Application of Decaying Boundary Layer and Switching Function Method Thorough Error Feedback for Sliding Mode Control on Spacecraft’s Attitude

Effective operation of small spacecraft implies processors with low cost, energy efficiency and low computational burdens while retaining accurate output tracking. This paper presents the extension of work in [1] on eliminating the chattering for Sliding Mode Control (SMC) using a decaying boundary layer design which is able to achieve these small spacecraft operation needs. The extension is applied on a spacecraft's attitude control, while orbiting the earth with angular velocity, ω0. In SMC, chattering is a main drawback as it can cause wear and tear to moving mechanical parts. Earlier work on a decaying boundary layer design was capable of reducing the chattering phenomena for a limited time only and hence this paper proposes a novel decaying boundary layer and switching function to improve the earlier version. The proposed technique is shown to reduce chattering permanently and also retain control output accuracy

Exertional oxygen uptake kinetics: a stamen of stamina?

The fundamental pulmonary O2 uptake (o2) response to moderate, constant-load exercise can be characterized as (do2/dt)(τ) + Δo2 (t) = Δo2SS where Δo2SS is the steady-state response, and τ is the time constant, with the o2 kinetics reflecting intramuscular O2 uptake (o2) kinetics, to within 10%. The role of phosphocreatine (FCr) turnover in o2 control can be explored using 31P-MR spectroscopy, simultaneously with o2. Although τo2 and τPCr vary widely among subjects (approx. 20–65 s), they are not significantly different from each other, either at the on- or off-transient. A caveat to interpreting the ‘well-fit’ exponential is that numerous units of similar Δo2SS but with a wide τ distribution can also yield a o2 response with an apparent single τ. This τ is, significantly, inversely correlated with lactate threshold and o2max (but is poorly predictive; a frail stamen, therefore), consistent with τ not characterizing a compartment with uniform kinetics. At higher intensities, the fundamental kinetics become supplemented with a slowly-developing phase, setting o2 on a trajectory towards maximum o2. This slow component is also demonstrable in Δ[PCr]: the decreased efficiency thereby reflecting a predominantly high phosphate-cost of force production rather than a high O2-cost of phosphate production. We also propose that the O2-deficit for the slow-component is more likely to reflect shifting Δo2SS rather than a single one with a single τ

Negative accumulated oxygen deficit during heavy and very heavy intensity cycle ergometry in humans

The concept of the accumulated O2 deficit (AOD) assumes that the O2 deficit increases monotonically with increasing work rate (WR), to plateau at the maximum AOD, and is based on linear extrapolation of the relationship between measured steady-state oxygen uptake (V̇O2) and WR for moderate exercise. However, for high WRs, the measured V̇O2 increases above that expected from such linear extrapolation, reflecting the superimposition of a "slow component" on the fundamental V̇O2 mono-exponential kinetics. We were therefore interested in determining the effect of the V̇O2 slow component on the computed AOD. Ten subjects [31 (12) years] performed square-wave cycle ergometry of moderate (40%, 60%, 80% and 90% θˆL ), heavy (40%Δ), very heavy (80%Δ) and severe (110% V̇O2 peak) intensities for 10–15 min, where θˆL is the estimated lactate threshold and Δ is the WR difference between θˆL and V̇O2 peak. V̇O2 was determined breath-by-breath. Projected "steady-state" V̇O2 values were determined from sub- θˆL tests. The measured V̇O2 exceeded the projected value after ~3 min for both heavy and very heavy intensity exercise. This led to the AOD actually becoming negative. Thus, for heavy exercise, while the AOD was positive [0.63 (0.41) l] at 5 min, it was negative by 10 min [−0.61 (1.05) l], and more so by 15 min [−1.70 (1.64) l]. For the very heavy WRs, the AOD was [0.42 (0.67) l] by 5 min and reached −2.68 (2.09) l at exhaustion. For severe exercise, however, the AOD at exhaustion was positive in each case: +1.69 (0.39) l. We therefore conclude that the assumptions underlying the computation of the AOD are invalid for heavy and very heavy cycle ergometry (at least). Physiological inferences, such as the "anaerobic work capacity", are therefore prone to misinterpretation

On-off asymmetries in oxygen consumption kinetics of single Xenopus laevis skeletal muscle fibres suggest higher-order control

The mechanisms controlling skeletal muscle oxygen consumption (V(o)₂) during exercise are not well understood. We determined whether first-order control could explain V(o)₂kinetics at contractions onset (V(o)₂(on)) and cessation (V(o)₂off)) in single skeletal muscle fibres differing in oxdidative capacity, and across stimulation intensities up to V(o)₂(max). Xenopus laevis fibres (n = 21) were suspended in a sealed chamber with a fast response P(o)₂ electrode to measure V(o)₂ every second before, during and after stimulated isometric contractions. A first-order model did not well characterize on-transient V(o)₂ kinetics. Including a time delay (TD) in the model provided a significantly improved characterization than a first-order fit without TD (F-ratio; P < 0.05), and revealed separate 'activation' and 'exponential' phases in 15/21 fibres contracting at V(o)₂(max) (mean ± SD TD: 14 ± 3s). On-transient kinetics (τV(o)₂(on)) was weakly and linearly related to V(o)₂(max) (R² = 0.271, P = 0.015). Off-transient kinetics, however, were first-order, and τV(o)₂(off) was greater in low-oxidative (V(o)₂max < 0.05 nmol mm⁻³s⁻¹ than high-oxidative fibres (V(o)₂(max > 0.10 nmol mm ⁻³ s⁻¹; 170 ± 70 vs. 29 ± 6 s, P < 0.001). 1/ τV(o)₂(off) was proportional to V(o)₂(max) (R² = 0.727, P < 0.001), unlike in the on-transient. The calculated oxygen deficit was larger (P < 0.05) than the post-contraction volume of consumed oxygen at all intensities except V(o)₂(max). These data show a clear dissociation between the kinetic control of V(o)₂at the onset and cessation of contractions and across stimulation intensities. More complex models are therefore required to understand the activation of mitochondrial respiration in skeletal muscle at the start of exercise

The effect of resistive breathing on leg muscle oxygenation using near-infrared spectroscopy during exercise in men

The effect of added respiratory work on leg muscle oxygenation during constant-load cycle ergometry was examined in six healthy adults. Exercise was initiated from a baseline of 20 W and increased to a power output corresponding to 90 % of the estimated lactate threshold (moderate exercise) and to a power output yielding a tolerance limit of 11.8 min (± 1.4, S.D.) (heavy exercise). Ventilation and pulmonary gas exchange were measured breath-by-breath. Profiles of leg muscle oxygenation were determined throughout the protocol using near-infrared (NIR) spectroscopy (Hamamatsu NIRO 500) with optodes aligned midway along the vastus lateralis of the dominant leg. Four conditions were tested: (i) control (Con) where the subjects breathed spontaneously throughout, (ii) controlled breathing (Con Br) where breathing frequency and tidal volume were matched to the Con profile, (iii) increased work of breathing (Resist Br) in which a resistance of 7 cmH2O l-1 s-1 was inserted into the mouthpiece assembly, and (iv) partial leg blood flow occlusion (Leg Occl), where muscle perfusion was reduced by inflating a pressure cuff (~90 mmHg) around the upper right thigh. During Resist Br and Leg Occl, subjects controlled their breathing pattern to reproduce the ventilatory profile of Con. An ~3 min period with respiratory resistance or pressure cuff was introduced ~4 min after exercise onset. NIR spectroscopy data for reduced haemoglobin-myoglobin ([Delta][Hb]) were extracted from the continuous display at specific times prior to, during and after removal of the resistance or pressure cuff. While the [Delta][Hb] increased during moderate- and heavy-intensity exercise, there was no additional increase in [Delta][Hb] with Resist Br. In contrast, [Delta][Hb] increased further with Leg Occl, reflecting increased muscle O2 extraction during the period of reduced muscle blood flow. In conclusion, increasing the work of breathing did not increase leg muscle deoxygenation during heavy exercise. Assuming that leg muscle O2 consumption did not decrease, this implies that leg blood flow was not reduced consequent to a redistribution of flow away from the working leg muscle

Negative accumulated oxygen deficit during heavy and very heavy intensity cycle ergometry in humans

The concept of the accumulated O-2 deficit (AOD) assumes that the O-2 deficit increases monotonically with increasing work rate (WR), to plateau at the maximum AOD, and is based on linear extrapolation of the relationship between measured steady-state oxygen uptake ((V) over dot O-2) and WR for moderate exercise. However, for high WRs, the measured (V) over dot O-2 increases above that expected from such linear extrapolation, reflecting the superimposition of a 'slow component' on the fundamental (V) over dot O-2 mono-exponential kinetics. We were therefore interested in determining the effect of the (V) over dot O-2 slow component on the computed AOD. Ten subjects [31 (12) years] performed square-wave cycle ergometry of moderate (40%, 60%, 80% and 90% theta(L)) heavy (40%Delta), very heavy (80%Delta) and severe (110% (V) over dot O-2peak) intensities for 10-15 min, where (theta) over capL is the estimated lactate threshold and Delta is the WR difference between (theta) over cap (L) and (V) over dot O-2peak. (V) over dot O-2 was determined breath-by-breath. Projected 'steady-state' (V) over dot O-2 values were determined from sub-(theta) over capL tests. The measured (V) over dot O-2 exceeded the projected value after similar to3 min for both heavy and very heavy intensity exercise. This led to the AOD actually becoming negative. Thus, for heavy exercise, while the AOD was positive [0.63 (0.41) l] at 5 min, it was negative by 10 min [-0.61 (1.05) l], and more so by 15 min [-1.70 (1.64) l]. For the very heavy WRs, the AOD was [0.42 (0.67) l] by 5 min and reached -2.68 (2.09) l at exhaustion. For severe exercise, however, the AOD at exhaustion was positive in each case: +1.69 (0.39) l. We therefore conclude that the assumptions underlying the computation of the AOD are invalid for heavy and very heavy cycle ergometry (at least). Physiological inferences, such as the 'anaerobic work capacity', are therefore prone to misinterpretation

Slowed muscle oxygen uptake kinetics with raised metabolism are not dependent on blood flow or recruitment dynamics

Oxygen uptake kinetics (τ[Image: see text]) are slowed when exercise is initiated from a raised metabolic rate. Whether this reflects the recruitment of muscle fibres differing in oxidative capacity, or slowed blood flow ([Image: see text]) kinetics is unclear. This study determined τ[Image: see text] in canine muscle in situ, with experimental control over muscle activation and [Image: see text] during contractions initiated from rest and a raised metabolic rate. The gastrocnemius complex of nine anaesthetised, ventilated dogs was isolated and attached to a force transducer. Isometric tetanic contractions (50 Hz; 200 ms duration) via supramaximal sciatic nerve stimulation were used to manipulate metabolic rate: 3 min stimulation at 0.33 Hz (S1), followed by 3 min at 0.67 Hz (S2). Circulation was initially intact (SPON), and subsequently isolated for pump-perfusion (PUMP) above the greatest value in SPON. Muscle [Image: see text] was determined contraction-by-contraction using an ultrasonic flowmeter and venous oximeter, and normalised to tension-time integral (TTI). τ[Image: see text]/TTI and τ[Image: see text] were less in S1(SPON) (mean ± s.d.: 13 ± 3 s and 12 ± 4 s, respectively) than in S2(SPON) (29 ± 19 s and 31 ± 13 s, respectively; P < 0.05). τ[Image: see text]/TTI was unchanged by pump-perfusion (S1(PUMP), 12 ± 4 s; S2(PUMP), 24 ± 6 s; P < 0.001) despite increased O(2) delivery; at S2 onset, venous O(2) saturation was 21 ± 4% and 65 ± 5% in SPON and PUMP, respectively. [Image: see text] kinetics remained slowed when contractions were initiated from a raised metabolic rate despite uniform muscle stimulation and increased O(2) delivery. The intracellular mechanism may relate to a falling energy state, approaching saturating ADP concentration, and/or slowed mitochondrial activation; but further study is required. These data add to the evidence that muscle [Image: see text] control is more complex than previously suggested