Controlling stick balancing on a linear track: Delayed state feedback or delay-compensating predictor feedback?

A planar stick balancing task was investigated using stabilometry parameters (SP); a concept initially developed to assess the stability of human postural sway. Two subject groups were investigated: 6 subjects (MD) with many days of balancing a 90 cm stick on a linear track and 25 subjects (OD) with only one day of balancing experience. The underlying mechanical model is a pendulum-cart system. Two control force models were investigated by means of numerical simulations: (1) delayed state feedback (DSF); and (2) delay-compensating predictor feedback (PF). Both models require an internal model and are subject to certainty thresholds with delayed switching. Measured and simulated time histories were compared quantitatively using a cost function in terms of some essential SPs for all subjects. Minimization of the cost function showed that the control strategy of both OD and MD subjects can better be described by DSF. The control mechanism for the MD subjects was superior in two aspects: (1) they devoted less energy to controlling the cart's position; and (2) their perception threshold for the stick's angular velocity was found to be smaller. Findings support the concept that when sufficient sensory information is readily available, a delay-compensating PF strategy is not necessary.

Introduction to Focus Issue: Dynamical disease: A translational approach.

The concept of Dynamical Diseases provides a framework to understand physiological control systems in pathological states due to their operating in an abnormal range of control parameters: this allows for the possibility of a return to normal condition by a redress of the values of the governing parameters. The analogy with bifurcations in dynamical systems opens the possibility of mathematically modeling clinical conditions and investigating possible parameter changes that lead to avoidance of their pathological states. Since its introduction, this concept has been applied to a number of physiological systems, most notably cardiac, hematological, and neurological. A quarter century after the inaugural meeting on dynamical diseases held in Mont Tremblant, Québec [Bélair et al., Dynamical Diseases: Mathematical Analysis of Human Illness (American Institute of Physics, Woodbury, NY, 1995)], this Focus Issue offers an opportunity to reflect on the evolution of the field in traditional areas as well as contemporary data-based methods.

The effects of sensory quantization and control torque saturation on human balance control.

The effect of reaction delay, temporal sampling, sensory quantization, and control torque saturation is investigated numerically for a single-degree-of-freedom model of postural sway with respect to stability, stabilizability, and control effort. It is known that reaction delay has a destabilizing effect on the balancing process: the later one reacts to a perturbation, the larger the possibility of falling. If the delay is larger than a critical value, then stabilization is not even possible. In contrast, numerical analysis showed that quantization and control torque saturation have a stabilizing effect: the region of stabilizing control gains is greater than that of the linear model. Control torque saturation allows the application of larger control gains without overcontrol while sensory quantization plays a role of a kind of filter when sensory noise is present. These beneficial effects are reflected in the energy demand of the control process. On the other hand, neither control torque saturation nor sensory quantization improves stabilizability properties. In particular, the critical delay cannot be increased by adding saturation and/or sensory quantization.

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

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.

An integrate-and-fire model for pulsatility in the neuroendocrine system.

A model for pulsatility in neuroendocrine regulation is proposed which combines Goodwin-type feedback control with impulsive input from neurons located in the hypothalamus. The impulsive neural input is modeled using an integrate-and-fire mechanism; namely, inputs are generated only when the membrane potential crosses a threshold, after which it is reset to baseline. The resultant model takes the form of a functional-differential equation with continuous and impulsive components. Despite the impulsive nature of the inputs, realistic hormone profiles are generated, including ultradian and circadian rhythms, pulsatile secretory patterns, and even chaotic dynamics.

Mineral profiling of muscle and hepatic tissues of Australian Merino, Damara and Dorper lambs: Effect of weight loss.

Seasonal weight loss (SWL) is a major constraint to extensive animal production systems. The Australian sheep production is based on merino sheep, a European breed not tolerant to SWL. Tolerant alternative breeds such as the fat-tailed Damara and the Dorper have been increasingly used in Australia and elsewhere, due to their robustness. The aim of this study was to understand the mineral profile of muscle and liver tissues of Australian Merino, Damara and Dorper, when subjected to SWL in order to understand SWL-tolerance physiology. Twenty-four lambs were divided randomly between growing (control) and nutritionally restricted groups for each breed. The trial lasted 42 days. Animals were weighed bi-weekly and at the end of the trial, lambs were slaughtered. Liver and muscle samples were taken immediately after slaughter. Mineral assessment was carried out using inductively coupled plasma-optical emission spectrometry. Analysis of variance showed mineral concentrations were generally increased in the muscle of restricted animals, mainly because of fat tissue mobilization. An increase in Zn and Fe concentrations indicates an increase of enzymatic activity in the liver of restricted sheep as well as differential abundance of Fe-containing proteins. High concentrations of Cu in the liver of Dorper indicate higher ability to accumulate this element, even under SWL.

Outgrowing seizures in Childhood Absence Epilepsy: time delays and bistability.

We formulate a conductance-based model for a 3-neuron motif associated with Childhood Absence Epilepsy (CAE). The motif consists of neurons from the thalamic relay (TC) and reticular nuclei (RT) and the cortex (CT). We focus on a genetic defect common to the mouse homolog of CAE which is associated with loss of GABAA receptors on the TC neuron, and the fact that myelination of axons as children age can increase the conduction velocity between neurons. We show the combination of low GABAA mediated inhibition of TC neurons and the long corticothalamic loop delay gives rise to a variety of complex dynamics in the motif, including bistability. This bistability disappears as the corticothalamic conduction delay shortens even though GABAA activity remains impaired. Thus the combination of deficient GABAA activity and changing axonal myelination in the corticothalamic loop may be sufficient to account for the clinical course of CAE.

Acting together, destabilizing influences can stabilize human balance.

The causes of falling in the elderly are multi-factorial. Three factors that influence balance stability are the time delay, a sensory dead zone and the maximum ankle torque that can be generated by muscular contraction. Here, the effects of these contributions are evaluated in the context of a model of an inverted pendulum stabilized by time-delayed proportional-derivative (PD) feedback. The effect of the sensory dead zone is to produce a hybrid type of control in which the PD feedback is switched ON or OFF depending on whether or not the controlled variable is larger or smaller than the detection threshold, Π. It is shown that, as Π increases, the region in the plane of control parameters where the balance time (BT) is greater than 60 s is increased slightly. However, when maximum ankle torque is also limited, there is a dramatic increase in the parameter region associated with BTs greater than 60 s. This increase is due to the effects of a torque limitation on over-control associated with bang-bang type switching controllers. These observations show that acting together influences, which are typically thought to destabilize balance, can actually stabilize balance. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Quantization improves stabilization of dynamical systems with delayed feedback.

We show that an unstable scalar dynamical system with time-delayed feedback can be stabilized by quantizing the feedback. The discrete time model corresponds to a previously unrecognized case of the microchaotic map in which the fixed point is both locally and globally repelling. In the continuous-time model, stabilization by quantization is possible when the fixed point in the absence of feedback is an unstable node, and in the presence of feedback, it is an unstable focus (spiral). The results are illustrated with numerical simulation of the unstable Hayes equation. The solutions of the quantized Hayes equation take the form of oscillations in which the amplitude is a function of the size of the quantization step. If the quantization step is sufficiently small, the amplitude of the oscillations can be small enough to practically approximate the dynamics around a stable fixed point.

Fatty acid composition of the ovine longissimus dorsi muscle: effect of feed restriction in three breeds of different origin.

BACKGROUND: Muscle fatty acid profile reflects the body condition of animals and has a noticeable effect on meat quality. Herein, longissimus dorsi muscle of three different sheep breeds, Damara (a fat-tailed breed), Dorper and Australian Merino sheep, was analysed for fatty acid composition. The three breeds were subjected to two distinctive feeding levels (ad libitum and restricted feeding) over 42 days. RESULTS: The Damara sheep revealed several differences compared to the other two breeds, namely a higher concentration of polyunsaturated fatty acids, which can be related to being a fat-tailed breed. Even in restricted feeding conditions, this breed revealed the highest levels compared to Merino and Dorper sheep respectively, of linoleic acid (+31% and +28%), linolenic acid (+97% and +51%), eicosapentaenoic acid (EPA) (+65% and +37%), docosapentanenoic acid (DPA) (+31% Merino) and dodosahexanenoic acid (DHA) (+63% and +77%). EPA, DPA and DHA are three omega-3 fatty acids, with described beneficial characteristics. CONCLUSION: With this work we show other qualities (higher levels of the omega-3 fatty acids, EPA, DPA and DHA) of Damara meat that might present this breed as an interesting alternative for animal production in semi-arid climates.