Repetitive sliding mode control for nondecouplable multivariable systems: Periodic disturbances rejection

Int. J. Robust. Nonlinear Control

2016

Self Cite

Summary The technique of linear matrix inequalities is a powerful method for solving optimization problems. In this paper, a sliding function vector was calculated using linear matrix inequalities approach. This technique provided optimal values of the coefficients of the sliding function vector, which led to the reduction of the reachability phase. Then, a discrete second‐order sliding mode control for multivariable systems was developed using this optimal sliding function vector. Two examples were used in order to illustrate the effectiveness of the proposed strategy. Simulation results prove good performances in terms of reduction of the reachability phase. Copyright © 2016 John Wiley & Sons, Ltd.

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“…For nondecouplable multivariable systems, the interactor matrix is defined as follows :

ξ (q) = {falsefalse}_{\sum}^{i = 1} ξ_{i} q^{i}

\begin{matrix} S (k + d) & = C (q^{- 1}) ξ (q) (Y (k) - Y_{r} (k)) \\ = C (q^{- 1}) ξ (q) E (k) \end{matrix}

Therefore, the new sliding function vector σ ( k ) is given by

σ (k) = S ((), k + d) + βS ((), k + d - 1)

Consider E ( q ) and N ( q −1 ) as the two polynomials matrices solutions of the diophantine polynomial matrix equation:

C ((), q^{- 1}) ξ ((), q) = E ((), q) normalΔ ((), q^{- 1}) A ((), q^{- 1}) + N ((), q^{- 1})

with E ( q ) = E 1 q + E 2 q 2 +⋯+ E d q d

N ((), q^{- 1}) = N_{0} + N_{1} q^{- 1} + \dots + N_{n_{N}} q^{- ...}

…”

Section: Discrete Second‐order Sliding Mode Control For Multivariablementioning

confidence: 99%

“…Consider the multivariable system described by :

A (q^{- 1}) Y (k) = B^{*} (q^{- 1}) U (k)

where

\{\begin{matrix} A ((), q^{- 1}) = I_{2} + A_{1} q^{- 1} + A_{2} q^{- 2} \\ B^{*} ((), q^{- 1}) = B_{1} q^{- 1} + B_{2} q^{- 2} \end{matrix}

A_{1} = I_{2}; A_{2} = I_{2}

B_{1} = [\begin{matrix} 1 & 1 \\ 2 & 2 \end{matrix}]; B_{2} = [\begin{matrix} 0.5 & 0.5 \\ 0 & 1 \end{matrix}]

Y (k) = [\begin{matrix} y_{1} ( \end{matrix}]

…”

Section: Simulation Examplesmentioning

confidence: 99%

Section: Decouplable Multivariable Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discrete second-order sliding mode control based on optimal sliding function vector for multivariable systems with input-output representation

Houda

Int. J. Robust. Nonlinear Control

2016

Self Cite

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“…The adaptive control and the sliding mode control were combined in order to synthesize a discrete robust adaptive sliding mode controller for multivariable systems [17] . Moreover, in the last few years, a discrete sliding mode control via input-output model was developed for decouplable and nondecouplable multivariable systems, respectively [18,19] . This work proposes a discrete second order sliding mode control for decouplable multivariable systems (2-MDSMC) via input-output model [20] and studies the robustness of this control.…”

Section: Introductionmentioning

confidence: 99%

Second order sliding mode control for discrete decouplable multivariable systems via input-output models

Houda

2015

Int. J. Autom. Comput.

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The problem of the chattering phenomenon is still the main drawback of the classical sliding mode control. To resolve this problem, a discrete second order sliding mode control via input-output model is proposed in this paper. The proposed control law is synthesized for decouplable multivariable systems. A robustness analysis of the proposed discrete second order sliding mode control is carried out. Simulation results are presented to illustrate the effectiveness of the proposed strategy.

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Conditions of Disturbances Rejection for Discrete First, Second Order and Repetitive Sliding Mode Controllers

Ltaïef

Applications of Sliding Mode Control

2016