In this paper combined algorithms for the control of nontriangular nonlinear systems with unmatched uncertainties will be presented. The controllers consist of a combination of Dynamical Adaptive Backstepping (DAB) and Sliding Mode Control (SMC) of first and second order. In order to solve a tracking problem, the DAB algorithm (a generalization of the backstepping technique) makes use of virtual functions as well as tuning functions to construct a transformed system for which a regulation problem has to be solved. The new state is extended by an order subsystem in canonical form where n is the order of the original system and ρ is the relative degree. The role of the sliding mode control is to replace the last step of the design of the control law to obtain more robustness toward disturbances and unmodeled dynamics. The main advantages of the second-order sliding mode algorithm are the prevention of chattering, higher accuracy, and a significant simplification of the control law. A comparative study of these first and second order sliding controllers will be presented. [S002-0434(00)02604]
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e-mail: j.c.scarratt@sheffield.ac.uk
e-mail: a.zinober@sheffield.ac.uk
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December 2000
Technical Papers
Dynamical Adaptive First and Second-Order Sliding Backstepping Control of Nonlinear Nontriangular Uncertain Systems
J. C. Scarratt,
e-mail: j.c.scarratt@sheffield.ac.uk
J. C. Scarratt
Department of Applied Mathematics, The University of Sheffield, Sheffield, United Kingdom
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A. Zinober,
e-mail: a.zinober@sheffield.ac.uk
A. Zinober
Department of Applied Mathematics, The University of Sheffield, Sheffield, United Kingdom
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R. E. Mills,
R. E. Mills
Department of Applied Mathematics, The University of Sheffield, Sheffield, United Kingdom
r.e.mills@sheffield.ac.uk
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Miguel Rios-Bolı´var,
Miguel Rios-Bolı´var
Department de Sistemas de Control, Universidad de Los Andes, Merida 5101, Venezula
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A. Ferrara,
A. Ferrara
Department of Comp. and Systems Engineering, University of Pavia, Pavia, Italy
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L. Giacomini
L. Giacomini
Department of Electrical Engineering and Comp. Science, Aston University, Aston, United Kingdom
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J. C. Scarratt
Department of Applied Mathematics, The University of Sheffield, Sheffield, United Kingdom
e-mail: j.c.scarratt@sheffield.ac.uk
A. Zinober
Department of Applied Mathematics, The University of Sheffield, Sheffield, United Kingdom
e-mail: a.zinober@sheffield.ac.uk
R. E. Mills
r.e.mills@sheffield.ac.uk
Department of Applied Mathematics, The University of Sheffield, Sheffield, United Kingdom
Miguel Rios-Bolı´var
Department de Sistemas de Control, Universidad de Los Andes, Merida 5101, Venezula
A. Ferrara
Department of Comp. and Systems Engineering, University of Pavia, Pavia, Italy
L. Giacomini
Department of Electrical Engineering and Comp. Science, Aston University, Aston, United Kingdom
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division March 1, 2000. Associate Technical Editor: E. Misawa.
J. Dyn. Sys., Meas., Control. Dec 2000, 122(4): 746-752 (7 pages)
Published Online: March 1, 2000
Article history
Received:
March 1, 2000
Citation
Scarratt, J. C., Zinober, A., Mills, R. E., Rios-Bolı´var, M., Ferrara, A., and Giacomini, L. (March 1, 2000). "Dynamical Adaptive First and Second-Order Sliding Backstepping Control of Nonlinear Nontriangular Uncertain Systems ." ASME. J. Dyn. Sys., Meas., Control. December 2000; 122(4): 746–752. https://doi.org/10.1115/1.1321051
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