Mathematical models for balancing tasks on a see-saw with reaction time delay

Buza, Gergely; Insperger, Tamás

doi:10.1016/j.ifacol.2018.07.238

Cited by 2 publications

(4 citation statements)

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“…Numerical analysis shows that this system can only be stabilized by delayed PD feedback for delays less than τ crit = 180 ms (Buza and Insperger 2018). For the ball and beam balancing τ > 180 ms (see Sect.…”

Section: Control Torque As Manipulated Variablementioning

confidence: 99%

Establishing metrics and control laws for the learning process: ball and beam balancing

Buza

Milton

Bencsik³

et al. 2020

Biol Cybern

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Understanding how dexterity improves with practice is a fundamental challenge of motor control and neurorehabilitation. Here we investigate a ball and beam implementation of a dexterity puzzle in which subjects stabilize a ball at the mid-point of a beam by manipulating the angular position of the beam. Stabilizability analysis of different biomechanical models for the ball and beam task with time-delayed proportional-derivative feedback identified the angular position of the beam as the manipulated variable. Consequently, we monitored the changes in the dynamics with learning by measuring changes in the control parameters. Two types of stable motion are possible: node type (nonoscillatory) and spiral type (oscillatory). Both types of motion are observed experimentally and correspond to well-defined regions in the parameter space of the control gains. With practice the control gains for each subject move close to or on the portion of the boundary which separates the node-type and spiral-type solutions and which is associated with the rightmost characteristic exponent of smallest real part. These observations suggest that with learning the control gains for ball and beam balancing change in such a way that minimizes overshoot and the settling time. This study provides an example of how mathematical analysis together with careful experimental observations can shed light onto the early stages of skill acquisition. Since the difficulty of this task depends on the length of the beam, ball and beam balancing tasks may be useful for the rehabilitation of children with dyspraxia and those recovering from a stroke. Keywords Human balancing • Reaction time • Visual feedback • Motor control • Learning Communicated by Benjamin Lindner.

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Section: Control Torque As Manipulated Variablementioning

confidence: 99%

Establishing metrics and control laws for the learning process: ball and beam balancing

Buza

Milton

Bencsik³

et al. 2020

Biol Cybern

Self Cite

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“…Due to the more advanced study on the ball-beam systems, we were particularly interested in the models referenced in sources [6]- [9]. These models may be classified into two distinct types.…”

Section: Introductionmentioning

confidence: 99%

“…These models may be classified into two distinct types. The first group employs neutral functional differential equations [11], whereas the second category utilizes retarded functional differential equations [9]- [12]. Therefore, we suggest utilizing a ball and plate system model that relies on retarded functional equations [9], together with frequency domain synthesis techniques (refer to [2] and [10]), to construct a state feedback control rule [2].…”

Section: Introductionmentioning

confidence: 99%

“…The first group employs neutral functional differential equations [11], whereas the second category utilizes retarded functional differential equations [9]- [12]. Therefore, we suggest utilizing a ball and plate system model that relies on retarded functional equations [9], together with frequency domain synthesis techniques (refer to [2] and [10]), to construct a state feedback control rule [2]. This method may ascertain the stability zone of the system in the control parameter space, while considering the impact of feedback delay.…”

Section: Introductionmentioning

confidence: 99%

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State-Feedback Control of Ball-Plate System: Geometric Approach

Lefrouni,

Taibi

2024

IJACSA

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This research focuses on investigating the issue of accurately controlling the location of the ball in the ball and plate system. The findings of this research have practical applications across several domains, including optimizing the alignment of solar panels to enhance their energy generation capacity. In this work, we propose the development of a system dynamics model using the Euler-Lagrangian approach. Furthermore, we analyze a technique in the frequency domain known as the geometric approach to create a state-feedback control that ensures the stability of the system. This study primarily focuses on analyzing the characteristic equations associated with the closed-loop system, while also considering the impact of feedback delay. Ultimately, the proposed technique is substantiated by presenting simulation data for validation.

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Mathematical models for balancing tasks on a see-saw with reaction time delay

Cited by 2 publications

References 11 publications

Establishing metrics and control laws for the learning process: ball and beam balancing

Establishing metrics and control laws for the learning process: ball and beam balancing

State-Feedback Control of Ball-Plate System: Geometric Approach

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