Lyapunov stability analysis of second-order sliding-mode control and its application to chattering reduction design

Chang, Jeang‐Lin; Lin, Shih-Yu; Chu, Kuan-Chao; Chen, Min‐Shin

doi:10.1007/s12555-015-0149-1

Cited by 13 publications

(7 citation statements)

References 20 publications

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“…The adaptation laws of the IT2-AFSs defined in (11) and the adaptive systems given by (12) are expressed as…”

Section: Sliding Mode Control Law Designmentioning

confidence: 99%

“…Using the IT2-AFSs defined in (11) and (29), the adaptive systems defined in (12), the adaptation laws given by (20) and (32), the global control law (31) developed for the underactuated quadrotor (8) is stable in the sense of Lyapunov, and the asymptotic convergence of the tracking error is established despite the unknown dynamics, unknown physical parameters, and all of the unknown and unpredictable disturbances that affect quadrotor dynamics.…”

Section: Theoremmentioning

confidence: 99%

“…However, the chattering phenomenon resulting from the fact that the SMC law is discontinuous can be harmful to the actuators [10]. To eliminate or at least decrease the chattering, higher order SMC (HO-SMC) and boundary layer techniques are usually adopted in the literature to guarantee the desired objective of control [11][12][13][14][15]. However, these methods are only employed when the upper bounds of the different kinds of disturbances that influence the control system are known, which constrains their implementation in control systems.…”

Section: Introductionmentioning

confidence: 99%

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Robust Full Tracking Control Design of Disturbed Quadrotor UAVs with Unknown Dynamics

et al. 2018

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In this study, we develop a rigorous tracking control approach for quadrotor unmanned aerial vehicles (UAVs) with unknown dynamics, unknown physical parameters, and subject to unknown and unpredictable disturbances. In order to better estimate the unknown functions, seven interval type-2-adaptive fuzzy systems (IT2-AFSs) and five adaptive systems are designed. Then, a new IT2 adaptive fuzzy reaching sliding mode system (IT2-AFRSMS) which generates an optimal smooth adaptive fuzzy reaching sliding mode control law (AFRSMCL) using IT2-AFSs is introduced. The AFRSMCL is designed a way that ensures that its gains are efficiently estimated. Thus, the global proposed control law can effectively achieve the predetermined performances of the tracking control while simultaneously avoiding the chattering phenomenon, despite the approximation errors and all disturbances acting on the quadrotor dynamics. The adaptation laws are designed by utilizing the stability analysis of Lyapunov. A simulation example is used to validate the robustness and effectiveness of the proposed method of control. The obtained results confirm the results of the mathematical analysis in guaranteeing the tracking convergence and stability of the closed loop dynamics despite the unknown dynamics, unknown disturbances, and unknown physical parameters of the controlled system.

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“…The adaptation laws of the IT2-AFSs defined in (11) and the adaptive systems given by (12) are expressed as…”

Section: Sliding Mode Control Law Designmentioning

confidence: 99%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Full Tracking Control Design of Disturbed Quadrotor UAVs with Unknown Dynamics

et al. 2018

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“…Moreover, to design the control is necessary to know a priori, the upper bounds of uncertainties and disturbances. In practice, the control chattering is undesirable since it can damage the actuator and the system [32]; also, the bounds of the uncertainties and disturbances are not always known.…”

Section: Introductionmentioning

confidence: 99%

Robust Continuous Control for a Class of Mechanical Systems Based on Nonsingular Terminal Sliding Mode

2020

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In this paper is proposed a control structure for a class of mechanical systems; this structure consists of a continuous controller based on nonsingular terminal sliding mode control plus uncertainty and disturbance estimator. Closed-loop stability is proved by designing an adequate sliding surface and showing the existence of sliding modes by the fulfillment of the reaching law. A controllers comparison using the nonsingular terminal sliding mode, first-order sliding mode, PID, and the proposed control structure is carried out through numerical simulations of a pendulum system, where the l 2 index is used to measure the performance of the controllers. Moreover, real-time experiments are performed in a mechanical system with a pneumatic actuator. The theoretical, numerical, and experimental results validate the feasibility, performance, and robustness of the proposed control structure. INDEX TERMS Mechanical systems, nonsingular terminal sliding mode control, robust control, uncertainty and disturbance estimator.

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“…In recent years a robust software sensor for the IM drives is developed for estimation the stator resistance that improve the performance of the drives [27] but that software only estimate the stator resistance. In this paper a second order SMC with the new proposed control law based on lyapunov stability theory [28] is used to estimate and also compensate the rotor and stator resistance, using online adaptation method. A singular perturbation theory is used to reduce the order of the induction motor from fifth order to second order [29]- [31] and the second order SMC in place of 9th or higher order decreases the complexity of the system and make it simple.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Rotor and Stator Resistance for Induction Motor Drives using Second order of Sliding Mode Controller

Tak¹,

Kumar²,

Rajpurohit³

2017

JESTR

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The continues operation of vector controlled induction motor drives faces the problem of the stator and rotor resistance variation due to saturation, skin effect or in temperature variations. These resistance variations affect the controller performance. This paper illustrates about a new closed loop approach for estimation followed by compensation of the stator and rotor resistance of induction motor by using the second order sliding mode controller. The motor resistances estimated by online and the error between the actual and desired state variables of the induction motor track the sliding surface, the proposed method are based on the rigorous Lyapunov stability criteria. The simulation results show that the high frequency variation in the output waveform reduces as compared to the classical sliding mode controller and the mathematical analysis is simple to reduce the complexity faces in the higher order controller. For the estimation of the control variables of proposed algorithm only current measurement is needed and the controller is independent of the unknown parameter variation as the property of the sliding mode controller. The proposed method has been analyzed and verified with the help of Matlab/Simulink.

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Lyapunov stability analysis of second-order sliding-mode control and its application to chattering reduction design

Cited by 13 publications

References 20 publications

Robust Full Tracking Control Design of Disturbed Quadrotor UAVs with Unknown Dynamics

Robust Full Tracking Control Design of Disturbed Quadrotor UAVs with Unknown Dynamics

Robust Continuous Control for a Class of Mechanical Systems Based on Nonsingular Terminal Sliding Mode

Estimation of Rotor and Stator Resistance for Induction Motor Drives using Second order of Sliding Mode Controller

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