This paper studies control problems of underactuated mechanical systems with model uncertainties. The control is designed with the method of backstepping. The first-order low-pass filters are used to estimate the unknown quantities and to avoid the “explosion of terms.” A novel method is also proposed to implement the control without the knowledge of the control coefficient, which makes the whole process of backstepping control data-driven. The stability of the proposed control in the Lyapunov sense is studied. It is numerically and experimentally validated, and compared with the well-known model-based linear quadratic regulator (LQR) control. The data-driven backstepping control is found to provide comparable performances to that of the LQR control with the advantage of being model-free and robust.
Issue Section:
Research Papers
References
1.
Fantoni
, I.
, and Lozano
, R.
, 2002
, Non-Linear Control for Underactuated Mechanical Systems
, Springer-Verlag
, London
.2.
Lai
, X. Z.
, She
, J. H.
, and Wu
, M.
, 2016
, Control of Underactuated Mechanical Systems
, Science Publishing
, Beijing, China
.3.
Rudra
, S.
, Barai
, R. K.
, and Maitra
, M.
, 2017
, Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems
, Springer
, Singapore
.4.
Shah
, I.
, and Rehman
, F. U.
, 2018
, “Smooth Second Order Sliding Mode Control of a Class of Underactuated Mechanical Systems
,” IEEE Access
, 6
, pp. 7759
–7771
.5.
Rudra
, S.
, Barai
, R. K.
, and Maitra
, M.
, 2014
, “Nonlinear State Feedback Controller Design for Underactuated Mechanical System: A Modified Block Backstepping Approach
,” ISA Trans.
, 53
(2
), pp. 317
–326
.6.
Wu
, S.
, and Huo
, W.
, 2012
, “Passivity-Based Tracking Control Design for Underactuated Mechanical Systems
,” International Conference on Electronics, Communications and Control
, Zhoushan, China, pp. 3139
–3143
.7.
Tuan
, L. A.
, Lee
, S.-G.
, Nho
, L. C.
, and Cuong
, H. M.
, 2015
, “Robust Controls for Ship-Mounted Container Cranes With Viscoelastic Foundation and Flexible Hoisting Cable
,” Proc. Inst. Mech. Eng., Part I
, 229
(7
), pp. 662
–674
.8.
Tuan
, L. A.
, Cuong
, H. M.
, Lee
, S.-G.
, Nho
, L. C.
, and Moon
, K.
, 2016
, “Nonlinear Feedback Control of Container Crane Mounted on Elastic Foundation With the Flexibility of Suspended Cable
,” J. Vib. Control
, 22
(13
), pp. 3067
–3078
.9.
Le
, A. T.
, and Lee
, S.-G.
, 2017
, “3D Cooperative Control of Tower Cranes Using Robust Adaptive Techniques
,” J. Franklin Inst.
, 354
(18
), pp. 8333
–8357
.10.
Adhikary
, N.
, and Mahanta
, C.
, 2013
, “Integral Backstepping Sliding Mode Control for Underactuated Systems: Swing-Up and Stabilization of the Cart-Pendulum System
,” ISA Trans.
, 52
(6
), pp. 870
–880
.11.
Rudra
, S.
, Barai
, R. K.
, Maitra
, M.
, Mandal
, D.
, Dam
, S.
, Ghosh
, S.
, Bhattacharyya
, P.
, and Dutta
, A.
, 2013
, “Design of Nonlinear State Feedback Control Law for Underactuated TORA System: A Block Backstepping Approach
,” Seventh International Conference on Intelligent Systems and Control (ISCO
), Coimbatore, India, Jan. 4–5, pp. 93
–98
. 12.
Azimi
, M. M.
, and Koofigar
, H. R.
, 2015
, “Adaptive Fuzzy Backstepping Controller Design for Uncertain Underactuated Robotic Systems
,” Nonlinear Dyn.
, 79
(2
), pp. 1457
–1468
.13.
Olfati-Saber
, R.
, 2002
, “Normal Forms for Underactuated Mechanical Systems With Symmetry
,” IEEE Trans. Autom. Control
, 47
(2
), pp. 305
–308
.14.
Thakar
, P. S.
, Bandyopadhyay
, B.
, and Gandhi
, P. S.
, 2014
, “Sliding Mode Control for a Class of Underactuated Systems Using Feedforward Normal Form: A Slosh-Container System
,” 13th International Workshop on Variable Structure Systems
(VSS
), Nantes, France, June 29–July 2, pp. 1
–6
.15.
Ghommam
, J.
, and Chemori
, A.
, 2017
, “Adaptive RBFNN Finite-Time Control of Normal Forms for Underactuated Mechanical Systems
,” Nonlinear Dyn.
, 90
(1
), pp. 301
–315
.16.
Knoll
, C.
, and Röbenack
, K.
, 2015
, “Maneuver-Based Control of the 2-Degrees of Freedom Underactuated Manipulator in Normal Form Coordinates
,” Syst. Sci. Control Eng.
, 3
(1
), pp. 26
–38
.17.
Pan
, Y.
, Liu
, Y.
, and Yu
, H.
, 2016
, “Online Data-Driven Composite Adaptive Backstepping Control With Exact Differentiators
,” Int. J. Adapt. Control Signal Process.
, 30
(5
), pp. 779
–789
.18.
Nor
, E. M.
, Noor
, S. B. M.
, Zafira
, R.
, and Azrad
, S.
, 2017
, “Application of Sliding Mode Control With Extended High Gain Observer to Stabilize the Underactuated Quadrotor System
,” Pertanika J. Sci. Technol.
, 25
(S), pp. 343–352.19.
Dou
, L.
, and Fei
, L.
, 2017
, “Trajectory Tracking Control for Underactuated Quadrotor UAV Based on ESO and Backstepping
,” J. Tianjin Univ.
, 50
(5
), pp. 500
–506
.20.
Pan
, Y.
, Sun
, T.
, Liu
, Y.
, and Yu
, H.
, 2017
, “Composite Learning From Adaptive Backstepping Neural Network Control
,” Neural Networks
, 95
, pp. 134
–142
.21.
Sun
, J.
, Xu
, D.
, Zha
, S.
, and Le
, G.
, 2015
, “Model Free Backstepping Control for Marine Power Systems
,” Open Autom. Control Syst. J.
, 7
(1
), pp. 942
–948
.22.
Younes
, Y. A.
, Drak
, A.
, Noura
, H.
, Rabhi
, A.
, and Hajjaji
, A. E.
, 2014
, “Nonlinear Integral Backstepping—Model-Free Control Applied to a Quadrotor System
,” International Conference on Intelligent Unmanned Systems
, Montreal, QC, Canada, Sept. 29–Oct. 1, pp. 1–6.23.
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
.24.
Farrell
, J. A.
, Polycarpou
, M.
, Sharma
, M.
, and Dong
, W.
, 2008
, “Command Filtered Backstepping
,” American Control Conference
(ACC
), Seattle, WA, June 11–13, pp. 1923
–1928
. Copyright © 2019 by ASME
You do not currently have access to this content.
