Research Papers

Chattering-Free Error Integral Driven MIMO Sliding Mode Regulator for Linear Time-Invariant Systems

[+] Author and Article Information
Kerim Yunt

General Control Design,
am Holbrig 4,
Zurich 8049, Switzerland
e-mail: kerimyunt@web.de

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 14, 2015; final manuscript received March 25, 2016; published online May 16, 2016. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 138(7), 071010 (May 16, 2016) (8 pages) Paper No: DS-15-1271; doi: 10.1115/1.4033270 History: Received June 14, 2015; Revised March 25, 2016

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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


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. [CrossRef]
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. [CrossRef]
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.
Ackermann, J. , and Utkin, V. , 1998, “ Sliding Mode Control Design Based on Ackermann's Formula,” IEEE Trans. Autom. Control, 43(2), pp. 234–237. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.
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. [CrossRef]
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. [CrossRef]
Angulo, M. T. , Fridman, L. , and Levant, A. , 2012, “ Output-Feedback Finite-Time Stabilization of Disturbed LTI Systems,” Automatica, 48(4), pp. 606–611. [CrossRef]
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.
Bao, J. , and Lee, P. L. , 2007, Process Control: The Passive Systems Approach (Advances in Industrial Control), 1st ed., Springer-Verlag, London.
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.
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. [CrossRef]
Clarke, F. H. , and Vinter, R. B. , 2009, “ Stability Analysis of Sliding Mode Feedback Control,” J. Cybern. Control, 38, pp. 1169–1192.
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.
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. [CrossRef]
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. [CrossRef]
Slotine, J.-J. E. , 1984, “ Sliding Controller Design for Non-Linear Systems,” Int. J. Control, 40(2), pp. 421–434. [CrossRef]
Fridman, L. , 2001, “ An Averaging Approach to Chattering,” IEEE Trans. Autom. Control, 46(8), pp. 1260–1265. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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.


Grahic Jump Location
Fig. 1

The signal flowchart of the EID-SMC controlled LTI system

Grahic Jump Location
Fig. 2

The arrangement of the tanks, pipes, and pumps

Grahic Jump Location
Fig. 3

The response of the linear model and steady-state value

Grahic Jump Location
Fig. 4

The response of the nonlinear plant model

Grahic Jump Location
Fig. 5

The singular value plots of the linear model

Grahic Jump Location
Fig. 6

The step responses of the output to isolated step inputs of the linear model

Grahic Jump Location
Fig. 7

The step responses of the state to isolated step inputs of the linear model



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In