Δ-Modulated Feedback in Discretization of Sliding Mode Control

Abstract-In this paper, dynamical behaviors of the discretetime sliding-mode-control (DSMC) uncertain systems are studied. First, a discrete reaching law with a disturbance compensator is presented, and a sliding-mode controller is designed by using the proposed reaching law. Second, the time steps for the system trajectories to converge to the switching manifold are found. Then, a quasi-sliding-mode domain (QSMD) of the DSMC uncertain systems is obtained, and the system dynamics of the DSMC systems in QSMD are described. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed strategies.

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“…Lemma 1 [18], [28]: For a 1-D delta-modulated feedback system in the form of a discrete-time dynamics,…”

Section: System Descriptionmentioning

confidence: 99%

“…- [21] and delta modulation effects in the sliding direction [18]. The SMC of discrete-time systems is important, particularly when the implementation of the controller is realized by using computers with relatively low sampling frequencies [5]- [7], [9]- [15].…”

mentioning

confidence: 99%

Dynamics of Discrete-Time Sliding-Mode-Control Uncertain Systems With a Disturbance Compensator

Xia

Zhang

2014

IEEE Trans. Ind. Electron.

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178

157

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“…Proof: (a) When β > 0, then 0 < 1 − βT < 1 in (12). By Lemma 1(a-c), the switching function starting from any initial point will converge to a symmetric periodic-2 orbit (14).…”

Section: A Discretization Behaviors Of the Switching Function Along mentioning

confidence: 99%

“…Lemma 1 [12], [18]: For a one-dimensional delta-modulated feedback system in the form of discrete-time dynamics:…”

Section: Design Of Smc Systems Based Onmentioning

confidence: 99%

Dynamical Behaviors of an Euler Discretized Sliding Mode Control Systems

Xia

Zhang³

2014

IEEE Trans. Automat. Contr.

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Abstract-The dynamical behaviors of an Euler discretized sliding mode control (SMC) systems based on equivalent control strategy are studied. A periodic-2 orbit in steady state is found for the switching function of the Euler discretized SMC systems. The time steps for the switching function to converge toward the periodic-2 orbit are obtained. When the discretized SMC system is stable, it further shows that the system states of the SMC systems will also enter into some periodic-2 orbits, and these periodic-2 orbits are characterized by explicit analytic expressions. Finally, simulation examples are given to illustrate the theoretical results.

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“…Another reason is that the result can be easily extended to high-dimensional -modulated control systems, which will make the cryptosystem more secure. The complex behavior of this simple control system due to -modulated feedback has been investigated in [10], [21]- [24]. When some parameter in this particular 1-D discrete system, the system is chaotic ( [23], [24]) but not a self-map.…”

Section: Introductionmentioning

confidence: 99%

Improving the Security of Chaotic Synchronization With a $\Delta$-Modulated Cryptographic Technique

Liang

Zhang

Xia

2008

IEEE Trans. Circuits Syst. II

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Abstract-A secure chaos-based communication with a 1-modulated chaotic cryptographic technique is developed in this paper.We prove that a 1-modulated feedback control of a 1-D discretetime control system gives rise to a chaotic system. Base on this chaotic system, a modified parameter modulation scheme is proposed to improve security. As illustrated by numerical simulation, the parameter in the sender is protected by a secure cryptosystem against two popular attacks.

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Δ-Modulated Feedback in Discretization of Sliding Mode Control

Cited by 8 publications

References 13 publications

Dynamics of Discrete-Time Sliding-Mode-Control Uncertain Systems With a Disturbance Compensator

Dynamics of Discrete-Time Sliding-Mode-Control Uncertain Systems With a Disturbance Compensator

Dynamical Behaviors of an Euler Discretized Sliding Mode Control Systems

Improving the Security of Chaotic Synchronization With a $\Delta$-Modulated Cryptographic Technique

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