Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control

Alsubaie, Hajid; Alotaibi, Ahmed; Alotaibi, Naif D.; Jahanshahi, Hadi

doi:10.3390/math11040978

Cited by 11 publications

(9 citation statements)

References 45 publications

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“…Rehabilitation robots represent a significant advancement in medical technology, offering novel solutions in physical therapy and patient care (Tejima, 2001;Qian and Bi, 2015;Alotaibi and Alsubaie, 2023;Alsubaie and Alotaibi, 2023;Luo et al, 2023). These sophisticated machines are designed to assist patients in recovering motor functions lost due to injuries, strokes, or chronic illnesses.…”

Section: Introductionmentioning

confidence: 99%

Kriging-based Model Predictive Control for Lower-limb Rehabilitation Robots

Alotaibi,

Alsubaie

2024

Journal of Disability Research

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Model predictive control (MPC) has emerged as a predominant method in the realm of control systems; yet, it faces distinct challenges. First, MPC often hinges on the availability of a precise and accurate system model, where even minor deviations can drastically affect the control performance. Second, it entails a high computational load due to the need to solve complex optimization problems in real time. This study introduces an innovative method that harnesses the probabilistic nature of Gaussian processes (GPs), offering a solution that is robust, adaptive, and computationally efficient for optimal control. Our methodology commences with the collection of data to learn optimal control policies. We then proceed with offline training of GPs on these data, which enables these processes to accurately grasp system dynamics, establish input–output relationships, and, crucially, identify uncertainties, thereby informing the MPC framework. Utilizing the mean and uncertainty estimates derived from GPs, we have crafted a controller that is capable of adapting to system deviations and maintaining consistent performance, even in the face of unforeseen disturbances or model inaccuracies. The convergence of the closed-loop system is assured through the application of the Lyapunov stability theorem. In our numerical experiments, the exemplary performance of our approach is demonstrated, notably in its capacity to adeptly handle the complexities of dynamic systems, even with limited training data, underlining a significant leap forward in MPC strategies.

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Section: Introductionmentioning

confidence: 99%

Kriging-based Model Predictive Control for Lower-limb Rehabilitation Robots

Alotaibi,

Alsubaie

2024

Journal of Disability Research

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“…Another anomaly of MEMS of non-integer order is that the deviation of the actual system order from the classical integer order results in a modification of the damping of the system, which indirectly affects its stability. The issue is illustrated, for example, by publications analyzing transversely oscillating MEMS viscometers [ 45 ] or fractional-order arch MEMS resonators [ 46 , 47 ]. A number of papers focus on advanced control techniques that help to improve the stability and performance of fractional-order MEMS [ 45 , 46 , 47 , 48 , 49 ], which are implemented using the sliding mode or fractional-order controllers.…”

Section: Introductionmentioning

confidence: 99%

“…The issue is illustrated, for example, by publications analyzing transversely oscillating MEMS viscometers [ 45 ] or fractional-order arch MEMS resonators [ 46 , 47 ]. A number of papers focus on advanced control techniques that help to improve the stability and performance of fractional-order MEMS [ 45 , 46 , 47 , 48 , 49 ], which are implemented using the sliding mode or fractional-order controllers. Such units can then exhibit complex fractional-order dynamics.…”

Section: Introductionmentioning

confidence: 99%

Extended Higher-Order Elements with Frequency-Doubled Parameters: The Hysteresis Loops Are Always of Type II

Biolek

Biolková

et al. 2023

Sensors

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Current MEMS (Micro Electro Mechanical Systems) can be modeled by state-dependent elements that exhibit hysteretic behavior. Examples include capacitors and inductors whose capacitances and inductances are dependent on the instantaneous state of the electromechanical system, resistors whose resistances exhibit temperature changes when the elements are actually heated, etc. Regardless of the physical background, such hysteresis manifestations can be studied uniformly in the broader framework of generic and extended higher-order elements, in which a classification of hysteretic loops into types I and II is established. The loop type is an important dynamical parameter of an element, having the potential to indicate, for example, its (in)volatility. Thus far, there is no reliable criterion to determine the type of steady loop from the defining relations of an element. This work reports on one special class of extended elements that produces type II loops under all circumstances. The paper presents hitherto unpublished connections between the frequency-doubling parameters of an element and the type of its hysteresis loop. The new findings are expressed by several theorems that allow the type of hysteresis to be inferred from the frequency behavior of the element parameter or state, and vice versa. These procedures are demonstrated with examples and verified by computer simulations.

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“…In [32], fractional calculus is incorporated with the observer's gain, providing an improved solution that effectively balances anti-noise capabilities with control performance considerations for disturbance rejection in hypersonic vehicles. In [33], a combination of disturbance observer-based control and fractional-order control is employed to enhance robustness and performance. This approach is specifically applied in the presence of nonlinearities, uncertainties, and external perturbations to stabilize nonlinear vibrations in fractional-order arch MEMS resonators.…”

Section: Introductionmentioning

confidence: 99%

An Adaptation of a Sliding Mode Classical Observer to a Fractional-Order Observer for Disturbance Reconstruction of a UAV Model: A Riemann–Liouville Fractional Calculus Approach

Hernández-Pérez,

Delgado-Reyes,

Borja-Jaimes

et al. 2023

Mathematics

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This paper proposes a modification of a Sliding Mode Classical Observer (SMCO) to adapt it to the fractional approach. This adaptation involves using a set of definitions based on fractional calculus theory, particularly the approach developed by Riemann–Liouville, resulting in a Sliding Mode Fractional Observer (SMFO). Both observers are used to perform disturbance reconstruction considered additive in a Quadrotor Unmanned Aerial Vehicle (UAV) model. Then, this work presents the fractional-order sliding mode observer’s mathematical formulation and integration into the Quadrotor UAV model. To validate the quality of the disturbance reconstruction process of the proposed SMFO observer scheme, numerical simulations are carried out, where a reconstruction quality indicator (BQR) is proposed based on the analysis of performance indices such as the Mean Square Error (MSE), the First Probability Moment (FPM), and Second Probability Moment (SPM), which were obtained for both the SMCO and the SMFO. The simulation results demonstrate the efficacy of the proposed observer in accurately reconstructing disturbances under various environmental conditions. Comparative analyses with SMCO highlight the advantages of the fractional-order approach in terms of reconstruction accuracy and improvement of its transitory performance. Finally, the presented SMFO offers a promising avenue for enhancing the reliability and precision of disturbance estimation, ultimately contributing to the advancement of robust control strategies for Quadrotor UAV systems.

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Stabilization of Nonlinear Vibration of a Fractional-Order Arch MEMS Resonator Using a New Disturbance-Observer-Based Finite-Time Sliding Mode Control

Cited by 11 publications

References 45 publications

Kriging-based Model Predictive Control for Lower-limb Rehabilitation Robots

Kriging-based Model Predictive Control for Lower-limb Rehabilitation Robots

Extended Higher-Order Elements with Frequency-Doubled Parameters: The Hysteresis Loops Are Always of Type II

An Adaptation of a Sliding Mode Classical Observer to a Fractional-Order Observer for Disturbance Reconstruction of a UAV Model: A Riemann–Liouville Fractional Calculus Approach

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