Non-linear discrete variable structure systems in quasi-sliding mode

1991 ◽  
Vol 54 (5) ◽  
pp. 1171-1187 ◽  
Author(s):  
HEBERTT SIRA-RAMIREZ
Keyword(s):  
Sliding Mode ◽  
Variable Structure ◽  
Discrete Variable ◽  
Variable Structure Systems ◽  
Non Linear

scholarly journals Discrete variable structure system with pseudo-sliding mode

1991 ◽  
Vol 32 (4) ◽  
pp. 365-376 ◽  
Author(s):  
R. B. Potts ◽  
X. Yu
Keyword(s):  
Numerical Solutions ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Continuous System ◽  
Variable Structure ◽  
Sliding Modes ◽  
Discrete Variable ◽  
Variable Structure Systems ◽  
Variable Structure System ◽  
Necessary And Sufficient

AbstractVariable structure systems with sliding modes have been widely discussed and used in many different fields of applications. The precise behaviour at a switching surface is complicated because there the system is non-analytic. The damped simple harmonic oscillator with a nonlinear variable structure is discretised and analysed in detail, revealing the occurrence and structure of pseudo-sliding modes which give insight to the corresponding sliding modes for the continuous system. Necessary and sufficient conditions are obtained and the analysis illustrated with graphs from numerical solutions.

Sliding Mode Control of a Three Degrees of Freedom Anthropoid Robot by Driving the Controller Parameters to an Equivalent Regime

2000 ◽  
Vol 122 (4) ◽  
pp. 632-640 ◽  
Author(s):  
M. Onder Efe ◽  
Okyay Kaynak ◽  
Xinghuo Yu
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Tracking Error ◽  
Variable Structure ◽  
Mathematical Representation ◽  
Dynamic Complexity ◽  
Variable Structure Systems ◽  
Sliding Motion ◽  
Three Degrees Of Freedom

Noise rejection, handling the difficulties coming from the mathematical representation of the system under investigation and alleviation of structural or unstructural uncertainties constitute prime challenges that are frequently encountered in the practice of systems and control engineering. Designing a controller has primarily the aim of achieving the tracking precision as well as a degree of robustness against the difficulties stated. From this point of view, variable structure systems theory offer well formulated solutions to such ill-posed problems containing uncertainty and imprecision. In this paper, a simple controller structure is discussed. The architecture is known as Adaptive Linear Element (ADALINE) in the framework of neural computing. The parameters of the controller evolve dynamically in time such that a sliding motion is obtained. The inner sliding motion concerns the establishment of a sliding mode in controller parameters, which aims to minimize the error on the controller outputs. The outer sliding motion is designed for the plant. The algorithm discussed drives the error on the output of the controller toward zero learning error level, and the state tracking error vector of the plant is driven toward the origin of the phase space simultaneously. The paper gives the analysis of the equivalence between the two sliding motions and demonstrates the performance of the algorithm on a three degrees of freedom, anthropoid robotic manipulator. In order to clarify the performance of the scheme, together with the dynamic complexity of the plant, the adverse effects of observation noise and nonzero initial conditions are studied. [S0022-0434(00)01704-4]

Slip parameter estimation of a single wheel using a non-linear observer

Robotica ◽  
2008 ◽  
Vol 27 (6) ◽  
pp. 801-811 ◽  
Author(s):  
Z. B. Song ◽  
L. D. Seneviratne ◽  
K. Althoefer ◽  
X. J. Song ◽  
Y. H. Zweiri
Keyword(s):  
Sliding Mode ◽  
Kinematic Model ◽  
Variable Structure ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Observer ◽  
Slip Angle ◽  
Wheel Slip ◽  
Variable Structure System ◽  
Non Linear ◽  
Linear Observer

SUMMARYSliding mode observer is a variable structure system where the dynamics of a nonlinear system is altered via application of a high-frequency switching control. This paper presents a non-linear sliding mode observer for wheel linear slip and slip angle estimation of a single wheel based on its kinematic model and velocity measurements with added noise to simulate actual on-board sensor measurements. Lyapunov stability theory is used to establish the stability conditions for the observer. It is shown that the observer will converge in a finite time, provided the observer gains satisfy constraints based on a stability analysis. To validate the observer, linear and two-dimensional (2D) test rigs are specially designed. The sliding mode observer is tested under a variety of conditions and it is shown that the sliding mode observer can estimate wheel slip and slip angle to a high accuracy. It is also shown that the sliding mode observer can accurately predict wheel slip and slip angle in the presence of noise, by testing the performance of the sliding mode observer after adding white noise to the measurements. An extended Kalman filter is also developed for comparison purposes. The sliding mode observer is better in terms of prediction accuracy.

scholarly journals Variable Structure Controller for Surface Ship Steering

2017 ◽  
Vol 2 (2) ◽  
Author(s):  
Ringo Rimbe ◽  
Raidandi Danwe ◽  
Babagana M Mustapha
Keyword(s):  
Sliding Mode ◽  
Linear Time ◽  
Variable Structure ◽  
Time Varying ◽  
Variable Structure Systems ◽  
Ship Model ◽  
Linear Time Invariant ◽  
Surface Ship ◽  
Ship Steering ◽  
Time Varying Environment

A Lyapunov approach to constructing switching surfaces for variable structure systems is investigated in this paper. The method guarantees sliding mode for any initial condition of the state vector and asymptotic stability is always achieved during sliding motion. An application for  the design of  a variable structure ship steering controller is carried out and  simulation results are presented. The designed controller exhibits robustness as applied to a linear time-invariant ship model and a time varying non-linear  ship model operating in  an uncertain and  time-varying environment.

Sliding Mode Control Techniques in E-Learning Systems

2016 ◽  
pp. 78-95
Author(s):  
I. Boiko ◽  
H. Hussein ◽  
A. Al Durra
Keyword(s):  
Sliding Mode Control ◽  
Dynamic Models ◽  
Sliding Mode ◽  
Variable Structure ◽  
Optimal Level ◽  
Learning Systems ◽  
Variable Structure Systems ◽  
Control Techniques ◽  
Mode Control ◽  
E Learning

Perspectives of using sliding mode control in e-learning are discussed. The concepts of variable structure systems and sliding mode control are given. Analysis of convergence based on the second Lyapunov's method is presented. The analysis presented is based on the dynamic models of learning available in the literature. The suitability of the use of sliding mode to adaptation of level of challenge of the tasks in e-learning is demonstrated. It is shown that with frequent enough evaluation of tasks, optimal level of task challenge can be ensured.

Self-Tuning Fuzzy Sliding Controller for the Ship Heading Problem

2010 ◽  
Author(s):  
Nassim Khaled ◽  
Nabil G. Chalhoub
Keyword(s):  
Fuzzy Logic Controller ◽  
Sliding Mode ◽  
Variable Structure ◽  
Guidance System ◽  
Tuning Parameter ◽  
Variable Structure Systems ◽  
Modeling Uncertainties ◽  
Self Tuning ◽  
The Stability ◽  
Yaw Angle

A self-tuning fuzzy-sliding mode controller is presented in the current work. It aims at combining the advantages of the variable structure systems (VSS) theory with the self-tuning fuzzy logic controller. Neither the development of an accurate dynamic model of the plant nor the construction of a rule-based expert system is required for designing the controller. The only requirement is that the upper bound of the modeling uncertainties has to be known. The stability of the controlled system is ensured by forcing the tuning parameter to satisfy the sliding condition. The controller is implemented to control the heading of an under-actuated ship. The simulation results demonstrate the robust performance of the controller in accurately tracking the desired yaw angle specified by the guidance system in the presence of considerable modeling imprecision and environmental disturbances.

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