Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method

Lopes, António M.; Machado, J. A. Tenreiro

doi:10.3390/s21227736

Cited by 6 publications

(4 citation statements)

References 66 publications

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“…measuring transducer), the Ideal System block is the reference measuring system and the Real System block is the measuring system with an error in relation to the Ideal System. The Factor 𝜂 block determines an array of 𝜂 order values based on equation (12).…”

Section: Array 𝜼 𝒊 Datamentioning

confidence: 99%

“…The fractional calculus have found a range of applications, in particular, modelling of process dynamics and physical effects whose modelling with classic mathematical apparatus has not always been faithful to reality, e.g. modelling of such effects as memory process, PID controllers, robust control, heat transfer process, electrical drive, voltage regulator, charging and discharging of supercapacitors, robot manipulators, cell growth dynamics, biomedical engineering, image processing, chemical reaction processes, dynamics of automatic or electronic systems, photovoltaic systems, hybrid power systems or such non-technical issues as analysis of financial processes [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The fractional calculus seems an ideal tool for modelling of nonlinear and highly complex effects and processes.…”

Section: Introductionmentioning

confidence: 99%

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Processing characteristics correction of measuring systems by means a differintegral of variable order

Cioć

2024

jaeee

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The paper presents new methods for correcting the processing characteristics of measurement systems based on a modified Grünwald-Letnikov fractional calculus definition. The presented methods are based on the determination of the fractional order as an estimation factor. Two methods are presented: a fractional order array and a fractional order function. Both methods can be used in DSP systems as methods to correct the processing characteristics of systems with measuring transducers and measurement systems in general.

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Section: Array 𝜼 𝒊 Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Processing characteristics correction of measuring systems by means a differintegral of variable order

Cioć

2024

jaeee

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“…In [ 15 ], fractional calculus is applied to the control of a revolute planar robotic manipulator. The fractional derivatives required by the control can be obtained by adopting numerical real-time signal processing.…”

Section: Previous Workmentioning

confidence: 99%

Improving Mobile Robot Maneuver Performance Using Fractional-Order Controller

Acosta

Fariña

Toledo

et al. 2023

Sensors

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In this paper, the low-level velocity controller of an autonomous vehicle is studied. The performance of the traditional controller used in this kind of system, a PID, is analyzed. This kind of controller cannot follow ramp references without error, so when the reference implies a change in the speed, the vehicle cannot follow the proposed reference, and there is a significant difference between the actual and desired vehicle behaviors. A fractional controller is proposed which changes the ordinary dynamics allowing faster responses for small times, at the cost of slower responses for large times. The idea is to take advantage of this fact to follow fast setpoint changes with a smaller error than that obtained with a classic non-fractional PI controller. Using this controller, the vehicle can follow variable speed references with zero stationary error, significantly reducing the difference between reference and actual vehicle behavior. The paper presents the fractional controller, studies its stability in function of the fractional parameters, designs the controller, and tests its stability. The designed controller is tested on a real prototype, and its behavior is compared to a standard PID controller. The designed fractional PID controller overcomes the results of the standard PID controller.

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“…The application of fractional calculus to control robotic systems has gained interest in the last few years because it yields controllers with enhanced robustness to external disturbances and parametric uncertainties. FO controllers have been applied to ensure control performances as tip position accuracy and suppression of the residual vibrations: FO adaptive back-stepping control [23], FO PID controller based on Kalman filter estimation [24], FO PID control [25], FO modeling and PI control of soft robotic arms [26], FO optimal control [27] and variable structure system fractional sliding mode controller [28], and a comparison was realized between the sliding mode controller and the fractional sliding mode controller in a non-commensurate order in [29]. The latest review about fractional order modeling and control of flexible and rigid robotic manipulators is presented in [30].…”

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confidence: 99%

Fractional Modeling and Control of Lightweight 1 DOF Flexible Robots Robust to Sensor Disturbances and Payload Changes

2023

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Model design and motion control are considered the cornerstones of the robotic field that allow for achieving performance tasks. This article proposes a new dynamic modeling and control approach for very lightweight mechanical systems carrying payloads. The selection of the model and the design of the control are elaborated on using a fractional order framework under different conditions. The use of fractional order calculus is justified by the better performance that reveals a fractional order model compared to an integer order model of similar complexity. The mechanical structure of very lightweight manipulators has vibrations that impede the accurate positioning of their end effector. Moreover, they have actuators with high friction and sensors to measure the vibrations, which often are strain gauges, that have offset and high-frequency noise. All these mentioned problems might degrade the mechanical system’s performance. Hence, to overcome these inconveniences, two nested-loop controls are examined: an inner loop that controls the motor dynamics and removes the friction effects and an outer loop implemented to eliminate the beam vibrations by adapting the input-state feedback linearization technique. Then, we propose a new fractional order control scheme that (1) removes the strain gauge offset disturbances, (2) reduces the risk of the actuator’s saturation caused by the high-frequency noise of strain gauges and (3) reduces the dynamic effects of huge payload changes. We prove that our fractional controller has enhanced robustness with respect to the above-mentioned problems. Finally, the investigated approach is validated experimentally by applying it to a lightweight robot mounted on an air table.

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Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method

Cited by 6 publications

References 66 publications

Processing characteristics correction of measuring systems by means a differintegral of variable order

Processing characteristics correction of measuring systems by means a differintegral of variable order

Improving Mobile Robot Maneuver Performance Using Fractional-Order Controller

Fractional Modeling and Control of Lightweight 1 DOF Flexible Robots Robust to Sensor Disturbances and Payload Changes

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