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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.

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Figures

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Fig. 1

The signal flowchart of the EID-SMC controlled LTI system

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Fig. 2

The arrangement of the tanks, pipes, and pumps

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Fig. 3

The response of the linear model and steady-state value

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Fig. 4

The response of the nonlinear plant model

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Fig. 5

The singular value plots of the linear model

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Fig. 6

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

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Fig. 7

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

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