scholarly journals 1D and 2D Tracking Solvers for Solving Algebraic Equations Based upon Sliding Mode Control

2008 ◽  
Vol 3 (1) ◽  
pp. 216-227 ◽  
Author(s):  
Osami MATSUSHITA ◽  
Hiroyuki FUJIWARA
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Algebraic Equations ◽  
Mode Control

scholarly journals A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1134
Author(s):  
Yongpeng Tai ◽  
Ning Chen ◽  
Lijin Wang ◽  
Zaiyong Feng ◽  
Jun Xu
Keyword(s):  
Fractional Calculus ◽  
Sliding Mode Control ◽  
Numerical Method ◽  
Present Method ◽  
Sliding Mode ◽  
Constitutive Relations ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Mode Control ◽  
Fractional Differential

Fractional calculus is widely used in engineering fields. In complex mechanical systems, multi-body dynamics can be modelled by fractional differential-algebraic equations when considering the fractional constitutive relations of some materials. In recent years, there have been a few works about the numerical method of the fractional differential-algebraic equations. However, most of the methods cannot be directly applied in the equations of dynamic systems. This paper presents a numerical algorithm of fractional differential-algebraic equations based on the theory of sliding mode control and the fractional calculus definition of Grünwald–Letnikov. The algebraic equation is considered as the sliding mode surface. The validity of the present method is verified by comparing with an example with exact solutions. The accuracy and efficiency of the present method are studied. It is found that the present method has very high accuracy and low time consumption. The effect of violation corrections on the accuracy is investigated for different time steps.

Sliding Modes for the Simulation of Mechanical and Electrical Systems Defined by Differential-Algebraic Equations

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Sachit Rao ◽  
Vadim Utkin ◽  
Martin Buss
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Differential Algebraic Equations ◽  
Engineering Systems ◽  
Sliding Modes ◽  
Algebraic Equations ◽  
Electric Networks ◽  
Electrical Systems ◽  
Mode Control

We offer a technique, motivated by feedback control and specifically sliding mode control, for the simulation of differential-algebraic equations (DAEs) that describe common engineering systems such as constrained multibody mechanical structures and electric networks. Our algorithm exploits the basic results from sliding mode control theory to establish a simulation environment that then requires only the most primitive of numerical solvers. We circumvent the most important requisite for the conventional simulation of DAEs: the calculation of a set of consistent initial conditions. Our algorithm, which relies on the enforcement and occurrence of sliding mode, will ensure that the algebraic equation is satisfied by the dynamic system even for inconsistent initial conditions and for all time thereafter.

Combined Sliding Mode Control with a Feedback Linearization for Speed Control of Induction Motor

2011 ◽  
Vol 7 (1) ◽  
pp. 19-24
Author(s):  
Aamir Hashim Obeid Ahmed ◽  
Martino O. Ajangnay ◽  
Shamboul A. Mohamed ◽  
Matthew W. Dunnigan
Keyword(s):  
Sliding Mode Control ◽  
Induction Motor ◽  
Feedback Linearization ◽  
Sliding Mode ◽  
Speed Control ◽  
Mode Control

Adjust Method of Nonlinear Gain in Four-Wheel Steering Control Using Sliding Mode Control

2009 ◽  
Vol 129 (7) ◽  
pp. 1389-1396 ◽  
Author(s):  
Misawa Kasahara ◽  
Yuki Kanai ◽  
Ryoko Shiraki ◽  
Yasuchika Mori
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Steering Control ◽  
Nonlinear Gain ◽  
Mode Control
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