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Actuators, Volume 12, Issue 12 (December 2023) – 43 articles

Cover Story (view full-size image): Virtual reality systems lack wearable interfaces that provide users with tactile feedback on the softness of virtual objects. They require actuators that can stimulate fingertips via quasi-static forces through a deformable surface to control both the contact area with the skin and its indentation. This paper presents an electroencephalographic study on a recently described pneumatic, wearable, soft display made of small inflatable chambers at the fingertips. The somatosensory-evoked potentials (SEPs) in response to the stimulation of multiple fingers at different pressures showed that this device can elicit predictable perceptual responses that are consistent with the stimulations, and the SEPs may be used with this technology in the future for objective assessments. View this paper
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19 pages, 16867 KiB  
Article
Research on the Anti-Swing Control Methods of Dual-Arm Wheeled Inspection Robots for High-Voltage Transmission Lines
Actuators 2023, 12(12), 472; https://doi.org/10.3390/act12120472 - 18 Dec 2023
Viewed by 1024
Abstract
This paper presents an anti-swing control method to prevent situations where inspection robots detach and fall off transmission lines during obstacle crossing due to excessive swing angles caused by the rotation of the robot around the transmission line. Firstly, an obstacle-crossing model for [...] Read more.
This paper presents an anti-swing control method to prevent situations where inspection robots detach and fall off transmission lines during obstacle crossing due to excessive swing angles caused by the rotation of the robot around the transmission line. Firstly, an obstacle-crossing model for the inspection robot was constructed and the causes of robot swinging phenomena were analyzed, in addition to their impact on obstacle crossing stability. By combining this with the obstacle-crossing model, a moment balance equation was established for the inspection robot. This equation can be used to solve mapping relationships between body offset and the tilt angle of transmission line gripping arms. We propose an anti-swing control strategy by adjusting the angle of the transmission line gripping arm’s pitching joint to make the body offset approach zero, and by utilizing the advantages of fuzzy logic in the fuzzy PID algorithm compared with the traditional PID algorithm, it can adaptively avoid the occurrence of robot swinging phenomena. The experimental results of obstacle-crossing experiments under no wind and wind turbulence conditions indicated that the proposed anti-swing control method in this study can effectively keep the body offset to within 3 mm. Compared with the methods of not using anti-swing control and using traditional PID anti-swing control, in the absence of wind effects, the peak values of body offset were reduced by 96.53% and 18.85%, respectively. Under the influence of wind turbulence, the peak values of body offset were reduced by 97.02% and 27.12%, respectively. The effectiveness of the anti-swing control method proposed in this paper has thus been verified. Full article
(This article belongs to the Section Actuators for Robotics)
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19 pages, 9453 KiB  
Article
Vibration Suppression of a Flexible Beam Structure Coupled with Liquid Sloshing via ADP Control Based on FBG Strain Measurement
Actuators 2023, 12(12), 471; https://doi.org/10.3390/act12120471 - 17 Dec 2023
Viewed by 922
Abstract
In this study, an adaptive dynamic programming (ADP) control strategy based on the strain measurement of a fiber Bragg grating (FGB) sensor array is proposed for the vibration suppression of a complicated flexible-sloshing coupled system, which usually exists in aerospace engineering, such as [...] Read more.
In this study, an adaptive dynamic programming (ADP) control strategy based on the strain measurement of a fiber Bragg grating (FGB) sensor array is proposed for the vibration suppression of a complicated flexible-sloshing coupled system, which usually exists in aerospace engineering, such as launch vehicles with a large amount of liquid propellant as well as a flexible beam structure. To simplify the flexible-sloshing coupled dynamics model, the equivalent spring-mass-damper (SMD) model of liquid sloshing is employed, and a finite-element method (FEM) dynamic model for the beam structure coupled with the liquid sloshing is mathematically established. Then, a strain-based vibration dynamic model is derived by employing a transformation matrix based on the relationship between displacement and strain of the beam structure. To facilitate the design of a strain-based control, a tracking differentiator is designed to provide the strains’ derivative signals as partial states’ estimations. Feeding the system with the strain measurements and their derivatives’ estimations, an ADP controller with an action-dependent heuristic dynamic programming structure is proposed to suppress the vibration of the flexible-sloshing coupled system, and the corresponding Lyapunov stability of the closed-loop system is theoretically guaranteed. Numerical results show the proposed method can effectively suppress coupled vibration depending on limited strain measurements irrespective of external disturbances. Full article
(This article belongs to the Special Issue Dynamics and Control of Aerospace Systems)
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15 pages, 48951 KiB  
Article
A 4 mm Micro Servo Control System in Fiber Positioner
Actuators 2023, 12(12), 470; https://doi.org/10.3390/act12120470 - 17 Dec 2023
Viewed by 931
Abstract
As multi-object spectrographs (MOSs) continue to evolve, a notable trend has emerged—the increasing accommodation of fiber positioners on ever-more compact focal planes. This progression has seen the traditional stepper motors being supplanted by more space-efficient miniature hollow-cup motors. A significant challenge faced in [...] Read more.
As multi-object spectrographs (MOSs) continue to evolve, a notable trend has emerged—the increasing accommodation of fiber positioners on ever-more compact focal planes. This progression has seen the traditional stepper motors being supplanted by more space-efficient miniature hollow-cup motors. A significant challenge faced in the employment of these 4 mm diameter motors is the absence of compatible angle sensors, resulting in reliance on open-loop control methods for positioning. Addressing this challenge, this paper introduces a novel miniature angle sensor designed specifically for 4 mm hollow-cup motors, and presents a newly formulated closed-loop control scheme, which leverages this sensor to achieve accurate positioning. This marks the first implementation of an angle closed-loop control system within a 4 mm miniature hollow-cup motor used in MOS fiber positioners. Experimental evidence suggests that this sensored closed-loop mode substantially improves upon the energy efficiency and precision of fiber positioner placement, compared with traditional open-loop stepper control methods. Furthermore, the integration of these microsensors mitigates collision risks during the concurrent operation of fiber positioners by deactivating the motor power supply to prevent potential damage to the system. Full article
(This article belongs to the Section Precision Actuators)
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15 pages, 9945 KiB  
Article
An Adaptive Magnetorheological Fluid-Based Robotic Claw with an Electro-Permanent Magnet Array
Actuators 2023, 12(12), 469; https://doi.org/10.3390/act12120469 - 16 Dec 2023
Viewed by 1026
Abstract
The increasing demand for the adept handling of a diverse range of objects in various grasp scenarios has spurred the development of more efficient and adaptable robotic claws. This study specifically focuses on the creation of an adaptive magnetorheological fluid (MRF)-based robotic claw, [...] Read more.
The increasing demand for the adept handling of a diverse range of objects in various grasp scenarios has spurred the development of more efficient and adaptable robotic claws. This study specifically focuses on the creation of an adaptive magnetorheological fluid (MRF)-based robotic claw, driven by electro-permanent magnet (EPM) arrays to enhance gripping capabilities across different task requirements. In pursuit of this goal, a two-finger MRF-based robotic claw was introduced, featuring two magnetorheological (MR) grippers equipped with MR elastomer (MRE) bladders and EPM arrays at the fingertips. The operational principle involved placing a target object between these MR grippers and adjusting the normal force applied to the object for effective grasping. During this process, the contact stiffness of the MR grippers was altered by activating the EPM arrays in three distinct operation modes: passive, short-range (SR), and long-range (LR). Through experimentation on a benchtop material testing machine, the holding performance of the MRF-based robotic claw with the integrated EPM arrays was systematically evaluated. This study empirically validates the feasibility and effectiveness of the MRF-based robotic claw when equipped with EPM arrays. Full article
(This article belongs to the Special Issue Advancement in the Design and Control of Robotic Grippers)
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14 pages, 2395 KiB  
Article
Fault Diagnosis of Mine Truck Hub Drive System Based on LMD Multi-Component Sample Entropy Fusion and LS-SVM
Actuators 2023, 12(12), 468; https://doi.org/10.3390/act12120468 - 16 Dec 2023
Viewed by 1078
Abstract
As the main transportation equipment in ore mining, the wheel drive system of mining trucks plays a crucial role in the transportation capacity of mining trucks. The internal components of the hub drive system are mainly composed of bearings, gears, etc. The vibration [...] Read more.
As the main transportation equipment in ore mining, the wheel drive system of mining trucks plays a crucial role in the transportation capacity of mining trucks. The internal components of the hub drive system are mainly composed of bearings, gears, etc. The vibration signals caused during operation are nonlinear and nonstationary complex signals, and there may be more than one factor that causes faults, which causes certain difficulties for the fault diagnosis of the hub drive system. A fault diagnosis method based on local mean decomposition (LMD) multi-component sample entropy fusion and LS-SVM is proposed to address this issue. Firstly, the LMD method is used to decompose the vibration signals in different states to obtain a finite number of PF components. Then, based on the typical correlation analysis method, the distribution characteristics and correlation coefficients of vibration signals in the frequency domain under different states are calculated, and effective PF multi-component sample entropy features are constructed. Finally, the LS-SVM multi-fault classifier is used to train and test the extracted multi-component sample entropy features to verify the effectiveness of the method. The experimental results show that, even in small-sample data, the LMD multi-component sample entropy fusion and LS-SVM method can accurately extract fault features of vibration signals and complete classification, achieving fault diagnosis of wheel drive systems. Full article
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28 pages, 94398 KiB  
Article
Effect of Plasma Actuator Layout on the Passage Vortex Reduction in a Linear Turbine Cascade for a Wide Range of Reynolds Numbers
Actuators 2023, 12(12), 467; https://doi.org/10.3390/act12120467 - 15 Dec 2023
Viewed by 965
Abstract
This study examined how various plasma actuator (PA) configurations affect the passage vortex (PV) reduction in a linear turbine cascade (LTC) utilizing dielectric barrier discharge PAs. The experiments were carried out under three specific layout conditions: axial placement of the PA, slanted placement [...] Read more.
This study examined how various plasma actuator (PA) configurations affect the passage vortex (PV) reduction in a linear turbine cascade (LTC) utilizing dielectric barrier discharge PAs. The experiments were carried out under three specific layout conditions: axial placement of the PA, slanted placement at the blade inlet, and slanted placement inside the blade. Particle image velocimetry was employed to measure the velocity distribution of the secondary flow at the LTC exit, followed by an analysis of the streamline patterns, turbulence intensity distribution, and vorticity distribution. At a Reynolds number of 3.7 × 104, the PA with an oblique orientation at the blade inlet provided the most effective PV suppression. The average value of the secondary flow velocity and the peak vorticity value at the LTC exit decreased by 59.0% and 68.8%, respectively, compared to the no-control case. Furthermore, the wind tunnel blower’s rotation speed was modified, adjustments were made to the LTC’s mainstream velocity, and the Reynolds number transitioned from 1.0 × 104 to 9.9 × 104, approximately 10 times. When the slanted PA was used at the blade inlet, the PV suppression effect was the highest. The peak vorticity value owing to the PV at the LTC exit decreased by 62.9% at the lowest Reynolds number of 1.0 × 104. The Reynolds number increased with a higher mainstream velocity and decreased flow induced by the PA, consequently reducing the PV suppression effect. However, the drive of the PA was effective even under the most severe conditions (9.9 × 104), and the peak vorticity value was reduced by 20.2%. Full article
(This article belongs to the Section Precision Actuators)
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26 pages, 7727 KiB  
Article
Bearing Fault Diagnosis Method Based on Adversarial Transfer Learning for Imbalanced Samples of Portal Crane Drive Motor
Actuators 2023, 12(12), 466; https://doi.org/10.3390/act12120466 - 15 Dec 2023
Viewed by 1072
Abstract
Due to their unique structural design, portal cranes have been extensively utilized in bulk cargo and container terminals. The bearing fault of their drive motors is a critical issue that significantly impacts their operational efficiency. Moreover, the problem of imbalanced fault samples has [...] Read more.
Due to their unique structural design, portal cranes have been extensively utilized in bulk cargo and container terminals. The bearing fault of their drive motors is a critical issue that significantly impacts their operational efficiency. Moreover, the problem of imbalanced fault samples has a more pronounced influence on the application of novel fault diagnosis methods. To address this, the paper presents a new method called bidirectional gated recurrent domain adversarial transfer learning (BRDATL), specifically designed for imbalanced samples from portal cranes’ drive motor bearings. Initially, a bidirectional gated recurrent unit (Bi-GRU) is used as a feature extractor within the network to comprehensively extract features from both source and target domains. Building on this, a new Correlation Maximum Mean Discrepancy (CAMMD) method, integrating both Correlation Alignment (CORAL) and Maximum Mean Discrepancy (MMD), is proposed to guide the feature generator in providing domain-invariant features. Considering the real-time data characteristics of portal crane drive motor bearings, we adjusted the CWRU and XJTU-SY bearing datasets and conducted comparative experiments. The experimental results show that the accuracy of the proposed method is up to 99.5%, which is obviously higher than other methods. The presented fault diagnosis model provides a practical and theoretical framework for diagnosing faults in portal cranes’ field operation environments. Full article
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20 pages, 4175 KiB  
Article
Reliability Analysis and Optimization Method of a Mechanical System Based on the Response Surface Method and Sensitivity Analysis Method
Actuators 2023, 12(12), 465; https://doi.org/10.3390/act12120465 - 15 Dec 2023
Viewed by 1018
Abstract
Mechanical system reliability analysis constitutes a primary research focus in the field of engineering. This study aims to address the issue of complex mechanical systems with intricate mechanisms and nonlinear reliability equations that are challenging to solve. To this end, we present a [...] Read more.
Mechanical system reliability analysis constitutes a primary research focus in the field of engineering. This study aims to address the issue of complex mechanical systems with intricate mechanisms and nonlinear reliability equations that are challenging to solve. To this end, we present a reliability analysis and optimization methodology that merges the response surface and sensitivity analysis methods. A comprehensive formation of reliability assessment and optimization of complex mechanical systems is achieved by creating a response surface model to fit the complex state function and solving the reliability parameters, followed by an error sensitivity analysis to determine the mechanical system’s reliability adjustment strategy. Finally, these methods are applied to a cylindrical material transport device to preliminarily realize the reliability assessment and average reliability optimization goals. The study’s findings may offer a theoretical framework and research opportunities to evaluate and enhance the reliability of intricate mechanical systems. Full article
(This article belongs to the Section Control Systems)
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17 pages, 5103 KiB  
Article
Research on Neural Network Terminal Sliding Mode Control of Robotic Arms Based on Novel Reaching Law and Improved Salp Swarm Algorithm
Actuators 2023, 12(12), 464; https://doi.org/10.3390/act12120464 - 13 Dec 2023
Viewed by 944
Abstract
Modeling errors and external disturbances have significant impacts on the control accuracy of robotic arm trajectory tracking. To address this issue, this paper proposes a novel method, the neural network terminal sliding mode control (ALSSA-RBFTSM), which combines fast nonsingular terminal sliding mode (FNTSM) [...] Read more.
Modeling errors and external disturbances have significant impacts on the control accuracy of robotic arm trajectory tracking. To address this issue, this paper proposes a novel method, the neural network terminal sliding mode control (ALSSA-RBFTSM), which combines fast nonsingular terminal sliding mode (FNTSM) control, radial basis function (RBF) neural network, and an improved salp swarm algorithm (ALSSA). This method effectively enhances the trajectory tracking accuracy of robotic arms under the influence of uncertain factors. Firstly, the fast nonsingular terminal sliding surface is utilized to enhance the convergence speed of the system and achieve finite-time convergence. Building upon this, a novel multi-power reaching law is proposed to reduce system chattering. Secondly, the RBF neural network is utilized to estimate and compensate for modeling errors and external disturbances. Then, an improved salp swarm algorithm is proposed to optimize the parameters of the controller. Finally, the stability of the control system is demonstrated using the Lyapunov theorem. Simulation and experimental results demonstrate that the proposed ALSSA-RBFTSM algorithm exhibits superior robustness and trajectory tracking performance compared to the global fast terminal sliding mode (GFTSM) algorithm and the RBF neural network fast nonsingular terminal sliding mode (RBF-FNTSM) algorithm. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Robotic Systems)
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15 pages, 1090 KiB  
Article
Enhancing Vibration Control in Cable–Tip–Mass Systems Using Asymmetric Peak Detector Boundary Control
Actuators 2023, 12(12), 463; https://doi.org/10.3390/act12120463 - 11 Dec 2023
Viewed by 979
Abstract
In this study, a boundary controller based on a peak detector system has been designed to reduce vibrations in the cable–tip–mass system. The control procedure is built upon a recent modification of the controller, incorporating a non-symmetric peak detector mechanism to enhance the [...] Read more.
In this study, a boundary controller based on a peak detector system has been designed to reduce vibrations in the cable–tip–mass system. The control procedure is built upon a recent modification of the controller, incorporating a non-symmetric peak detector mechanism to enhance the robustness of the control design. The crucial element lies in the identification of peaks within the boundary input signal, which are then utilized to formulate the control law. Its mathematical representation relies on just two tunable parameters. Numerical experiments have been conducted to assess the performance of this novel approach, demonstrating superior efficacy compared to the boundary damper control, which has been included for comparative purposes. Full article
(This article belongs to the Special Issue New Control Schemes for Actuators)
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26 pages, 11800 KiB  
Article
A Novel Hierarchical Recursive Nonsingular Terminal Sliding Mode Control for Inverted Pendulum
Actuators 2023, 12(12), 462; https://doi.org/10.3390/act12120462 - 11 Dec 2023
Viewed by 992
Abstract
This paper aims to develop a novel hierarchical recursive nonsingular terminal sliding mode controller (HRNTSMC), which is designed to stabilize the inverted pendulum (IP). In contrast to existing hierarchical sliding mode controllers (HSMC), the HRNTSMC significantly reduces the chattering problem in control input [...] Read more.
This paper aims to develop a novel hierarchical recursive nonsingular terminal sliding mode controller (HRNTSMC), which is designed to stabilize the inverted pendulum (IP). In contrast to existing hierarchical sliding mode controllers (HSMC), the HRNTSMC significantly reduces the chattering problem in control input and improves the convergence speed of errors. In the HRNTSMC design, the IP system is first decoupled into pendulum and cart subsystems. Subsequently, a recursive nonsingular terminal sliding mode controller (RNTSMC) surface is devised for each subsystem to enhance the error convergence rate and attenuate chattering effects. Following this design, the HRNTSMC surface is constructed by the linear combination of the RNTSMC surfaces. Ultimately, the control law of the HRNTSMC is synthesized using the Lyapunov theorem to ensure that the system states converge to zero within a finite time. By invoking disturbances estimation, a linear extended state observer (LESO) is developed for the IP system. To validate the effectiveness, simulation results, including comparison with a conventional hierarchical sliding mode control (CHSMC) and a hierarchical nonsingular terminal sliding mode control (HNTSMC) are presented. These results clearly showcase the excellent performance of this approach, which is characterized by its strong robustness, fast convergence, high tracking accuracy, and reduced chattering in control input. Full article
(This article belongs to the Special Issue Recent Developments in Precision Actuation Technologies)
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24 pages, 10809 KiB  
Article
Design and Analysis of an Adaptive Cable-Driven Manipulator Capable of Actively Transitioning between Two-Point Clamping and Envelope Grasping
Actuators 2023, 12(12), 461; https://doi.org/10.3390/act12120461 - 11 Dec 2023
Viewed by 984
Abstract
Actively transitioning between clamping and grasping is a challenging problem for most manipulators with limited degrees of freedom. To overcome this problem, a cable-driven rigid–flexible combined manipulator capable of actively transitioning between clamping and grasping is proposed in this paper, which has a [...] Read more.
Actively transitioning between clamping and grasping is a challenging problem for most manipulators with limited degrees of freedom. To overcome this problem, a cable-driven rigid–flexible combined manipulator capable of actively transitioning between clamping and grasping is proposed in this paper, which has a certain adaptability and compliance to achieve adaptive operation. First, the cable-driven unit and compliant unit of the cable-driven rigid–flexible combined manipulator are designed. Then, the sensitivity of the mechanism parameters is analyzed using the Monte Carlo method, and then the structure of the cable-driven rigid–flexible combined manipulator is optimized. After that, the force on the finger in two-point clamping mode is modelled using Newton’s second law. Furthermore, the input–output relationship modelling of the finger in envelope grasping mode is deeply analyzed using the principle of energy conservation. Finally, the stable grasping performance of the cable-driven rigid–flexible combined manipulator is verified using numerical simulation and physical prototype tests. The results show that the cable-driven rigid–flexible combined manipulator has good adaptability and compliance, which verifies the effectiveness and rationality of the design and modelling. Full article
(This article belongs to the Special Issue Advancement in the Design and Control of Robotic Grippers)
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22 pages, 5785 KiB  
Article
A Novel Physics-Informed Hybrid Modeling Method for Dynamic Vibration Response Simulation of Rotor–Bearing System
Actuators 2023, 12(12), 460; https://doi.org/10.3390/act12120460 - 11 Dec 2023
Viewed by 969
Abstract
For rotor–bearing systems, their dynamic vibration models must be built to simulate the vibration responses that affect the safe and reliable operation of rotating machinery under different operating conditions. Single physics-based modeling methods can be used to produce sufficient but inaccurate vibration samples [...] Read more.
For rotor–bearing systems, their dynamic vibration models must be built to simulate the vibration responses that affect the safe and reliable operation of rotating machinery under different operating conditions. Single physics-based modeling methods can be used to produce sufficient but inaccurate vibration samples at the cost of computational complexity. Moreover, single data-driven modeling methods may be more accurate, employing larger numbers of measured samples and reducing computational complexity, but these methods are affected by the insufficient and imbalanced samples in engineering applications. This paper proposes a physics-informed hybrid modeling method for simulating the dynamic responses of rotor–bearing systems to vibration under different rotor speeds and bearing health statuses. Firstly, a three-dimensional model of a rolling bearing and its supporting force are introduced, and a physics-based dynamic vibration model that couples flexible rotors and rigid bearings is constructed using multibody dynamics simulation. Secondly, combining the simulation vibration data obtained using the physics-based model with measured vibration data, algorithms are designed to learn vibration generation and data mapping networks in series connection to form a physics-informed hybrid model, which can quickly and accurately output the vibration responses of a rotor–bearing system. Finally, a case study on the single-span rotor platform is provided. By comparing the signal output by the proposed physics-informed hybrid modeling method with the measured signal in the time and frequency domains, the effectiveness of proposed method under both constant- and variable-speed operating conditions are illustrated. Full article
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20 pages, 7199 KiB  
Article
Multi-Objective Point Motion Planning for Assembly Robotic Arm Based on IPQ-RRT* Connect Algorithm
Actuators 2023, 12(12), 459; https://doi.org/10.3390/act12120459 - 09 Dec 2023
Viewed by 1086
Abstract
Six-axis industrial assembly robotic arms are pivotal in the manufacturing sector, playing a crucial role in the production line. The IPQ-RRT* connect motion planning algorithm for the robotic arm is proposed to improve the assembly process by reducing the time of motion planning [...] Read more.
Six-axis industrial assembly robotic arms are pivotal in the manufacturing sector, playing a crucial role in the production line. The IPQ-RRT* connect motion planning algorithm for the robotic arm is proposed to improve the assembly process by reducing the time of motion planning and improving the assembly efficiency. The new IPQ-RRT* connect algorithm improves the original PQ-RRT* algorithm applied to UAVs in two dimensions by adding a node-greedy bidirectional scaling strategy. An obstacle detection range is set on the node-greedy bidirectional scaling strategy, in which the existence of obstacles is judged, and different sampling strategies are used according to the judgment results to get rid of obstacles faster, while bidirectional sampling can further improve the operation efficiency of the algorithm. In addition, effective collision detection is realized by combining the hierarchical wraparound box method. Finally, the Bezier curve is utilized to smooth the trajectory of the assembly robotic arm, which improves the trajectory quality while ensuring that the assembly robotic arm does not collide with obstacles. This paper takes the actual assembly process of an intelligent assembly platform as an example and proves the feasibility and effectiveness of the algorithm through simulation experiments and real I5 assembly robotic arm experiments. Full article
(This article belongs to the Section Actuators for Robotics)
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19 pages, 2501 KiB  
Article
Design and Unbiased Control of Nine-Pole Radial Magnetic Bearing
Actuators 2023, 12(12), 458; https://doi.org/10.3390/act12120458 - 09 Dec 2023
Viewed by 1005
Abstract
Typical radial active magnetic bearings are structurally symmetric. For example, an eight-pole bearing uses two opposing pairs to control one axis by winding the pair in series. The magnetic force produced by an active magnetic bearing is quadratically proportional to coil currents and [...] Read more.
Typical radial active magnetic bearings are structurally symmetric. For example, an eight-pole bearing uses two opposing pairs to control one axis by winding the pair in series. The magnetic force produced by an active magnetic bearing is quadratically proportional to coil currents and inversely proportional to the square of the gap between the bearing and the journal. Bias linearization is widely used to linearize the relationship of coil currents to the magnetic force. However, the bias currents increase ohmic losses and require a larger than necessary capacity of power amplifiers to supply the sum of bias and control currents. Unbiased control of symmetric bearings has the critical issue of slew-rate limiting. Unbiased control of unsymmetrical bearings can eliminate the need for bias currents while avoiding slew-rate singularity except in extreme cases. Although a generalized inversion of the force–current relationship of unbiased unsymmetrical bearings has been proposed previously, no experimental validation is reported. The main objective of this research is to implement the unbiased control strategy and show that exactly the same linear control strategy for eight-pole symmetric bearings can be applied to nine-pole unsymmetrical bearings on industry-scale compressor test rigs. Two test rigs are built: one with eight-pole symmetric bearings and another with nine-pole unsymmetrical bearings. Linear control algorithms are designed and applied. Both control algorithms are linear and consist of lead filters and notch filters. The test results show that the linear control design used for unsymmetrical bearings can achieve the same level of stability that the symmetric bearings provide, satisfying the sensitivity criterion specified by ISO 14839-3. Full article
(This article belongs to the Section Control Systems)
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29 pages, 1103 KiB  
Review
A Review of Piezoelectric Energy Harvesting: Materials, Design, and Readout Circuits
Actuators 2023, 12(12), 457; https://doi.org/10.3390/act12120457 - 08 Dec 2023
Viewed by 1511
Abstract
Mechanical vibrational energy, which is provided by continuous or discontinuous motion, is an infinite source of energy that may be found anywhere. This source may be utilized to generate electricity to replenish batteries or directly power electrical equipment thanks to energy harvesters. The [...] Read more.
Mechanical vibrational energy, which is provided by continuous or discontinuous motion, is an infinite source of energy that may be found anywhere. This source may be utilized to generate electricity to replenish batteries or directly power electrical equipment thanks to energy harvesters. The new gadgets are based on the utilization of piezoelectric materials, which can transform vibrating mechanical energy into useable electrical energy owing to their intrinsic qualities. The purpose of this article is to highlight developments in three independent but closely connected multidisciplinary domains, starting with the piezoelectric materials and related manufacturing technologies related to the structure and specific application; the paper presents the state of the art of materials that possess the piezoelectric property, from classic inorganics such as PZT to lead-free materials, including biodegradable and biocompatible materials. The second domain is the choice of harvester structure, which allows the piezoelectric material to flex or deform while retaining mechanical dependability. Finally, developments in the design of electrical interface circuits for readout and storage of electrical energy given by piezoelectric to improve charge management efficiency are discussed. Full article
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19 pages, 3625 KiB  
Review
A Review of Nonlinear Mechanisms for Frequency Up-Conversion in Energy Harvesting
Actuators 2023, 12(12), 456; https://doi.org/10.3390/act12120456 - 08 Dec 2023
Viewed by 1289
Abstract
Vibration-based energy harvesting has garnered considerable attention from researchers over the past two decades, using different transduction mechanisms. In this context, the utilization of piezoelectric materials has proven to be highly successful, due to their power density, across a broad range of voltages. [...] Read more.
Vibration-based energy harvesting has garnered considerable attention from researchers over the past two decades, using different transduction mechanisms. In this context, the utilization of piezoelectric materials has proven to be highly successful, due to their power density, across a broad range of voltages. A primary challenge in environmental vibration harvesting lies in the frequency mismatch between the devices, which typically exhibit optimal performance at hundreds or thousands of hertz due to their small size (centimeter or millimeter) and the environmental vibration. The latter has considerable energy density around tens of hertz. For this reason, over the last 15 years, the scientific community has concentrated on exploring techniques for band broadening or frequency up-conversion by intentionally introduced (or designed) nonlinearities. This review, following an introduction to the topic of vibration energy harvesting, provides a description of the primarily developed mechanisms, presenting a chronological development for each, from the initial works to the most recent advancements. Additionally, the review touches upon implementation efforts at the micro-electromechanical systems (MEMS) scale for each described technique. Finally, the incorporation of nonlinearities through electronic circuits to enhance performance is briefly discussed. Full article
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17 pages, 13662 KiB  
Article
Soft Coiled Pneumatic Actuator with Integrated Length-Sensing Function for Feedback Control
Actuators 2023, 12(12), 455; https://doi.org/10.3390/act12120455 - 08 Dec 2023
Viewed by 1125
Abstract
SPIRA Coil actuators are formed from thin sheets of PET plastic laminated into a coil shape that unfurls like a “party horn” when inflated, while many soft actuators require large pressures to create only modest strains, SPIRA Coils can easily be designed and [...] Read more.
SPIRA Coil actuators are formed from thin sheets of PET plastic laminated into a coil shape that unfurls like a “party horn” when inflated, while many soft actuators require large pressures to create only modest strains, SPIRA Coils can easily be designed and fabricated to extend over dramatic distances with relatively low working pressures. Internal metalized PET strips separate in the extended portion of the actuator, creating an electrical circuit with a resistance that corresponds to the actuator length. This paper presents and experimentally validates easy-to-use design models for the actuators’ self-retracting spring stiffness, its pneumatic extension force, and its internal length-sensing electrical resistance. Testing of the self-sensing capabilities demonstrates that the embedded sensor can be used to determine the actuator length with virtually no hysteresis. Feedback control with the resistance-based sensing resulted in length-control errors within 5% of the extended actuator length (i.e., 3 cm of 60 cm). Full article
(This article belongs to the Special Issue Soft Actuators and Robotics)
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18 pages, 3935 KiB  
Article
An Accurate Dynamic Model Identification Method of an Industrial Robot Based on Double-Encoder Compensation
Actuators 2023, 12(12), 454; https://doi.org/10.3390/act12120454 - 07 Dec 2023
Viewed by 1110
Abstract
Aiming at the challenges to accurately simulate complex friction models, link dynamics, and part uncertainty for high-precision robot-based manufacturing considering mechanical deformation and resonance, this study proposes a high-precision dynamic identification method with a double encoder. Considering the influence of the dynamic model [...] Read more.
Aiming at the challenges to accurately simulate complex friction models, link dynamics, and part uncertainty for high-precision robot-based manufacturing considering mechanical deformation and resonance, this study proposes a high-precision dynamic identification method with a double encoder. Considering the influence of the dynamic model of the manipulator on its control accuracy, a three-iterative global parameter identification method based on the least square method and GMM (Gaussian Mixture Model) under the optimized excitation trajectory is proposed. Firstly, a bidirectional friction model is constructed to avoid using residual torque to reduce the identification accuracy. Secondly, the condition number of the block regression matrix is used as the optimization objective. Finally, the joint torque is theoretically identified with the weighted least squares method. A nonlinear model distinguishing between high and low speeds was established to fit the nonlinear friction of the robot. By converting the position and velocity of the motor-side encoder to the linkage side using the deceleration ratio, the deformation quantity could be calculated based on the discrepancy between theoretical and actual values. The GMM algorithm is used to compensate the uncertainty torque that was caused by model inaccuracy. The effectiveness of the proposed method is verified by a simulation and experiment on a 6-DoF industrial robot. Results prove that the proposed method can enhance the online torque estimation performance by up to 20%. Full article
(This article belongs to the Special Issue Actuators in Robotic Control: Volume II)
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16 pages, 6905 KiB  
Article
Parameter Identification of Permanent Magnet Synchronous Motor with Dynamic Forgetting Factor Based on H∞ Filtering Algorithm
Actuators 2023, 12(12), 453; https://doi.org/10.3390/act12120453 - 07 Dec 2023
Viewed by 963
Abstract
To address system parameter changes during permanent magnet synchronous motor (PMSM) operation, an H∞ filtering algorithm with a dynamic forgetting factor is proposed for online identification of motor resistance and inductance. First, a standard linear discrete PMSM parameter identification model is established; then, [...] Read more.
To address system parameter changes during permanent magnet synchronous motor (PMSM) operation, an H∞ filtering algorithm with a dynamic forgetting factor is proposed for online identification of motor resistance and inductance. First, a standard linear discrete PMSM parameter identification model is established; then, the discrete H∞ filtering algorithm is derived using game theory reducing state and measurement noise influence. A cost function is defined, solving extremes values of different terms. A dynamic forgetting factor is introduced to the weighted combination of initial and current measurement noise covariance matrices, eliminating identification issues from different initial values. On this basis, a dynamic forgetting factor is added to weigh the combination of the initial measurement noise covariance matrix and the current measurement noise covariance matrix, which eliminates the influence of the discrimination error caused by the different initial values. Finally, the identification model is built in MATLAB/Simulink for simulation analysis to verify the feasibility of the proposed algorithm. The simulation results show the proposed H∞ filtering algorithm rapidly and accurately identifies resistance and inductance values with significantly improved robustness. The forgetting factor enables quick stable recognition even with poor initial values, enhancing PMSM control performance. Full article
(This article belongs to the Special Issue Power Electronics and Actuators)
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21 pages, 13554 KiB  
Article
A Bimodal Hydrostatic Actuator for Robotic Legs with Compliant Fast Motion and High Lifting Force
Actuators 2023, 12(12), 452; https://doi.org/10.3390/act12120452 - 07 Dec 2023
Viewed by 1009
Abstract
Robotic legs, such as for lower-limb exoskeletons and prostheses, have bimodal operation: (1) within a task, like for walking (high speed and low force for the swing phase and low speed and higher force when the leg bears the weight of the system); [...] Read more.
Robotic legs, such as for lower-limb exoskeletons and prostheses, have bimodal operation: (1) within a task, like for walking (high speed and low force for the swing phase and low speed and higher force when the leg bears the weight of the system); (2) between tasks, like between walking and sit–stand motions. Sizing a traditional single-ratio actuation system for such extremum operations leads to oversized heavy electric motor and poor energy efficiency at low speeds. This paper explores a bimodal actuation concept where a hydrostatic transmission is dynamically reconfigured using custom motorized ball valves to suit the requirements of a robotic leg with a smaller and more efficient actuation system. First, this paper presents an analysis of the mass and efficiency advantages of the bimodal solution over a baseline solution, for three operating points: high-speed, high-force, and braking modes. Second, an experimental demonstration with a custom-built actuation system and a robotic leg test bench is presented. Control challenges regarding dynamic transition between modes are discussed and a control scheme solution is proposed and tested. The results show the following findings: (1) The actuator prototype can meet the requirements of a leg bimodal operation in terms of force, speed, and compliance while using smaller motors than a baseline solution. (2) The proposed operating principle and control schemes allow for smooth and fast mode transitions. (3) Motorized ball valves exhibit a good trade-off between size, speed, and flow restriction. (4) Motorized ball valves are a promising way to dynamically reconfigure a hydrostatic transmission while allowing energy to be dissipated. Full article
(This article belongs to the Special Issue Actuation Solutions for Wearable Robots)
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18 pages, 8156 KiB  
Article
A Study on Eddy Current Reduction Shape of Single-Phase Claw-Pole Motor
Actuators 2023, 12(12), 451; https://doi.org/10.3390/act12120451 - 07 Dec 2023
Viewed by 941
Abstract
The claw-pole motor, known for its simple structure, is widely used in various fields due to its cost competitiveness. However, a drawback of the fixed-stator-type claw-pole motor is its vulnerability to eddy current losses. Therefore, this paper presents a single-phase claw-pole motor applied [...] Read more.
The claw-pole motor, known for its simple structure, is widely used in various fields due to its cost competitiveness. However, a drawback of the fixed-stator-type claw-pole motor is its vulnerability to eddy current losses. Therefore, this paper presents a single-phase claw-pole motor applied as a motor for cooling fans, with the aim of reducing eddy current losses and improving performance based on shape optimization, ultimately resulting in a single-phase claw-pole motor that meets the desired performance. The validity of this approach is verified through 3D finite element analysis (FEA). Full article
(This article belongs to the Section High Torque/Power Density Actuators)
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23 pages, 13426 KiB  
Article
Mechanical Design and Experiments of a New Rotational Variable Stiffness Actuator for Hybrid Passive–Active Stiffness Regulation
Actuators 2023, 12(12), 450; https://doi.org/10.3390/act12120450 - 04 Dec 2023
Viewed by 1103
Abstract
To improve collision safety in robot–human collaborative applications, increasing attention has been paid to rotational variable stiffness actuators. A new rotational variable stiffness actuator, which works in two stages, is proposed for hybrid passive–active stiffness regulation. The passive stage is based on the [...] Read more.
To improve collision safety in robot–human collaborative applications, increasing attention has been paid to rotational variable stiffness actuators. A new rotational variable stiffness actuator, which works in two stages, is proposed for hybrid passive–active stiffness regulation. The passive stage is based on the motions of springs driven by the rack-and-pinion systems, elastically converting the shaft’s rotation into the inner shell rotation fixed to the internal gear of the active stage. The active stage is designed to achieve the movement of the pivot point located on the roller actuated by the adjustment motor, providing the output angle of the output shaft. The two pairs of rack-and-pinion systems of the passive stage and the two pairs of planetary gears of the active stage are designed for side-by-side placement, improving the stability and balance of the stiffness regulation process. Two symmetrical cam-slider mechanisms acting as leverage pivots ensure the synchronous movements of the two rollers. The variable stiffness actuator is designed and validated by simulations and experiments. Strength analysis and stiffness analysis are presented. The designed actuator can obtain the range of stiffness adjustment of 35–3286 N·mm/deg. The range of the angle difference between the input and output shafts is ±48°. Full article
(This article belongs to the Section Actuators for Robotics)
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14 pages, 7208 KiB  
Article
Assessment of the Dynamic Range of Magnetorheological Gradient Pinch-Mode Prototype Valves
Actuators 2023, 12(12), 449; https://doi.org/10.3390/act12120449 - 04 Dec 2023
Viewed by 973
Abstract
Magnetorheological (MR) fluids have been known to react to magnetic fields of sufficient magnitudes. While in the presence of the field, the material develops a yield stress. The tunable property has made it attractive in, e.g., semi-active damper applications in the vibration control [...] Read more.
Magnetorheological (MR) fluids have been known to react to magnetic fields of sufficient magnitudes. While in the presence of the field, the material develops a yield stress. The tunable property has made it attractive in, e.g., semi-active damper applications in the vibration control domain in particular. Within the context of a given application, MR fluids can be exploited in at least one of the fundamental operating modes (flow, shear, squeeze, or gradient pinch mode) of which the gradient pinch mode has been the least explored. Contrary to the other operating modes, the MR fluid volume in the flow channel is exposed to a non-uniform magnetic field in such a way that a Venturi-like contraction is developed in a flow channel solely by means of a solidified material in the regions near the walls rather than the mechanically driven changes in the channel’s geometry. The pinch-mode rheology of the material has made it a potential candidate for developing a new category of MR valves. By convention, a pinch-mode valve features a single flow channel with poles over which a non-uniform magnetic field is induced. In this study, the authors examine ways of extending the dynamic range of pinch-mode valves by employing a number of such arrangements (stages) in series. To accomplish this, the authors developed a prototype of a multi-stage (three-stage) valve, and then compared its performance against that of a single-stage valve across a wide range of hydraulic and magnetic stimuli. To summarize, improvements of the pinch-mode valve dynamic range are evident; however, at the same time, it is hampered by the presence of serial air gaps in the flow channel. Full article
(This article belongs to the Special Issue Magnetorheological Actuators and Dampers)
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25 pages, 7282 KiB  
Article
Development of Vibratory Microinjection System for Instantaneous Cell Membrane Piercing in Cytoplasmic Microinjection into Fertilized Eggs
Actuators 2023, 12(12), 448; https://doi.org/10.3390/act12120448 - 02 Dec 2023
Viewed by 1122
Abstract
To complete microinjection as quickly as possible, we have developed Vibratory Microinjection Systems (VMSs) that vibrate a micropipette in its longitudinal direction and can significantly reduce the time needed for pronuclear microinjection compared to ordinary (non-vibratory) microinjection. The longest breakdown of the time [...] Read more.
To complete microinjection as quickly as possible, we have developed Vibratory Microinjection Systems (VMSs) that vibrate a micropipette in its longitudinal direction and can significantly reduce the time needed for pronuclear microinjection compared to ordinary (non-vibratory) microinjection. The longest breakdown of the time is the time required to pierce the cell membrane and the pronuclear membrane simultaneously. Because cytoplasmic microinjection, which pierces the cell membrane alone, is far more difficult and time-consuming than pronuclear microinjection, we next aimed to develop a VMS capable of penetrating the cell membrane instantly. In this new and latest version, two types of ultrasonic-wave vibrators were developed: the first for commercially available micropipettes (Femtotip) and the second for self-made micropipettes. The two vibrators differ only in their airtight structure, where the micropipettes connect to their respective vibrators: a female screw plus O-ring for the first vibrator (VMS6_1) and a silicone-rubber tube for the second (VMS6_2). The tube-type joint used in VMS6_2 only slightly damped or amplified vibrations from the vibrator to the micropipette tip, propagating them much more accurately than the screw-type joint in VMS6_1. In addition, VMS6_2 significantly shortened the time taken to pierce the cell membrane of a fertilized egg: an average of 1.52 s (N = 410) vs. 3.62 s (N = 65) in VMS6_1. The VMS6_2 group achieved a piercing time of zero in 86.1% of the allocated eggs, while only 10.8% of the VMS6_1 group did. In each vibrator, we also compared vibratory microinjection (VM; N = 475) and ordinary microinjection (OM; N = 457), which uses injection pressure in place of vibration. None of the eggs in the OM group achieved the zero-second piercing time. Compared to the OM, the VM group showed a significantly shorter piercing time, 1.80 vs. 10.69 s on average, and a significantly better survival rate, 90.3 vs. 81.8% on average. VMS6_2 not only improved on the already demonstrated superiority of VM to OM but also enabled instantaneous piercing of the cell membrane. Full article
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12 pages, 777 KiB  
Article
A Novel Approach for Train Tracking in Virtual Coupling Based on Soft Actor-Critic
Actuators 2023, 12(12), 447; https://doi.org/10.3390/act12120447 - 01 Dec 2023
Viewed by 965
Abstract
The development of virtual coupling technology provides solutions to the challenges faced by urban rail transit systems. Train tracking control is a crucial component in the operation of virtual coupling, which plays a pivotal role in ensuring the safe and efficient movement of [...] Read more.
The development of virtual coupling technology provides solutions to the challenges faced by urban rail transit systems. Train tracking control is a crucial component in the operation of virtual coupling, which plays a pivotal role in ensuring the safe and efficient movement of trains within the train and along the rail network. In order to ensure the high efficiency and safety of train tracking control in virtual coupling, this paper proposes an optimization algorithm based on Soft Actor-Critic for train tracking control in virtual coupling. Firstly, we construct the train tracking model under the reinforcement learning architecture using the operation states of the train, Proportional Integral Derivative (PID) controller output, and train tracking spacing and speed difference as elements of reinforcement learning. The train tracking control reward function is designed. Then, the Soft Actor-Critic (SAC) algorithm is used to train the virtual coupling train tracking reinforcement learning model. Finally, we took the Deep Deterministic Policy Gradient as the comparison algorithm to verify the superiority of the algorithm proposed in this paper. Full article
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11 pages, 4382 KiB  
Article
Design of Soft Pneumatic Actuator with Two Oblique Chambers for Coupled Bending and Twisting Movements
Actuators 2023, 12(12), 446; https://doi.org/10.3390/act12120446 - 01 Dec 2023
Viewed by 1268
Abstract
Soft pneumatic network (Pneu-net) actuators are frequently used to achieve sophisticated movements, but they face challenges in producing both bending and twisting motions concurrently. In this paper, we present a new Pneu-net twisting and bending actuator (PTBA) design that enables them to perform [...] Read more.
Soft pneumatic network (Pneu-net) actuators are frequently used to achieve sophisticated movements, but they face challenges in producing both bending and twisting motions concurrently. In this paper, we present a new Pneu-net twisting and bending actuator (PTBA) design that enables them to perform complex motions. We achieved this by adjusting the chamber angle, ranging from 15 to 75 degrees, to optimize the bending and twisting movements through finite element analysis and experimental verification. We also investigated the variation trends in bending and twisting motions and determined the actuator’s workspace and maximum grasping force for a variety of objects with different shapes, materials, and sizes. Our findings suggest that PTBA is a promising candidate for advanced applications requiring intricate and bioinspired movements. This new design method offers a path toward achieving these goals. Full article
(This article belongs to the Special Issue Soft Actuators for Medical Robotics)
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19 pages, 10084 KiB  
Article
Research on Friction Compensation Method of Electromechanical Actuator Based on Improved Active Disturbance Rejection Control
Actuators 2023, 12(12), 445; https://doi.org/10.3390/act12120445 - 30 Nov 2023
Viewed by 986
Abstract
The friction factor of harmonic reducers affects the transmission accuracy in electromechanical actuators (EMAs). In this study, we proposed a friction feedforward compensation method based on improved active disturbance rejection control (IADRC). A mathematical model of EMA was developed. The relationship between friction [...] Read more.
The friction factor of harmonic reducers affects the transmission accuracy in electromechanical actuators (EMAs). In this study, we proposed a friction feedforward compensation method based on improved active disturbance rejection control (IADRC). A mathematical model of EMA was developed. The relationship between friction torque and torque current was derived. Furthermore, the compound ADRC control method of second-order speed loop and position loop was studied, and an IADRC control method was proposed. A real EMA was developed, and the working principles of the EMA driving circuit and current sampling were analyzed. The three methods—PI, ADRC, and IADRC—were verified by conducting speed step experiments and sinusoidal tracking experiments. The integral values of time multiplied by the absolute error of the three control modes under the step speed mode were approximately 47.7, 32.1, and 15.5, respectively. Disregarding the inertia of the reducer and assuming that the torque during no-load operation equals the friction torque during constant motion, the findings indicate that, under a load purely driven by inertia, the IADRC control method enhances tracking accuracy. Full article
(This article belongs to the Special Issue New Control Schemes for Actuators)
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19 pages, 1351 KiB  
Article
A Sliding Mode Control-Based Guidance Law for a Two-Dimensional Orbit Transfer with Bounded Disturbances
Actuators 2023, 12(12), 444; https://doi.org/10.3390/act12120444 - 29 Nov 2023
Viewed by 943
Abstract
The aim of this paper is to analyze the performance of a state-feedback guidance law, which is obtained through a classical sliding mode control approach, in a two-dimensional circle-to-circle orbit transfer of a spacecraft equipped with a continuous-thrust propulsion system. The paper shows [...] Read more.
The aim of this paper is to analyze the performance of a state-feedback guidance law, which is obtained through a classical sliding mode control approach, in a two-dimensional circle-to-circle orbit transfer of a spacecraft equipped with a continuous-thrust propulsion system. The paper shows that such an inherently robust control technique can be effectively used to obtain possible transfer trajectories even when the spacecraft equations of motion are affected by perturbations. The problem of the guidance law design is first addressed in the simplified case of an unperturbed system, where it is shown how the state-feedback control may be effectively used to obtain simple mathematical relationships and graphs that allow the designer to determine possible transfer trajectories that depend on a few control parameters. It is also shown that a suitable combination of the controller parameters may be exploited to obtain trade-off solutions between the flight time and the transfer velocity change. The simplified control strategy is then used to investigate a typical heliocentric orbit raising/lowering in the presence of bounded disturbances and measurement errors. Full article
(This article belongs to the Special Issue Dynamics and Control of Aerospace Systems)
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16 pages, 442 KiB  
Article
Fault-Estimation Design Based on an Iterative Learning Scheme for Interconnected Multi-Flexible Manipulator Systems with Arbitrary Initial Value
Actuators 2023, 12(12), 443; https://doi.org/10.3390/act12120443 - 28 Nov 2023
Viewed by 1005
Abstract
This paper reports the design of an iterative-learning-scheme-based fault-estimation method for interconnected nonlinear multi-flexible manipulator systems with arbitrary initial value. For state estimation, observers are employed to reconstruct the state. The proposed scheme ensures that each flexible manipulator subsystem’s states can track their [...] Read more.
This paper reports the design of an iterative-learning-scheme-based fault-estimation method for interconnected nonlinear multi-flexible manipulator systems with arbitrary initial value. For state estimation, observers are employed to reconstruct the state. The proposed scheme ensures that each flexible manipulator subsystem’s states can track their desired reference signals within a finite time. In the next step, an iterative learning fault-estimation law is proposed to track the actual fault signal. In contrast to the previous literature, this approach utilizes potential information from previous iterations to enhance the accuracy of the estimation in the current iteration. Based on these efforts, the obstacle caused by the arbitrary initial value is circumvented, and addressing the fault-estimation errors of each flexible manipulator subsystem are uniformly ultimately bounded is successfully achieved. Then, the λ-norm is developed to explore the convergence conditions of the presented methods. Finally, the effectiveness and feasibility of the proposed approach are verified through assessment of simulation results. Full article
(This article belongs to the Topic Industrial Robotics: 2nd Volume)
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