Discrete-Time Implementation of Super-Twisting Control With Semi-Implicit Euler Method

Xiong, Xiaogang; Chen, Guangzeng; Lou, Yunjiang; Huang, Ruining

doi:10.1109/tcsii.2021.3078526

Cited by 8 publications

(14 citation statements)

References 13 publications

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“…The third known discrete-time version of the STC that is considered in this paper was published in [10] by Xiong et al and is obtained by a semi-implicit discretization. It consists of the controller functions…”

Section: Semi-implicit Discretizationmentioning

confidence: 99%

“…Also, φ k as well as ∆ k are virtual values, and not samples of the continuoustime signals ∆(t) and φ(t). Note that even though (10) is structurally equivalent to an Euler forward discretization of (1) the state x 1,k coincides with the samples x 1 (kh).…”

Section: Proposed Discrete-time Stcmentioning

confidence: 99%

“…are proposed in this paper for the discrete-time plant model (10). It is worth noting that the controller functions (11) resemble the terms of the implicit controller functions (5), with x 1,k + hν k replaced by x 1,k , and extended by the saturation term in the first equation.…”

Section: Proposed Discrete-time Stcmentioning

confidence: 99%

“…Note that Ψ Let the unknown virtual state x 2,k be defined as x 2,k := ν k + φ k . The closed-loop system resulting from the discrete-time plant (10) and the controller C proposed is…”

Section: Proposed Discrete-time Stcmentioning

confidence: 99%

“…Therefore, a proper discrete-time implementation of the Super-Twisting Controller (STC) is essential for many applications. There have been different approaches to achieve an implicitly discretized version of the STC [9], [10]. Also, non-implicit discretization techniques can be applied to the STC, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Modified Implicit Discretization of the Super-Twisting Controller

Andritsch,

Watermann,

Koch

et al. 2024

IEEE Trans. Automat. Contr.

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In this paper a novel discrete-time realization of the super-twisting controller is proposed. The closed-loop system is proven to converge to an invariant set around the origin in finite time. Furthermore, the steady-state error is shown to be independent of the controller gains. It only depends on the sampling time and the unknown disturbance. The proposed discrete-time controller is evaluated comparative to previously published discrete-time supertwisting controllers by means of the controller structure and in extensive simulation studies. The continuous-time supertwisting controller is capable of rejecting any unknown Lipschitz-continuous perturbation and converges in finite time. Furthermore, the convergence time decreases, if any of the gains is increased. The simulations demonstrate that the closed-loop systems with each of the known controllers lose one of these properties, introduce discretization-chattering, or do not yield the same accuracy level as with the proposed controller. The proposed controller, in contrast, is beneficial in terms of the above described properties.

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Section: Semi-implicit Discretizationmentioning

confidence: 99%

Section: Proposed Discrete-time Stcmentioning

confidence: 99%

Section: Proposed Discrete-time Stcmentioning

confidence: 99%

“…Note that Ψ Let the unknown virtual state x 2,k be defined as x 2,k := ν k + φ k . The closed-loop system resulting from the discrete-time plant (10) and the controller C proposed is…”

Section: Proposed Discrete-time Stcmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modified Implicit Discretization of the Super-Twisting Controller

Andritsch,

Watermann,

Koch

et al. 2024

IEEE Trans. Automat. Contr.

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A semi-implicit homogeneous discretized differentiator based on two projectors: experimental validation on a cable-driven parallel robot

Michel,

Métillon,

Caro

et al. 2024

Mechanics & Industry

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This work is dedicated to the application of a semi-implicit homogeneous differentiator to estimate the angular velocity and the angular acceleration of each of the eight electric motors of the CRAFT cable-driven parallel robot from the recording of the angular position of their respective output shaft. These motors drive the winding or unwinding of eight cables to move the robot moving-platform. The results show that this differentiator, whose the definition is respectively based on two projectors, is an extremely efficient tool for estimating the angular velocities and accelerations of the eight motors. These estimated velocities and accelerations are much less noisy than their reference signals obtained by backward difference. Moreover, the estimated quantities obtained with this differentiator are successfully compared to those obtained by a non-linear observer based on the interpolation and numerical difference of the measured position variable. Those promising results will definitely contribute to a better control of the CRAFT robot.

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