Robust Discrete-Time Sliding Mode Control with Arbitrarily Small Boundary Layer

2018 ◽  
Author(s):  
Jorge E. Ruiz-Duarte ◽  
Alexander G. Loukianov ◽  
Juan J. Ley-Rosas
Keyword(s):  
Boundary Layer ◽  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Mode Control

Discrete-Time Sliding Mode Control for Nonlinear Systems With Unmatched Uncertainties and Uncertain Control Vector

1997 ◽  
Vol 119 (3) ◽  
pp. 503-512 ◽  
Author(s):  
E. A. Misawa
Keyword(s):  
Boundary Layer ◽  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Control Technique ◽  
Control Vector ◽  
Smooth Functions ◽  
Mode Control ◽  
Modeling Errors ◽  
Unmatched Uncertainties

This paper presents a technique for control system design that provides robust stability in the presence of bounded modeling errors. The proposed method is a discrete-time version of a well known sliding mode control technique with saturation functions that generates the boundary layer without requiring either matched uncertainties or smooth functions. It is shown that the boundary layer can be made attractive and that the boundary layer thickness is bounded under mild coditions. It is also shown that asymptotic stability can be guaranteed if the available model is assumed to be perfect. An example is used to illustrate the proposed design technique.

Boundary Layer Eigenvalues in SISO Discrete-Time Sliding Mode Control with Observer

2006 ◽  
Vol 128 (3) ◽  
pp. 729-730
Author(s):  
Hanz Richter ◽  
Eduardo A. Misawa
Keyword(s):  
Boundary Layer ◽  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Tracking Error ◽  
System Matrix ◽  
Mode Control ◽  
Sliding Manifold ◽  
Error Dynamics ◽  
Linear State

A result that allows us to specify the sliding manifold in observer-based discrete-time sliding mode control is presented. Selection of coefficients is done by analyzing the tracking error dynamics inside the boundary layer, where the closed-loop system has a linear state feedback configuration, rather than assuming that ideal sliding occurs. The result facilitates assignment of eigenvalues for the system matrix which defines such linear dynamics.

A New Discrete-time Sliding Mode Control Method Based on Restricted Variable Trending Law

2014 ◽  
Vol 39 (9) ◽  
pp. 1552-1557 ◽  
Author(s):  
Xi LIU ◽  
Xiu-Xia SUN ◽  
Wen-Han DONG ◽  
Peng-Song YANG
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Control Method ◽  
Sliding Mode ◽  
Mode Control

Design of funnel function-based discrete-time sliding mode control

2020 ◽  
Vol 14 (16) ◽  
pp. 2413-2418
Author(s):  
Haifeng Ma ◽  
Yangmin Li ◽  
Zhenhua Xiong
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Mode Control

scholarly journals Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3011
Author(s):  
Paweł Latosiński ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Control Strategies ◽  
Relative Degree ◽  
Band Width ◽  
Representative Point ◽  
Mode Control ◽  
Sliding Motion ◽  
Selection Of

Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width.

scholarly journals Reaching Law Based Sliding Mode Control of Sampled Time Systems

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1882
Author(s):  
Piotr Leśniewski ◽  
Andrzej Bartoszewicz
Keyword(s):  
Sliding Mode Control ◽  
Discrete Time ◽  
Sliding Mode ◽  
Rate Of Change ◽  
Reaching Law ◽  
Mode Control ◽  
Sliding Motion ◽  
Control Precision ◽  
Continuous Time Systems ◽  
Time Systems

In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.

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