Designing robust sliding hyperplanes for parametric uncertain systems: a Riccati approach

Kim, Kyung-Soo; Park, Youngjin; Oh, Shi-Hwan

doi:10.1016/s0005-1098(00)00014-5

Cited by 132 publications

(76 citation statements)

References 15 publications

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“…. , 3, applying the decomposition procedure given by (11)- (12) We remark that none of the traditional design methods of Kim et al (2000), Choi (2001) or Xia and Jia (2003) nor the integral SMC methods given by Cao and Xu (2004), Shaocheng and Yongji (2006) Figures 3 and 4 indicate the evolution of switching function components, controller components, and accelerations using the proposed ISMC (28) and AFISMC (37)- (43), respectively. The displacement evolution for both ISMC and AFISMC methods is shown in Fig.…”

Section: Unauthenticatedmentioning

confidence: 99%

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LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems

Mnasri¹,

Gasmi²

2011

International Journal of Applied Mathematics and Computer Science

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Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guaranteed by the proposed control law. The improvement of the proposed control scheme performances, such as chattering elimination and estimation of norm bounds of uncertainties, is then considered with the application of an adaptive fuzzy integral sliding mode control law. The validity and efficiency of the proposed approaches are investigated through a sixth order uncertain mechanical system.

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Section: Unauthenticatedmentioning

confidence: 99%

“…A majority of the existing methods are based on Classic SMC (CSMC) (Kim et al, 2000;Choi, 2001;Xia and Jia, 2003). These methods are affected by the aforementioned insufficiency of SMC with the reaching phase.…”

Section: Introductionmentioning

confidence: 99%

LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems

Mnasri¹,

Gasmi²

2011

International Journal of Applied Mathematics and Computer Science

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“…However, the control law u (k) must be designed such that some reaching law must be fulfilled considering these uncertainties, mostly when the matching conditions are not achieved (Furuta, 1990;Gao et al, 1995;Kim et al, 2000;Sira-Ramírez, 1991;Yu et al, 2000;Yadav and Singh, 2012;Mondal et al, 2012;Qu et al, 2014). This part of the design of DVSC controllers is not directly carried out during switching the surface design phase.…”

Section: Lemma 1 Consider P (X U) a Linearized And Discretized Mimmentioning

confidence: 99%

A Novel Method for the Design of Switching Surfaces for Discretized MIMO Nonlinear Systems

Luis-Delgado

Al‐Hadithi

Jiménez

2017

International Journal of Applied Mathematics and Computer Science

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Designing variable structure control with sliding mode (VSC-SM) control schemes needs a switching function or a sliding surface which guarantees the global stability of the closed-loop system. Despite the fact that a wide range of design approaches has been proposed for solving this mathematical problem, the number of proposed methodologies for nonlinear systems is not very extensive, especially for discrete time nonlinear MIMO systems, and most of them require some coordinate system transformation. Therefore, it is not an easy task to find a design scheme that can be applied to discrete time nonlinear MIMO systems. The proposed methodology introduces a mathematical tool: a switching surface equation for a class of MIMO nonlinear systems through an explicit equation without any coordinate transformation. This equation makes use of an implicit linearizing process via the Taylor expansion that allows the use of linear procedures for the design of switching surfaces and the forward Euler method to obtain a discrete time dynamics representation. An illustrative example is included to show the advantages of the proposed design methodology.

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“…As discussed in [40], for nonlinear uncertain systems with unmatched uncertainties, Lyapunov's direct method becomes an important approach for the design and analysis. The design techniques in [14], [41], and [42] yield the hyperplane robust against unmatched parametric uncertainties in the system matrix with the assumption of a matched uncertain input matrix. Note that the system under consideration has unmatched uncertainties in the input matrix as well.…”

Section: A Motivationmentioning

confidence: 99%

Sliding Mode Observer Based Sliding Mode Controller for Slosh-Free Motion Through PID Scheme

Bandyopadhyay

Gandhi

Kurode

2009

IEEE Trans. Ind. Electron.

106

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Abstract-This paper presents a new approach to design a sliding mode controller for a class of mismatched uncertain systems. A method is proposed for the design of a switching surface in the presence of mismatched uncertainties. A design method for a sliding mode observer based on high gain is also proposed in this paper to reconstruct the states of the system for the implementation of sliding mode control. The design technique is simple and computationally efficient. A control problem for the slosh-free motion of a container is considered as the representative of a typical class of systems. A simple pendulum model is considered to represent the lateral slosh. The validity of the proposed scheme is demonstrated by simulation along with the experimental results.Index Terms-Sliding mode control (SMC), sliding mode observer (SMO), slosh.

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Designing robust sliding hyperplanes for parametric uncertain systems: a Riccati approach

Cited by 132 publications

References 15 publications

LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems

LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems

A Novel Method for the Design of Switching Surfaces for Discretized MIMO Nonlinear Systems

Sliding Mode Observer Based Sliding Mode Controller for Slosh-Free Motion Through PID Scheme

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