A design of discrete-time SMC for nonlinear systems based on fuzzy T-S model

Nadzinski, Gorjan; Vladev, Goran; Zheng, Yadan

doi:10.1109/is.2012.6335236

Cited by 3 publications

(6 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…On the contrary, for nonlinear systems, a reduced number of proposals have been carried out. Nevertheless, the problem has been analyzed from the middle of the 80s (see, for example, related studies 3,[40][41][42][43][44][45] and more recent works [46][47][48].…”

Section: Problem Statementmentioning

confidence: 99%

“…More recently, Gaffari and Yasdanpanah 45 proposed a method for computing a nonlinear stable SM surfaces applied to nonaffine continuous time systems and Dong and Shi 47 introduced an algorithm for designing optimal sliding surface for nonlinear discrete-time systems using the nonlinear two-point boundary problem approach. Finally, some approaches intended to apply DVSC with SM to discrete-time nonlinear systems based on T-S fuzzy models 46,48 had proposed linear methods such that LMI. The general nonlinear sliding surface problem can be stated as follows.…”

Section: Nonlinear Discrete-time Systems Sm Hyperplane Designmentioning

confidence: 99%

“…• Estimating f i using (48) and considering that C = [c T 1 c T 2 c T 3 ] T , c i defined in (45), then the sliding surface coefficients are as follows: With this C, the equivalent matrix Φ equ for the ideal SM mode is…”

Section: Solution 2 (Ackermann's Approach)mentioning

confidence: 99%

See 2 more Smart Citations

Discrete‐time systems sliding mode switching hyperplane design: A survey

Luis-Delgado

Al‐Hadithi

Jiménez

2019

Optim Control Appl Methods

View full text Add to dashboard Cite

Summary As regards to variable structure control with sliding mode (VSC‐SM), it is known that designing sliding surface is a critical task because sliding surfaces must guarantee that the steady state of the controlled system achieves some desired performance including global (or global asymptotic) stability. This problem has been extensively analyzed for a wide class of systems: scalar, multivariable, linear, nonlinear, time‐variant, discrete‐time system, etc. The main purpose of this paper is to present a thorough survey about the main approaches related to the design of discrete‐time switching surfaces applied to VSC‐SM. Research works covering the design of sliding surfaces for the aforementioned systems are considered and some illustrative examples are also included to explain some of the design methodologies.

show abstract

Section: Problem Statementmentioning

confidence: 99%

Section: Nonlinear Discrete-time Systems Sm Hyperplane Designmentioning

confidence: 99%

See 1 more Smart Citation

Discrete‐time systems sliding mode switching hyperplane design: A survey

Luis-Delgado

Al‐Hadithi

Jiménez

2019

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

“…More recently, Ghaffari and Yazdanpanah (2008) proposed a method for computing nonlinear stable sliding mode surfaces, and Rui and Dong-wei (2011) introduced an algorithm for designing optimal sliding surface for nonlinear discrete time systems using the nonlinear two point boundary problem (TPBV) approach, while Bartoszewicz and Leśniewski (2014) made use of an optimal approach for designing a sliding hyperplane. Finally, some approaches intended to apply DVSC with an SM to discrete time nonlinear systems based on T-S fuzzy models use linear methods such as LMI for the design of switching surfaces (Zhang et al, 2010;Nadzinski et al, 2012).…”

Section: Problem 1 Consider a Nonlinear Discrete Time Systemmentioning

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

View full text Add to dashboard Cite

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.

show abstract

“…A diferencia del elevado n umero de propuestas de diseño de super cies deslizantes y de controladores DVSC-SM aplicados a sistema lineales existentes, algunas de ellas brevemente reseñados en los cap tulos anteriores, se puede veri car que el n umero de estudios realizados con respecto a sistemas no lineales es mucho m as reducido. Algunos trabajos relevantes presentados a partir de los ochenta se pueden consultar en [52], [80], [133], [158], [165], [166], [172], [176], [213]. La metodolog a de diseño de super cies deslizantes m as extendida consiste, primeramente, en obtener una representaci on de la din amica del proceso en alguna de las formas can onica para sistemas no-lineales como son la forma can onica reducida, la forma can onica normal y la forma can onica de Brunovsky, etc.…”

Section: Antecedentesunclassified

Análisis y Diseño de Algoritmos de Control Discreto de Sistemas MIMO Lineales y No Lineales Aplicando Técnicas de Control de Estructura Variable

Delgado¹

View full text Add to dashboard Cite

Over the last four decades, variable structure controllers with sliding mode (VSC-SM ) have been extensively studied, demonstrating to be a robust solution among robust nonlinear processes control techniques. Since the late 80s, several research works have been focused on the application of VSC controllers applied to discrete time or sampled data systems, which are known as DVSC-SM, where the most extensive source of analysis has been devoted to the robustness and invariance properties of VSC-SM controllers when applied to discrete systems. The main aim of this doctoral thesis work is to study, analyze and propose a design scheme of DVSC-SM controllers for lineal and nonlinear multivariable discrete time processes. For this purpose, a new design philosophy is proposed, where various design features have been considered that have not been analyzed in DVSC design approaches. Among them, the physical limitations and the nonideal dynamic sliding mode dynamics. The most innovative aspect is the inclusion of a new design methodology applied to lineal sliding surfaces MIMO systems and the extension to nonlinear multivariable systems, in addition to a new robust control law applied to lineal and nonlinear MIMO systems, including a chattering reduction scheme. Finally, to illustrate the e ciency of the proposed schemes, several numerical examples applied to lineal and nonlinear systems are included.

show abstract

A design of discrete-time SMC for nonlinear systems based on fuzzy T-S model

Cited by 3 publications

References 17 publications

Discrete‐time systems sliding mode switching hyperplane design: A survey

Discrete‐time systems sliding mode switching hyperplane design: A survey

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

Análisis y Diseño de Algoritmos de Control Discreto de Sistemas MIMO Lineales y No Lineales Aplicando Técnicas de Control de Estructura Variable

Contact Info

Product

Resources

About