In this work, an error-integral-driven sliding mode controller (EID-SMC) is discussed for multi-input multi-output (MIMO) linear time-invariant (LTI) systems. The boundary layer approach is utilized in order to eliminate the chattering problem. Though the sliding variable remains in the vicinity of the sliding surface without reaching it, it is shown that the steady-state error vanishes exponentially asymptotically within a boundary layer, for systems of relative order one, even if parameter uncertainty and unmatched input disturbances exist. The pole placement is accomplished indirectly with an iterative optimization procedure by considering limits on controls and state. Finally, the output-feedback controller is augmented with a Luenberger full-state and disturbance observer.
Issue Section:
Research Papers
References
1.
Ryan
, E.
, and Corless
, M.
, 1984
, “Ultimate Boundedness and Asymptotic Stability of a Class of Uncertain Dynamical Systems Via Continuous and Discontinuous Feedback Control
,” IMA J. Math. Control Inf.
, 1
(3
), pp. 223
–242
.2.
Dorling
, C.
, and Zinober
, A.
, 1986
, “Two Approaches to Hyperplane Design in Multivariable Variable Structure Control Systems
,” Int. J. Control
, 44
(1
), pp. 65
–82
.3.
Zhihong
, M.
, and Yu
, X. H.
, 1996
, “Terminal Sliding Mode Control of MIMO Linear Systems
,” 35th IEEE
Conference on Decision and Control
, Kobe, Japan, Dec. 11–13, Vol. 4
, pp. 4619
–4624
.4.
Ackermann
, J.
, and Utkin
, V.
, 1998
, “Sliding Mode Control Design Based on Ackermann's Formula
,” IEEE Trans. Autom. Control
, 43
(2
), pp. 234
–237
.5.
Chang
, J.-L.
, and Chen
, Y.-P.
, 2000
, “Sliding Vector Design Based on the Pole-Assignment Method
,” Asian J. Control
, 2
(1
), pp. 10
–15
.6.
Tang
, C. Y.
, and Misawa
, E. A.
, 1998
, “Discrete Variable Structure Control for Linear Multivariable Systems
,” ASME J. Dyn. Syst., Meas., Control
, 122
(4
), pp. 783
–792
.7.
Nunes
, E. V.
, Peixoto
, A. J.
, Oliveira
, T. R.
, and Hsu
, L.
, 2014
, “Global Exact Tracking for Uncertain MIMO Linear Systems by Output Feedback Sliding Mode Control
,” J. Franklin Inst.
, 351
(4
), pp. 2015
–2032
.8.
Martin
, J. C.
, and Leitmann
, G.
, 1981
, “Continuous State Feedback Guaranteeing Uniform Ultimate Boundedness for Uncertain Dynamic Systems
,” IEEE Trans. Autom. Control
, 26
(5
), pp. 1139
–1144
.9.
Cunha
, J. P. V.
, Hsu
, L.
, Costa
, R. R.
, and Lizarralde
, F.
, 2003
, “Output-Feedback Model-Reference Sliding Mode Control of Uncertain Multivariable Systems
,” IEEE Trans. Autom. Control
, 48
(12
), pp. 2245
–2250
.10.
Utkin
, V.
, and Shi
, J.
, 1996
, “Integral Sliding Mode in Systems Operating Under Uncertainty Conditions
,” 35th IEEE
Conference on Decision and Control
, Kobe, Japan, Dec. 11–13, Vol. 4
, pp. 4591
–4596
.11.
Sam
, Y. M.
, Osman
, J. H.
, and Ghani
, M. R. A.
, 2004
, “A Class of Proportional-Integral Sliding Mode Control With Application to Active Suspension System
,” Syst. Control Lett.
, 51
(3
), pp. 217
–223
.12.
Rubagotti
, M.
, Estrada
, A.
, Castanos
, F.
, Ferrara
, A.
, and Fridman
, L.
, 2011
, “Integral Sliding Mode Control for Nonlinear Systems With Matched and Unmatched Perturbations
,” IEEE Trans. Autom. Control
, 56
(11
), pp. 2699
–2704
.13.
Angulo
, M. T.
, Fridman
, L.
, and Levant
, A.
, 2012
, “Output-Feedback Finite-Time Stabilization of Disturbed LTI Systems
,” Automatica
, 48
(4
), pp. 606
–611
.14.
Cavallo
, A.
, and Natale
, C.
, 2002
, “A Robust Output Feedback Control Law for MIMO Plants
,” 15th IFAC
World Congress on Automatic Control
, Barcelona, Spain, July 21–26, Vol. 15
, pp. 13
–18
.15.
Bao
, J.
, and Lee
, P. L.
, 2007
, Process Control: The Passive Systems Approach
(Advances in Industrial Control), 1st ed., Springer-Verlag
, London
.16.
Lin
, C.-A.
, and Gündeş
, A. N.
, 2000
, “Multi-Input Multi-Output PI Controller Design
,” 39th IEEE
Conference on Decision and Control
, Sydney, Australia, Dec. 12–15, Vol. 4
, pp. 3702
–3707
.17.
Xiong
, Q.
, Cai
, W.-J.
, and He
, M.-J.
, 2007
, “Equivalent Transfer Function Method for PI/PID Controller Design of MIMO Processes
,” J. Process Control
, 17
(8
), pp. 665
–673
.18.
Clarke
, F. H.
, and Vinter
, R. B.
, 2009
, “Stability Analysis of Sliding Mode Feedback Control
,” J. Cybern. Control
, 38
, pp. 1169
–1192
.19.
Milosavljevic
, C.
, 1985
, “General Conditions for the Existence of a Quasi-Sliding Mode on the Switching Hyperplane in Discrete Variable Structure Systems
,” Autom. Remote Control
, 46
(3
), pp. 307
–314
.20.
Sarptürk
, S. Z.
, Istefanopulos
, Y.
, and Kaynak
, O.
, 1987
, “On the Stability of Discrete-Time Sliding Mode Control Systems
,” IEEE Trans. Autom. Control
, 32
(10
), pp. 930
–932
.21.
Slotine
, J.-J. E.
, and Sastry
, S. S.
, 1983
, “Tracking Control of Non-Linear Systems Using Sliding Surfaces, With Application to Robot Manipulators
,” Int. J. Control
, 38
(2
), pp. 465
–492
.22.
Slotine
, J.-J. E.
, 1984
, “Sliding Controller Design for Non-Linear Systems
,” Int. J. Control
, 40
(2
), pp. 421
–434
.23.
Fridman
, L.
, 2001
, “An Averaging Approach to Chattering
,” IEEE Trans. Autom. Control
, 46
(8
), pp. 1260
–1265
.24.
Young
, K. D.
, Utkin
, V. I.
, and Özgüner
, U.
, 1999
, “A Control Engineer's Guide to Sliding Mode Control
,” IEEE Trans. Control Syst. Technol.
, 7
(3
), pp. 328
–342
.25.
Johansson
, K. H.
, 2000
, “The Quadruple-Tank Process: A Multivariable Laboratory Process With an Adjustable Zero
,” IEEE Trans. Control Syst. Technol.
, 8
(3
), pp. 456
–465
.26.
Drazenovic
, B.
, Milosavljevic
, C.
, and Veselic
, B.
, 2013
, “Comprehensive Approach to Sliding Mode Design and Analysis in Linear Systems
,” Advances in Sliding Mode Control
(Lecture Notes in Control and Information Sciences, Vol. 440
), B.
Bandyopadhyay
, S.
Janardhanan
, and S. K.
Spurgeon
, eds., Springer
, Berlin
, pp. 1
–19
.Copyright © 2016 by ASME
You do not currently have access to this content.
