scholarly journals Robust block decomposition sliding mode control design

2002 ◽  
Vol 8 (4-5) ◽  
pp. 349-365 ◽  
Author(s):  
Alexander G. Loukianov
Keyword(s):  
Lyapunov Functions ◽  
Sliding Mode ◽  
Control Design ◽  
High Gain ◽  
Upper Bounds ◽  
Block Decomposition ◽  
Uncertain Nonlinear System ◽  
Recursive Procedure ◽  
Original Plant ◽  
Sliding Manifold

The paper examines the problem of sliding mode manifold design for uncertain nonlinear system with discontinuous control. The original plant first is decomposed such that the problem is divided into a number of simpler sub-problems. Then the block control recursive procedure is presented in which nonlinear sliding manifold is derived. Finally combined high gain and Lyapunov functions techniques are applied to establish hierarchy of the control gains and to estimate the upper bounds of the sliding mode equation solutions.

Nonlinear Robust Control Design for a Supercavitating Vehicle

2006 ◽  
Author(s):  
X. Mao ◽  
Q. Wang
Keyword(s):  
High Speed ◽  
Sliding Mode ◽  
Control Design ◽  
High Gain ◽  
System Stability ◽  
Control Surface ◽  
Supercavitating Vehicles ◽  
Supercavitating Vehicle ◽  
Final Design ◽  
Robust Control Design

Supercavitating vehicles can achieve very high speed but also pose technical challenges in maneuvering, system stability and control. Compared to a fully-wetted vehicle for which substantial lift is generated due to vortex shedding off the hull, the supercavitating vehicles are enveloped by gas surface thus the lift is provided by control surface deflections of cavitator and fins, as well as planing force between the vehicle and the cavity. The nonlinearity in the modeling of cavitator, fin, and in particular, the planing force make the control design more challenging. In this paper, a sliding-mode based controller is designed for the longitudinal dynamics of a supercavitating vehicle model. The stability and robustness of the final design are analyzed by the Lyapunov method and verified using simulation. A high-gain observer is also designed to estimate the vertical velocity of the supercavitating vehicle, which is not directly measurable, and then simulation results are presented for the (partial) output-feedback sliding-mode controller.

Lyapunov Functions and Sliding Mode Control for Two Degrees-of-Freedom and Multidegrees-of-Freedom Fractional Oscillators

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Youan Zhang ◽  
Jian Yuan ◽  
Jingmao Liu ◽  
Bao Shi
Keyword(s):  
Differential Equations ◽  
Sliding Mode Control ◽  
Lyapunov Functions ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Equations Of Motion ◽  
Control Design ◽  
State Equations ◽  
Two Degrees Of Freedom ◽  
Mode Control

This paper addresses the Lyapunov functions and sliding mode control design for two degrees-of-freedom (2DOF) and multidegrees-of-freedom (MDOF) fractional oscillators. First, differential equations of motion for 2DOF fractional oscillators are established by adopting the fractional Kelvin–Voigt constitute relation for viscoelastic materials. Second, a Lyapunov function candidate for 2DOF fractional oscillators is suggested, which includes the potential energy stored in fractional derivatives. Third, the differential equations of motion for 2DOF fractional oscillators are transformed into noncommensurate fractional state equations with six dimensions by introducing state variables with physical significance. Sliding mode control design and adaptive sliding mode control design are proposed based on the noncommensurate fractional state equations. Furthermore, the above results are generalized to MDOF fractional oscillators. Finally, numerical simulations are carried out to validate the above control designs.

scholarly journals Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 327 ◽  
Author(s):  
Chih-Hsueh Lin ◽  
Guo-Hsin Hu ◽  
Jun-Juh Yan
Keyword(s):  
Sliding Mode ◽  
Chaotic Behavior ◽  
Control Design ◽  
Sliding Mode Controller ◽  
Input Nonlinearity ◽  
Chaos Suppression ◽  
Control Scheme ◽  
Mismatched Uncertainties ◽  
Sliding Manifold ◽  
Robust Control Design

In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is designed such that the controlled dynamics in the sliding manifold becomes easy to analyze. Furthermore, only by using single rippling SMC even with input nonlinearity can we ensure the existence of the sliding mode for the controlled dynamics and suppress the chaotic behavior in a manner of rippling. Under the proposed control scheme, the chaos behavior in uncertain generalized 4D Lorenz–Stenflo systems subjected to mismatched uncertainties can be robustly suppressed to predictable bounds, which is not addressed in the literature. The numerical simulation results including matched/mismatched uncertainties and nonlinear inputs are presented to verify the robustness and validity of the rippling sliding mode controller.

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