J.
, 2009
, “From PID to Active Disturbance Rejection Control
,” IEEE Trans. Ind. Electron.
, 56
(3
), pp. 900
–906
.10.1109/TIE.2008.201162118.
Li
, S.
, Jun, Chen
, W.-H.
, and Chen
, X.
, 2012
, “Generalized Extended State Observer Based Control for Systems With Mismatched Uncertainties
,” IEEE Trans. Ind. Electron.
, 59
(12
), pp. 4792
–4802
.10.1109/TIE.2011.218201119.
Corless
, M.
, and Leitmann
, G.
, 1981
, “Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems
,” IEEE Trans. Autom. Control
, 26
(5
), pp. 1139
–1144
.10.1109/TAC.1981.110278520.
Yao
, J.
, Xia
, J.
, and Ma
, D.
, 2014
, “Extended-State-Observer-Based Output Feedback Nonlinear Robust Control of Hydraulic Systems With Backstepping
,” IEEE Trans. Ind. Electron.
, 61
(11
), pp. 6285
–6293
.10.1109/TIE.2014.230491221.
Yao
, J.
, Jiao
, Z.
, Ma
, D.
, and Yan
, L.
, 2014
, “High-Accuracy Tracking Control of Hydraulic Rotary Actuators With Modeling Uncertainties
,” IEEE/ASME Trans. Mechatronics
, 19
(2
), pp. 633
–641
.10.1109/TMECH.2013.225236022.
Daher
, N.
, and Ivantysynova
, M.
, 2014
, “An Indirect Adaptive Velocity Controller for a Novel Steer-By-Wire System
,” ASME J. Dyn. Syst., Meas., Control
, 136
(5
), p. 051012
.10.1115/1.402717223.
Xie
, Y.
, Alleyne
, A. G.
, Greer
, A.
, and Deneault
, D.
, 2013
, “Fundamental Limits in Combine Harvester Header Height Control
,” ASME J. Dyn. Syst., Meas., Control
, 135
(3
), p. 034503
.10.1115/1.402320924.
Han
, S.
, Jiao
, Z.
, Yao
, J.
, and Shang
, Y.
, 2014
, “Compound Velocity Synchronizing Control Strategy for Electro-Hydraulic Load Simulator and Its Engineering Application
,” ASME J. Dyn. Syst., Meas., Control
, 136
(5
), p. 051002
.10.1115/1.402692125.
Singh
, K. B.
, Arat
, M. A.
, and Taheri
, S.
, 2013
, “An Intelligent Tire Based Tire-Road Friction Estimation Technique and Adaptive Wheel Slip Controller for Antilock Brake System
,” ASME J. Dyn. Syst., Meas., Control
, 135
(3
), p. 031002
.10.1115/1.400770426.
Ahn
, K.
, Nam
, D.
, and Jin
, M.
, 2014
, “Adaptive Backstepping Control of an Electrohydraulic Actuator
,” IEEE/ASME Trans. Mechatronics
, 19
(3
), pp. 987
–995
.10.1109/TMECH.2013.226531227.
Quanser Inc.
, 2008
, “Dynamic Equations for the First Stage of the Serial Flexible Joint (2DSFJ) Robot—Maple Worksheet.”Copyright © 2015 by ASME
You do not currently have access to this content.
