Integral Sliding Mode Control for Markovian Jump T-S Fuzzy Descriptor Systems Based on the Super-Twisting Algorithm

This paper investigates integral sliding mode control problems for Markovian jump T-S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analyzed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed

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

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

Wind turbines controllers design based on the super-twisting algorithm

The continuous increase in the size of wind turbines (WTs) has led to new challenges in the design of novel torque and pitch controllers. Today’s WT control design must fulfill numerous specifications to assure effective electrical energy production and to hold the tower vibrations inside acceptable levels of operation. Hence, this paper presents modern torque and pitch control developments based on the super-twisting algorithm (STA) by using feedback of the fore- aft and side-to-side acceleration signals of the WT tower. According to numerical experiments realized using FAST, these controllers mitigate vibrations in the tower without affecting the quality of electrical power production. Moreover, the proposed controllers’ performance is better than the baseline controllers used for comparison.Postprint (author's final draft

Indirect adaptive higher-order sliding-mode control using the certainty-equivalence principle

Seit den 50er Jahren werden große Anstrengungen unternommen, Algorithmen zu entwickeln, welche in der Lage sind Unsicherheiten und Störungen in Regelkreisen zu kompensieren. Früh wurden hierzu adaptive Verfahren, die eine kontinuierliche Anpassung der Reglerparameter vornehmen, genutzt, um die Stabilisierung zu ermöglichen. Die fortlaufende Modifikation der Parameter sorgt dabei dafür, dass strukturelle Änderungen im Systemmodell sich nicht auf die Regelgüte auswirken. Eine deutlich andere Herangehensweise wird durch strukturvariable Systeme, insbesondere die sogenannte Sliding-Mode Regelung, verfolgt. Hierbei wird ein sehr schnell schaltendes Stellsignal für die Kompensation auftretender Störungen und Modellunsicherheiten so genutzt, dass bereits ohne besonderes Vorwissen über die Störeinflüsse eine beachtliche Regelgüte erreicht werden kann. Die vorliegende Arbeit befasst sich mit dem Thema, diese beiden sehr unterschiedlichen Strategien miteinander zu verbinden und dabei die Vorteile der ursprünglichen Umsetzung zu erhalten. So benötigen Sliding-Mode Verfahren generell nur wenige Informationen über die Störung, zeigen jedoch Defizite bei Unsicherheiten, die vom Systemzustand abhängen. Auf der anderen Seite können adaptive Regelungen sehr gut parametrische Unsicherheiten kompensieren, wohingegen unmodellierte Störungen zu einer verschlechterten Regelgüte führen. Ziel dieser Arbeit ist es daher, eine kombinierte Entwurfsmethodik zu entwickeln, welche die verfügbaren Informationen über die Störeinflüsse bestmöglich ausnutzt. Hierbei wird insbesondere Wert auf einen theoretisch fundierten Stabilitätsnachweis gelegt, welcher erst durch Erkenntnisse der letzten Jahre im Bereich der Lyapunov-Theorie im Zusammenhang mit Sliding-Mode ermöglicht wurde. Anhand der gestellten Anforderungen werden Regelalgorithmen entworfen, die eine Kombination von Sliding-Mode Reglern höherer Ordnung und adaptiven Verfahren darstellen. Neben den theoretischen Betrachtungen werden die Vorteile des Verfahrens auch anhand von Simulationsbeispielen und eines Laborversuchs nachgewiesen. Es zeigt sich hierbei, dass die vorgeschlagenen Algorithmen eine Verbesserung hinsichtlich der Regelgüte als auch der Robustheit gegenüber den konventionellen Verfahren erzielen.Since the late 50s, huge efforts have been made to improve the control algorithms that are capable of compensating for uncertainties and disturbances. Adaptive controllers that adjust their parameters continuously have been used from the beginning to solve this task. This adaptation of the controller allows to maintain a constant performance even under changing conditions. A different idea is proposed by variable structure systems, in particular by the so-called sliding-mode control. The idea is to employ a very fast switching signal to compensate for disturbances or uncertainties. This thesis deals with a combination of these two rather different approaches while preserving the advantages of each method. The design of a sliding-mode controller normally does not demand sophisticated knowledge about the disturbance, while the controller's robustness against state-dependent uncertainties might be poor. On the other hand, adaptive controllers are well suited to compensate for parametric uncertainties while unstructured influence may result in a degraded performance. Hence, the objective of this work is to design sliding-mode controllers that use as much information about the uncertainty as possible and exploit this knowledge in the design. An important point is that the design procedure is based on a rigorous proof of the stability of the combined approach. Only recent results on Lyapunov theory in the field of sliding-mode made this analysis possible. It is shown that the Lyapunov function of the nominal sliding-mode controller has a direct impact on the adaptation law. Therefore, this Lyapunov function has to meet certain conditions in order to allow a proper implementation of the proposed algorithms. The main contributions of this thesis are sliding-mode controllers, extended by an adaptive part using the certainty-equivalence principle. It is shown that the combination of both approaches results in a novel controller design that is able to solve a control task even in the presence of different classes of uncertainties. In addition to the theoretical analysis, the advantages of the proposed method are demonstrated in a selection of simulation examples and on a laboratory test-bench. The experiments show that the proposed control algorithm delivers better performance in regard to chattering and robustness compared to classical sliding-mode controllers

Second Order Sliding Mode Control For Direct Drive Positioning System

Second order sliding mode control is known for the ability to suppress chattering effect, often being associated with the implementation of a traditional sliding mode controller. The purpose of this paper is to demonstrate and compare the ability of super twisting sliding mode control to suppress chattering as well as to improve tracking performances against the traditional sliding mode controller. Both controllers were designed, numerically analysed and experimentally validated on a second order single-input single output system direct drive single axis positioning table. A continuous Kalman-Bucy filter was applied to estimate the velocity signal to further improve the overall tracking performance. Results showed that super twisting sliding mode controller was able to successfully suppress chattering effect by smoothening the control input through integration action to form a continuous function, thus dampening the effect of high frequency switching. The effectiveness of this control algorithm would promote its application in real-time application as it provides better control performance as compared to the standard sliding mode controlle

Rotor field orientation speed and torque control of BDFM with adaptive second order sliding mode

This paper presents two cascaded second order sliding mode controllers (SOSMCs) for brushless doubly fed motor (BDFM) adjustable speed system, which regulate the speed and torque. And an adaptive super twisting algorithm is incorporated into the SOSMCs to adaptively regulate the law of SOSMC. The proposed controllers for BDFM eliminate the average chattering encountered by most sliding mode control (SMC) schemes, and also possess the robustness and excellent static and dynamic performances of SMC. Simulation results show that the proposed control strategy is feasible, proper and effective. © 2013 IEEE

On Continuous Full-Order Integral-Terminal Sliding Mode Control with Unknown Apriori Bound on Uncertainty

This study aims at providing a solution to the problem of designing a continuous and finite-time control for a class of nonlinear systems in the presence of matched uncertainty with an unknown apriori bound. First, we propose a Full-Order Integral-Terminal Sliding Manifold (FOITSM) with a conventional (discontinuous) sliding mode to show that it provides the combined attributes of the nonsingular terminal and integral sliding mode algorithms. Secondly, an Adaptive Disturbance Observer (ADO) has been designed to alleviate the effect of the uncertainty acting on the system. On application of the ADO-based Full-Order Integral-Terminal Sliding Mode Control (FOITSMC), the chattering phenomenon in control input has been reduced substantially in the presence of conditionally known matched disturbances. Moreover, the adaptive gains of ADO are updated non-monotonically without over-bounding the acting disturbance, yet sustain the global boundedness of state trajectories within a specific bound. %Finally, an application of the proposed algorithm for attitude stabilization of a rigid spacecraft has been successively shown.Comment: 14 pages, 9 figure