Control of a flexible bevel-tipped needle using super-twisting controller based sliding mode observer

Hans, Surender; Joseph, Felix Orlando Maria

doi:10.1016/j.isatra.2020.09.011

Cited by 25 publications

(10 citation statements)

References 31 publications

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“…(Convergence of the weighted sum of the observer errors.) Consider the model ( 1), (2) subject to assumptions 1 to 3 and the observer ( 5)- (7), with definitions ( 8)- (10) and observer error 𝑥̅ = 𝑥 − 𝑥 . As a result of this observer: Ti) the function 𝑧 = 𝑥̅ − 𝜎𝜔𝑥̅ , 𝜎 = 𝑠𝑖𝑔𝑛(𝑏), satisfies…”

Section: Observer Design and Stability Analysismentioning

confidence: 99%

“…(Convergence of x 1 and boundedness of the updated parameter.) Consider the model (1), (2) subject to assumptions 1 to 3 and the observer ( 5)- (7), with definitions ( 8)- (10). As a result of this observer: (Ti) the updated parameter θδ remains bounded; (Tii) the observer error…”

Section: Remarkmentioning

confidence: 99%

“…Thus, statements Ti, Tii and Tiii are accomplished. 1), (2) subject to assumptions 1 to 3 and the observer ( 5)- (7), with definitions (8)- (10). As a result of this observer: (Ti) the transient response of the observer error x 2 = x2 − x 2 satisfies:…”

Section: Remarkmentioning

confidence: 99%

“…For instance, nonlinear state observers can be used to estimate biochemical reaction terms [4,5]. Furthermore, sliding mode and super twisting observers (STO) are capable of guaranteeing convergence of the estimation error towards zero or a small value, while accounting for disturbance terms, which can be caused by unmodelled variations, unknown model terms or measurement noise [6][7][8][9]. In addition, STOs achieve fast and finite time convergence [2,10,11].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Design and Evaluation of a Robust Observer Using Dead-Zone Lyapunov Functions—Application to Reaction Rate Estimation in Bioprocesses

2022

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This paper addresses the design and evaluation of a robust observer for second order bioprocesses considering unknown bounded disturbance terms and uncertainty in the dynamics of the unknown and known states. The observer design and the stability analysis are based on dead-zone Lyapunov functions, and a detailed procedure is provided. The transient response bounds and the convergence region of the unknown observer error are determined in terms of the disturbance bounds, considering persistent but bounded disturbances in the dynamics of both the known and unknown observer errors. This is a significant contribution to closely related observer design studies, in which the transient response bounds are determined, but persistent and bounded disturbances are not considered in the dynamics of the known observer error. Other important contributions are: (i) the procedure for defining the observer parameters is significantly simpler than common observer designs, since a solution to the Ricatti equation, solution to LMI constraints, or the accomplishment of eigenvalue inequality conditions are not required; (ii) discontinuous signals are not used in the observer; and (iii) the effect of the gain sign associated with the unknown state in the dynamics of the known state is explicitly and clearly considered in the observer design and in the convergence study. In addition, the guidelines for selecting the observer parameters are provided. Numerical simulation confirms the stability analysis results: the observer errors converge within a short time, with a low estimation error, if observer-parameters are properly defined.

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Section: Observer Design and Stability Analysismentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design and Evaluation of a Robust Observer Using Dead-Zone Lyapunov Functions—Application to Reaction Rate Estimation in Bioprocesses

2022

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“…[10][11][12][13] Different from linear observers, the sliding mode observer (SMO) enables the finite-time convergence of the estimation error which cannot be achieved by conventional linear observers. 14,15 It is well known that except for switching items, non-smooth non-linearities (such as terminal sliding mode) can also achieve high precision convergence in finite time. 16 Terminal sliding mode control (TSMC) strategies have been widely used in the controllers and the observers.…”

Section: Introductionmentioning

confidence: 99%

Output feedback sliding mode control based on non-singular terminal sliding mode observer

Chen

Chao

Dong

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this article, the finite-time output feedback sliding mode control problem is investigated for a class of continuous-time linear systems with unmeasurable states. First, a novel terminal sliding mode observer is established to estimate the unmeasured system states. Second, a novel integral sliding surface is introduced with tunable parameters. Then, an output feedback sliding mode controller with power terms is constructed to drive the given system to the origin in a finite time. A switching from the terminal sliding mode to a usual sliding manifold is taken to avoid singularity problem. Finally, two application-oriented examples are offered to verify the effectiveness of the proposed algorithm.

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Koopman‐based 3‐dimensional path following control for robotic flexible needles

Zhang,

Qi,

Chen

et al. 2024

Optim Control Appl Methods

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Robotic flexible needles have gained significant attention in minimally invasive medical procedures due to their ability to navigate complex anatomical structures and reach targets with high precision. Addressing the complex control problem in a 3‐dimensional environment, a Koopman‐based data‐driven control strategy is proposed in this paper. First, a 3‐dimensional (3D) path tracking problem is modeled using the simplified high‐dimensional bicycle model with the puncture kinematic. Then, with the Koopman operator theory, a finite linear approximation is designed and trained to simplify the nonlinear system of flexible needles. Finally, based on the linear approximation, a Koopman‐based model predictive control (MPC) scheme is proposed to realize 3‐dimensional path tracking for flexible needles. Based on simulations, the linear approximation and data‐driven control strategy are validated.

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Control of a flexible bevel-tipped needle using super-twisting controller based sliding mode observer

Cited by 25 publications

References 31 publications

Design and Evaluation of a Robust Observer Using Dead-Zone Lyapunov Functions—Application to Reaction Rate Estimation in Bioprocesses

Design and Evaluation of a Robust Observer Using Dead-Zone Lyapunov Functions—Application to Reaction Rate Estimation in Bioprocesses

Output feedback sliding mode control based on non-singular terminal sliding mode observer

Koopman‐based 3‐dimensional path following control for robotic flexible needles

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