Invariant manifolds for nonsmooth systems with sliding mode

2015 ◽  
Vol 110 ◽  
pp. 15-32 ◽  
Author(s):  
D. Weiss ◽  
T. Küpper ◽  
H.A. Hosham
Keyword(s):  
Invariant Manifolds ◽  
Sliding Mode ◽  
Nonsmooth Systems

Invariant manifolds for nonsmooth systems

2012 ◽  
Vol 241 (22) ◽  
pp. 1895-1902 ◽  
Author(s):  
D. Weiss ◽  
T. Küpper ◽  
H.A. Hosham
Keyword(s):  
Invariant Manifolds ◽  
Nonsmooth Systems

Sliding Mode Control Laws Design by the ADAR Method with Subsequent Invariant Manifolds Aggregation

2019 ◽  
Vol 20 (8) ◽  
pp. 451-460 ◽  
Author(s):  
A. A. Kolesnikov ◽  
A. A. Kuz’menko
Keyword(s):  
Robust Control ◽  
Invariant Manifolds ◽  
Closed Loop ◽  
Sliding Mode ◽  
Design Procedure ◽  
Sliding Surface ◽  
Closed Loop System ◽  
External Disturbances ◽  
Control Laws ◽  
The Stability

Sliding mode control (SMC) laws are commonly used in engineering to make a system robust to parameters change, external disturbances and control object unmodeled dynamics. State-of-the-art capabilities of the theory of adaptive and robust control, the theory of fuzzy systems, artificial neural networks, etc., which are combined with SMC, couldn’t resolve current issues of SMC design: vector design and stability analysis of a closed-loop system with SMC are involved with considerable complexity. Generally the classical problem of SMC design consists in solving subtasks for transit an object from an arbitrary initial position onto the sliding surface while providing conditions for existence of a sliding mode at any point of the sliding surface as well as ensuring stable movement to the desired state. As a general rule these subtasks are solved separately. This article presents a methodology for SMC design based on successive aggregation of invariant manifolds by the procedure of method of Analytical Design of Aggregated Regulators (ADAR) from the synergetic control theory. The methodology allows design of robust control laws and simultaneous solution of classical subtasks of SMC design for nonlinear objects. It also simplifies the procedure for closed-loop system stability analyze: the stability conditions are made up of stability criterions for ADAR method functional equations and the stability criterions for the final decomposed system which dimension is substantially less than dimension of the initial system. Despite our paper presents only the scalar SMC design procedure in details, the ideas are also valid for vector design procedure: the main difference is in the number of invariant manifolds introduced at the first and following stages of the design procedure. The methodology is illustrated with design procedure examples for nonlinear engineering systems demonstrating the achievement of control goals: hitting to target invariants, insensitivity to emerging parametric and external disturbances.

MULTI-SCALE DYNAMICS OF TWO COUPLED NONSMOOTH SYSTEMS

2012 ◽  
Vol 22 (12) ◽  
pp. 1250295 ◽  
Author(s):  
C.-H. LAMARQUE ◽  
A. TURE SAVADKOOHI ◽  
E. ETCHEVERRIA ◽  
Z. DIMITRIJEVIC
Keyword(s):  
Invariant Manifolds ◽  
Passive Control ◽  
Dynamical Behavior ◽  
Control Process ◽  
Nonlinear Energy Sink ◽  
Forced Oscillations ◽  
Multi Scale ◽  
Nonsmooth Systems ◽  
Energy Sink ◽  
Nonlinear Energy

Dynamical behavior of a nonsmooth master system which is coupled to a nonsmooth Nonlinear Energy Sink (NES) during free and forced oscillations is studied analytically and numerically. Invariant manifolds of the system and their stable zones at different time scales are revealed and finally application of coupled nonsmooth NES to the passive control process of the main nonsmooth system is highlighted.

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
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