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

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.

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Design of adaptive fuzzy backstepping sliding mode control for MIMO uncertain discrete-time nonlinear systems based on noisy measurements

Journal of Vibration and Control ◽

10.1177/1077546316642053 ◽

2016 ◽

Vol 24 (2) ◽

pp. 393-406 ◽

Cited By ~ 3

Author(s):

Toshio Yoshimura

Keyword(s):

Nonlinear Systems ◽

Sliding Mode Control ◽

Discrete Time ◽

Sliding Mode ◽

Weighted Least Squares ◽

Tracking Error ◽

Design Parameters ◽

Adaptive Fuzzy ◽

Mode Control ◽

Backstepping Sliding Mode Control

This paper presents an adaptive fuzzy backstepping sliding mode control for multi-input and multi-output uncertain nonlinear systems in semi-strict feedback form. The systems are described by a discrete-time state equation with uncertainties viewed as the modeling errors and the unknown external disturbances, and the observation of the states is taken with independent measurement noises. Combining the adaptive fuzzy backstepping control with the sliding mode control approach for the comprehensive improvement in the stability and the robustness, the adaptive fuzzy backstepping sliding mode control is approximately designed where the design parameters are selected using an appropriate Lyapunov function. The uncertainities are approximated as fuzzy logic systems using the fuzzy inference approach based on the extended single input rule modules to reduce the number of the fuzzy IF-THEN rules. The estimates for the un-measurable states and the adjustable parameters are taken by the proposed simplified weighted least squares estimator. It is proved that the trajectory of the tracking error and the sliding surface is uniformly ultimately bounded. The effectiveness of the proposed approach is indicated through the simulation experiment of a simple numerical system.

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Error-Dynamics-Based Performance Shaping Methodology for Discrete-time Sliding Mode Control with Disturbance Observer

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2019.11.718 ◽

2019 ◽

Vol 52 (15) ◽

pp. 460-464 ◽

Cited By ~ 1

Author(s):

Ji-Seok Han ◽

Tae-Il Kim ◽

Tae-Ho Oh ◽

Young-Seok Kim ◽

Ji-Hyung Lee ◽

...

Keyword(s):

Sliding Mode Control ◽

Discrete Time ◽

Disturbance Observer ◽

Sliding Mode ◽

Mode Control ◽

Error Dynamics

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Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

International Journal of Advanced Robotic Systems ◽

10.1177/1729881417694290 ◽

2017 ◽

Vol 14 (2) ◽

pp. 172988141769429 ◽

Cited By ~ 8

Author(s):

Dong Zhang ◽

Lin Cao ◽

Shuo Tang

Keyword(s):

Sliding Mode Control ◽

Fractional Order ◽

Control Strategy ◽

Sliding Mode ◽

Tracking Error ◽

Uncertain Nonlinear Systems ◽

Mode Control ◽

Output System ◽

System Uncertainties ◽

Error Dynamics

This article presents a new fractional-order sliding mode control (FOSMC) strategy based on a linear-quadratic regulator (LQR) for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.

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Boundary layer eigenvalues in observer-based discrete-time sliding mode control

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301) ◽

10.1109/acc.2002.1025237 ◽

2002 ◽

Cited By ~ 4

Author(s):

H. Richter ◽

E.A. Misawa

Keyword(s):

Boundary Layer ◽

Sliding Mode Control ◽

Discrete Time ◽

Sliding Mode ◽

Mode Control

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2801286 ◽

1997 ◽

Vol 119 (3) ◽

pp. 503-512 ◽

Cited By ~ 41

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.

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