A fixed-time second order sliding mode observer for a class of nonlinear systems

This paper presents a second order fixed time sliding mode observer based on an extension of the super-twisting algorithm. This observer can be applied to a class of nonlinear system with a block-wise representation. The block structure provides a straightforward form to the application of the proposed second order sliding mode algorithm, yielding to finite-time convergence with a settling time independent to the system initial conditions. Finally, as numerical simulation example, the case of a linear induction motor is studied, exposing the efficiency and feasibility of the proposal

A multivariable super-twisting sliding mode approach

Copyright © 2014 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica (2014), DOI: 10.1016/j.automatica.2013.12.032This communique proposes a multivariable super-twisting sliding mode structure which represents an extension of the well-known single input case. A Lyapunov approach is used to show finite time stability for the system in the presence of a class of uncertainty. This structure is used to create a sliding mode observer to detect and isolate faults for a satellite system. © 2014 Elsevier Ltd. All rights reserved

Super-Twisting-Algorithm-Based Terminal Sliding Mode Control for a Bioreactor System

This study proposes a class of super-twisting-algorithm-based (STA-based) terminal sliding mode control (TSMC) for a bioreactor system with second-order type dynamics. TSMC not only can retain the advantages of conventional sliding mode control (CSMC), including easy implementation, robustness to disturbances, and fast response, but also can make the system states converge to the equivalent point in a finite amount of time after the system states intersect the sliding surface. The chattering phenomena in TSMC will originally exist on the sliding surface after the system states achieve the sliding surface and before the system states reach the equivalent point. However, by using the super twisting algorithm (STA), the chattering phenomena can be obviously reduced. The proposed method is also compared with two other methods: (1) CSMC without STA and (2) TSMC without STA. Finally, the control schemes are applied to the control of a bioreactor system to illustrate the effectiveness and applicability. Simulation results show that it can achieve better performance by using the proposed method

On short-time stability notions for nonlinear systems

This paper introduces the notions of annular settling and output annular settling for general nonlinear systems. Also, we propose conditions for annular short-time stability, short time boundedness with a nonzero initial state, annular settling, and output annular settling for generalized Persidskii systems with an essentially bounded input. These conditions are based on the verification of linear matrix inequalities. An application to recurrent neural networks illustrates the usefulness of the proposed notions and conditions

Nonlinear Backstepping Control Design for Coupled Nonlinear Systems under External Disturbances

A nonlinear backstepping control is proposed for the coupled normal form of nonlinear systems. The proposed method is designed by combining the sliding-mode control and backstepping control with a disturbance observer (DOB). The key idea behind the proposed method is that the linear terms of state variables of the second subsystem are lumped into the virtual input in the first subsystem. A DOB is developed to estimate the external disturbances. Auxiliary state variables are used to avoid amplification of the measurement noise in the DOB. For output tracking and unmatched disturbance cancellation in the first subsystem, the desired virtual input is derived via the backstepping procedure. The actual input in the second subsystem is developed to guarantee the convergence of the virtual input to the desired virtual input by using a sliding-mode control. The stability of the closed-loop is verified by using the input-to-state stable (ISS) property. The performance of the proposed method is validated via numerical simulations and an application to a vehicle system based on CarSim platform.This research was supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education under Grant NRF-2016R1C1B1014831 and the Research Program, Development of High Voltage Brake System for Response to Safety Regulations of Micro eMobility (20003066), funded by the Ministry of Trade, Industry and Energy (MOTIE, Korea)