Continuous Twisting Algorithm for Third-Order Systems

This paper proposes a synchronization technique for uncertain hyperchaotic systems in the modified function projective manner using integral fast terminal sliding mode (I-FTSM) and adaptive second-order sliding mode algorithm. The new I-FTSM manifolds are introduced with the aim of having the fast convergence speed. The proposed continuous controller not only results in the robustness and highaccuracy synchronization in the presence of unknown external disturbances and/or model uncertainties but also helps alleviating the chattering effect significantly. Numerical simulation results are provided to illustrate the effectiveness of the proposed control design technique and verify the theoretical analysis.

show abstract

“…In this paper, the following assumption is required for the subsequent development (see [37] and [38]).…”

Section: Problem Description and Preliminaries A Problem Descripmentioning

confidence: 99%

Adaptive Second-Order Sliding Mode Algorithm-Based Modified Function Projective Synchronization of Uncertain Hyperchaotic Systems

Tran

Kwon

2020

IEEE Access

View full text Add to dashboard Cite

show abstract

“…That algorithm may conceivably be used in order to extend the proposed Lyapunov‐based saturated continuous twisting algorithm to systems of order more than two. In this case, the continuous twisting algorithm for the higher‐order systems (see the papers given by Mendoza‐Avila et al 18,19 ) can be employed for t ≥ T since a family of Lyapunov functions has been proposed for it.…”

Section: Stability Analysismentioning

confidence: 99%

“…The parameters of control law (5) are well tuned as k 1 = 1000, k 2 = 800, k 3 = 1500, and k 4 = 0. It is noted that eliminating the term

{⌈ z_{2} ⌋}^{0}

of the standard CTA, which is not necessary for the stability of the closed‐loop system origin (see, e.g., the work of Mendoza‐Avila et al 18,19 ), reduces the windup effect to some extent. However, this cannot prevent the actuator from being saturated and hence, cannot remove the overshoot as shown in the corresponding response curves of the control input and piston position.…”

Section: Experimental Implementationmentioning

confidence: 99%

Lyapunov‐based saturated continuous twisting algorithm

Golkani

Seeber

Reichhartinger

et al. 2020

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

In this article, a second‐order system, which is affected by disturbances and uncertainties, with a saturating actuator is considered. A novel robust feedback control law is designed based on the sliding mode technique. The twisting and the continuous twisting algorithms are incorporated into the design, which is based on level curves of a Lyapunov function. The performance of the standard continuous twisting algorithm is greatly improved in the case that the initial condition of the system is far away from the origin. A parameter setting for the controller is given by establishing global finite‐time stability properties of the closed‐loop system origin. Feasibility and effectiveness of the proposed approach are indicated in a real‐world application as well as numerical simulation.

show abstract

“…These algorithms consist in a static homogeneous finite‐time controller for the nominal model of the system and a discontinuous integral action, aimed at estimating and compensating the uncertainties and perturbations. They are an extension of the (classical) super‐twisting algorithm, 22‐27 and are related to the continuous twisting algorithm (CTA) 28‐30 and discontinuous integral algorithm (DIA) 19,20 …”

Section: Introductionmentioning

confidence: 99%

Robust global stabilization of a class of underactuated mechanical systems of two degrees of freedom

Gutiérrez‐Oribio

Mercado-Uribe

Moreno

2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary In this article, the global stabilization of a class of underactuated mechanical systems of two degrees of freedom (DoF) is addressed, despite the presence of Lipschitz disturbances and/or uncertainties and uncertain control coefficient in the model. Using two second‐order continuous sliding modes algorithms, the control task is performed, reaching finite‐time convergence in one part of the dynamics and generating a continuous control signal. The efficacy of the proposed controllers is illustrated via simulations for the reaction wheel pendulum (RWP) and the translational oscillator with rotational actuator (TORA) systems, and by means of experiments on the RWP system, comparing the presented algorithms with a linearizing controller.

show abstract

Continuous Twisting Algorithm for Third-Order Systems

Cited by 29 publications

References 29 publications

Adaptive Second-Order Sliding Mode Algorithm-Based Modified Function Projective Synchronization of Uncertain Hyperchaotic Systems

Adaptive Second-Order Sliding Mode Algorithm-Based Modified Function Projective Synchronization of Uncertain Hyperchaotic Systems

Lyapunov‐based saturated continuous twisting algorithm

Robust global stabilization of a class of underactuated mechanical systems of two degrees of freedom

Contact Info

Product

Resources

About