Dynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control

Simpson, David J. W.; Kuske, Rachel; Li, Yuexian

doi:10.1007/s00332-011-9111-4

Cited by 10 publications

(7 citation statements)

References 42 publications

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“…Since the obtained interpretations of the dynamics were quite reasonable, we are confident to conclude that the overall dynamics of the intermittent control model can be well captured by the finite dimensional direct sums of the approximated manifolds. Nevertheless, it is worth performing a theoretical analysis of the switching dynamics among the DDE models, such as the study by Simpson et al (2012) for the single pendulum case.…”

Section: Finite Dimensional Approximation Of the Delay Differential Ementioning

confidence: 99%

Intermittent control with ankle, hip, and mixed strategies during quiet standing: A theoretical proposal based on a double inverted pendulum model

Suzuki

Nomura

Casadio

et al. 2012

Journal of Theoretical Biology

187

168

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Human upright posture, as a mechanical system, is characterized by an instability of saddle type, involving both stable and unstable dynamic modes. The brain stabilizes such system by generating active joint torques, according to a time-delayed neural feedback control. What is still unsolved is a clear understanding of the control strategies and the control mechanisms that are used by the central nervous system in order to stabilize the unstable posture in a robust way while maintaining flexibility. Most studies in this direction have been limited to the single inverted pendulum model, which is useful for formalizing fundamental mechanical aspects but insufficient for addressing more general issues concerning neural control strategies. Here we consider a double inverted pendulum model in the sagittal plane with small passive viscoelasticity at the ankle and hip joints. Despite difficulties in stabilizing the double pendulum model in the presence of the large feedback delay, we show that robust and flexible stabilization of the upright posture can be established by an intermittent control mechanism that achieves the goal of stabilizing the body posture according to a "divide and conquer strategy", which switches among different controllers in different parts of the state space of the double inverted pendulum. Remarkably, it is shown that a global, robust stability is achieved even if the individual controllers are unstable and the information exploited for switching from one controller to another is severely delayed, as it happens in biological reality. Moreover, the intermittent controller can automatically resolve coordination among multiple active torques associated with the muscle synergy, leading to the emergence of distinct temporally coordinated active torque patterns, referred to as the intermittent ankle, hip, and mixed strategies during quiet standing, depending on the passive elasticity at the hip joint.

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Section: Finite Dimensional Approximation Of the Delay Differential Ementioning

confidence: 99%

Intermittent control with ankle, hip, and mixed strategies during quiet standing: A theoretical proposal based on a double inverted pendulum model

Suzuki

Nomura

Casadio

et al. 2012

Journal of Theoretical Biology

187

168

View full text Add to dashboard Cite

show abstract

“…In [13] a multistability and homoclinic bifurcation scenario in a switched model with dead-zone and delay in the switching function and in the delay in state variables is shown. These models are furthered analyzed in [21] where homoclinic bifurcations, complex bursting dynamics, so-called boundary bifurcations are investigated. Another context of human neuromuscular control where switched models could be applied is in modeling variations of threshold detection due to diabetes or aging.…”

Section: Introductionmentioning

confidence: 99%

A novel route to a Hopf bifurcation scenario in switched systems with dead-zone

Kowalczyk

2017

Physica D: Nonlinear Phenomena

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Planar switched system with dead-zone are analyzed. In particular, we consider the effects of perturbation of the linear control law from purely positional to position-velocity control. This type of perturbation leads to a novel Hopf-like discontinuity induced bifurcation. We show that this bifurcation leads to the creation of small scale limit cycle attractors, which scale as the square root of the bifurcation parameter. We note that a Hopf-like bifurcation analyzed in non-smooth systems (see [9]) is characterized by a linear scaling law. We then investigate numerically a planar switched system with positional feedback law, dead-zone and time delay in the switching function. Using the same parameter values as for the switched system without delay in the switching function, we show numerically a Hopf-like bifurcation scenario which matches qualitatively and quantitatively with the scenario analyzed for the non-delayed system.

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“…As shown in Liu and Hu (2008) and Landry et al (2005), a very small time delay can cause instability in a cart-pendulum system via Hopf bifurcation. The balancing of human beings can also be modeled by a delayed inverted pendulum, where time delay can result in the human swaying or falling over (Milton et al, 2009;Simpson et al, 2012;Stepan, 2009).…”

Section: Introductionmentioning

confidence: 99%

Balancing a wheeled inverted pendulum with a single accelerometer in the presence of time delay

Stépàn

Wang

2016

Journal of Vibration and Control

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The output of an accelerometer often has coupled components of displacement and acceleration, and is rarely used individually for balancing tasks. In order to balance a wheeled inverted pendulum like the Segway, the conventional control usually requires gyroscopes or a combination of accelerometers and gyroscopes. In this paper, we prove that even in the presence of time delay, a wheeled inverted pendulum can be well stabilized with only one accelerometer as the sensor when the mechanical structure is slightly modified. The key idea is the introduction of an additional damper that does not have a physical connection with the wheels. Moreover, we show that balancing can be achieved with an appropriately selected accelerometer position over a range of time delays.

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Dynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control

Cited by 10 publications

References 42 publications

Intermittent control with ankle, hip, and mixed strategies during quiet standing: A theoretical proposal based on a double inverted pendulum model

Intermittent control with ankle, hip, and mixed strategies during quiet standing: A theoretical proposal based on a double inverted pendulum model

A novel route to a Hopf bifurcation scenario in switched systems with dead-zone

Balancing a wheeled inverted pendulum with a single accelerometer in the presence of time delay

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