A Jacobian-Based Algorithm for Planning Attitude Maneuvers Using Forward and Reverse Rotations

Algorithms for planning quasistatic attitude maneuvers based on the Jacobian of the forward kinematic mapping of fully-reversed (FR) sequences of rotations are proposed in this paper. An FR sequence of rotations is a series of finite rotations that consists of initial rotations about the axes of a body-fixed coordinate frame and subsequent rotations that undo these initial rotations. Unlike the Jacobian of conventional systems such as a robot manipulator, the Jacobian of the system manipulated through FR rotations is a null matrix at the identity, which leads to a total breakdown of the traditional Jacobian formulation. Therefore, the Jacobian algorithm is reformulated and implemented so as to synthesize an FR sequence for a desired rotational displacement. The Jacobian-based algorithm presented in this paper identifies particular six-rotation FR sequences that synthesize desired orientations. We developed the single-step and the multiple-step Jacobian methods to accomplish a given task using six-rotation FR sequences. The single-step Jacobian method identifies a specific FR sequence for a given desired orientation and the multiple-step Jacobian algorithm synthesizes physically feasible FR rotations on an optimal path. A comparison with existing algorithms verifies the fast convergence ability of the Jacobian-based algorithm. Unlike closed-form solutions to the inverse kinematics problem, the Jacobian-based algorithm determines the most efficient FR sequence that yields a desired rotational displacement through a simple and inexpensive numerical calculation. The procedure presented here is useful for those motion planning problems wherein the Jacobian is singular or null.

Nonlinear Control Design for an Air-breathing Engine with State Estimation

A nonlinear control design approach is presented in this paper for a challenging application problem of ensuring robust performance of an air-breathing engine operating at supersonic speed. The primary objective of control design is to ensure that the engine produces the required thrust that tracks the commanded thrust as closely as possible by appropriate regulation of the fuel flow rate. However, since the engine operates in the supersonic range, an important secondary objective is to ensure an optimal location of the shock in the intake for maximum pressure recovery with a sufficient margin. This is manipulated by varying the throat area of the nozzle. The nonlinear dynamic inversion technique has been successfully used to achieve both of the above objectives. In this problem, since the process is faster than the actuators, independent control designs have also been carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, an extended Kalman Filter based state estimation design has been carried out both to filter out the process and sensor noises as well as to make the control design operate based on output feedback. Promising simulation results indicate that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing system.

Nonlinear Sliding Mode Control Design for an Air-breathing Engine with State Estimation

A modern system theory based nonlinear control design is discussed in this paper for successful operation of an air-breathing engine operating at supersonic speed. The primary objective of the control design of such an air-breathing engine is to ensure that the engine dynamically produces the thrust that tracks a commanded value of thrust as closely as possible by regulating the fuel flow to the combustion system. However, since the engine operates in the supersonic range, an important secondary objective is to manage the shock wave configuration in the intake section of the engine which is manipulated by varying the throat area of the nozzle. A nonlinear sliding mode control technique has been successfully used to achieve both of the above objectives. In this problem, since the process is faster than the actuators, independent control designs are also carried out for the actuators as well to assure the satisfactory performance of the system. Moreover, to filter out the sensor and process noises and to estimate the states for making the control design operate based on output feedback, an Extended Kalman Filter based state estimation design is also carried out. The promising simulation results suggest that the proposed control design approach is quite successful in obtaining robust performance of the air-breathing engine.

Nonlinear measures of heart rate time series: influence of posture and controlled breathing

In this study, we investigated measures of nonlinear dynamics and chaos theory in regards to heart rate variability in 27 normal control subjects in supine and standing postures, and 14 subjects in spontaneous and controlled breathing conditions. We examined minimum embedding dimension (MED), largest Lyapunov exponent (LLE) and measures of nonlinearity (NL) of heart rate time series. MED quantifies the system's complexity, LLE predictability and NL, a measure of deviation from linear processes. There was a significant decrease in complexity (P<0.00001), a decrease in predictability (P<0.00001) and an increase in nonlinearity (P=0.00001) during the change from supine to standing posture. Decrease in MED, and increases in NL score and LLE in standing posture appear to be partly due to an increase in sympathetic activity of the autonomous nervous system in standing posture. An improvement in predictability during controlled breathing appears to be due to the introduction of a periodic component. (C) 2000 published by Elsevier Science B.V.

A smart approach to precision attitude maneuvers of spacecrafts

A nonlinear adaptive approach is presented to achieve rest-to-rest attitude maneuvers for spacecrafts in the presence of parameter uncertainties and unknown disturbances. A nonlinear controller, designed on the principle of dynamic inversion achieves the goals for the nominal model but suffers performance degradation in the presence of off-nominal parameter values and unwanted inputs. To address this issue, a model-following neuro-adaptive control design is carried out by taking the help of neural networks. Due to the structured approach followed here, the adaptation is restricted to the momentum level equations.The adaptive technique presented is computationally nonintensive and hence can be implemented in real-time. Because of these features, this new approach is named as structured model-following adaptive real-time technique (SMART). From simulation studies, this SMART approach is found to be very effective in achieving precision attitude maneuvers in the presence of parameter uncertainties and unknown disturbances.

Modulation of redox regulatory molecules and electron transport chain activity in muscle of air breathing fish Heteropneustes fossilis under air exposure stress

Responses of redox regulatory system to long-term survival (> 18 h) of the catfish Heteropneustes fossilis in air are not yet understood. Lipid and protein oxidation level, oxidant (H2O2) generation, antioxidative status (levels of superoxide dismutase, catalase, glutathione peroxidase and reductase, ascorbic acid and non-protein sulfhydryl) and activities of respiratory complexes (I, II, III and IV) in mitochondria were investigated in muscle of H. fossilis under air exposure condition (0, 3, 6, 12 and 18 h at 25 A degrees C). The increased levels of both H2O2 and tissue oxidation were observed due to the decreased activities of antioxidant enzymes in muscle under water deprivation condition. However, ascorbic acid and non-protein thiol groups were the highest at 18 h air exposure time. A linear increase in complex II activity with air exposure time and an increase up to 12 h followed by a decrease in activity of complex I at 18 h were observed. Negative correlation was observed for complex III and V activity with exposure time. Critical time to modulate the above parameters was found to be 3 h air exposure. Dehydration induced oxidative stress due to modulation of electron transport chain and redox metabolizing enzymes in muscle of H. fossilis was clearly observed. Possible contribution of redox regulatory system in muscle tissue of the fish for long-term survival in air is elucidated. Results of the present study may be useful to understand the redox metabolism in muscle of fishes those are exposed to air in general and air breathing fishes in particular.

Capturability of Augmented Pure Proportional Navigation Guidance Against Time-Varying Target Maneuvers

This paper proposes a variation of the pure proportional navigation guidance law, called augmented pure proportional navigation, to account for target maneuvers, in a realistic nonlinear engagement geometry, and presents its capturability analysis. These results are in contrast to most work in the literature on augmented proportional navigation laws that consider a linearized geometry imposed upon the true proportional navigation guidance law. Because pure proportional navigation guidance law is closer to a realistic implementation of proportional navigation than true proportional navigation law, and any engagement process is predominantly nonlinear, the results obtained in this paper are more realistic than any available in the literature. Sufficient conditions on speed ratio, navigation gain, and augmentation parameter for capturability, and boundedness of lateral acceleration, against targets executing piecewise continuous maneuvers with time, are obtained. Further, based on a priori knowledge of the maximum maneuver capability of the target, a significant simplification of the guidance law is proposed in this paper. The proposed guidance law is also shown to require a shorter time of interception than standard pure proportional navigation and augmented proportional navigation. To remove chattering in the interceptor maneuver at the end phase of the engagement, a hybrid guidance law using augmented pure proportional navigation and pure proportional navigation is also proposed. Finally, the guaranteed capture zones of standard and augmented pure proportional navigation guidance laws against maneuvering targets are analyzed and compared in the normalized relative velocity space. It is shown that the guaranteed capture zone expands significantly when augmented pure proportional navigation is used instead of pure proportional navigation. Simulation results are given to support the theoretical findings.

Nonlinear control of an air-breathing engine including its validation with vehicle guidance

An implementable nonlinear control design approach is presented for a supersonic air-breathing ramjet engine. The primary objective is to ensure that the thrust generated by the engine tracks the commanded thrust without violating the operational constraints. An important constraint is to manage the shock wave location in the intake so that it neither gets detached nor gets too much inside the intake. Both the objectives are achieved by regulating the fuel flow to the combustion chamber and by varying the throat area of the nozzle simultaneously. The design approach accounts for the nonlinear cross-coupling effects and nullifies those. Also, an extended Kalman filter has been used to filter out the sensor and process noises as well as to make the states available for feedback. Furthermore, independent control design has been carried out for the actuators. To test the performance of the engine for a realistic flight trajectory, a representative trajectory is generated through a trajectory optimization process, which is augmented with a newly-developed finite-time state dependent Riccati equation technique for nullifying the perturbations online. Satisfactory overall performance has been obtained during both climb and cruise phases. (C) 2015 Elsevier Masson SAS. All rights reserved.

Structured model-following neuro-adaptive design for attitude maneuver of rigid bodies

A new structured model-following adaptive approach is presented in this paper to achieve large attitude maneuvers of rigid bodies. First, a nominal controller is designed using the dynamic inversion philosophy. Next, a neuro- adaptive design is proposed to augment the nominal design in order to assure robust performance in the presence of parameter inaccuracies as well as unknown constant external disturbances. The structured approach proposed in this paper (where kinematic and dynamic equations are handled separately), reduces the complexity of the controller structure. From simulation studies, this adaptive controller is found to be very effective in assuring robust performance.

An analysis of sun salutation

Sun salutation is a part of yoga. It consists of a sequence of postures done with synchronized breathing. The practice of few cycles of sun salutation is known to help in maintaining good health and vigor. The practice of sun salutation does not need any extra gadgets. Also it is very much aerobic and invigorates the body and the mind.

Models for spin-state transitions in solids

The model for spin-state transitions described by Bari and Sivardiere (1972) is static and can be solved exactly even when the dynamics of the lattice are included; the dynamic model does not, however, show any phase transition. A coupling between the octahedra, on the other hand, leads to a phase transition in the dynamical two-sublattice displacement model. A coupling of the spin states to the cube of the sublattice displacement leads to a first-order phase transition. The most reasonable model appears to be a two-phonon model in which an ion-cage mode mixes the spin states, while a breathing mode couples to the spin states without mixing. This model explains the non-zero population of high-spin states at low temperatures, temperature-dependent variations in the inverse susceptibility and the spin-state population ratio, as well as the structural phase transitions accompanying spin-state transitions found in some systems.

Optimal explicit terminal guidance for a launch vehicle

It is observed that general explicit guidance schemes exhibit numerical instability close to the injection point. This difficulty is normally attributed to the demand for exact injection which, in turn, calls for finite corrections to be enforced in a relatively short time. The deviations in vehicle state which need corrective maneuvers are caused by the off-nominal operating conditions. Hence, the onset of terminal instability depends on the type of off-nominal conditions encountered. The proposed separate terminal guidance scheme overcomes the above difficulty by minimizing a quadratic penalty on injection errors rather than demanding an exact injection. There is also a special requirement in the terminal phase for the faster guidance computations. The faster guidance computations facilitate a more frequent guidance update enabling an accurate terminal thrust cutoff. The objective of faster computations is realized in the terminal guidance scheme by employing realistic assumptions that are accurate enough for a short terminal trajectory. It is observed from simulations that one of the guidance parameters (P) related to the thrust steering angular rates can indicate the onset of terminal instability due to different off-nominal operating conditions. Therefore, the terminal guidance scheme can be dynamically invoked based on monitoring of deviations in the lone parameter P.

Electrochemical tuning and mechanical resilience of single-wall carbon nanotubes

Single-wall carbon nanotubes (SWNTs) are fascinating systems exhibiting many novel physical properties. In this paper, we give a brief review of the structural, electronic, vibrational, and mechanical properties of carbon nanotubes. In situ resonance Raman scattering of SWNTs investigated under electrochemical biasing demonstrates that the intensity of the radial breathing mode varies significantly in a nonmonotonic manner as a function of the cathodic bias voltage, but does not change appreciably under anodic bias. These results can be quantitatively understood in terms of the changes in the energy gaps between the 1 D van Hove singularities in the electron density of states, arising possibly due to the alterations in the overlap integral of pi bonds between the p-orbitals of the adjacent carbon atoms. In the second part of this paper, we review our high-pressure X-ray diffraction results, which show that the triangular lattice of the carbon nanotube bundles continues to persist up to similar to10 GPa. The lattice is seen to relax just before the phase transformation, which is observed at similar to10 GPa. Further, our results display the reversibility of the 2D lattice symmetry even after compression up to 13 GPa well beyond the 5 GPa value observed recently. These experimental results explicitly validate the predicted remarkable mechanical resilience of the nanotubes.

Nonlinear measures of respiration: Respiratory irregularity and increased chaos of respiration in patients with panic disorder

Background. Respiratory irregularity has been previously reported in patients with panic disorder using time domain measures. However, the respiratory signal is not entirely linear and a few previous studies used approximate entropy (APEN), a measure of regularity of time series. We have been studying APEN and other nonlinear measures including a measure of chaos, the largest Lyapunov exponent (LLE) of heart rate time series, in some detail. In this study, we used these measures of respiration to compare normal controls (n = 18) and patients with panic disorder (n = 22) in addition to the traditional time domain measures of respiratory rate and tidal volume. Methods: Respiratory signal was obtained by the Respitrace system using a thoracic and an abdominal belt, which was digitized at 500 Hz. Later, the time series were constructed at 4 Hz, as the highest frequency in this signal is limited to 0.5 Hz. We used 256 s of data (1,024 points) during supine and standing postures under normal breathing and controlled breathing at 12 breaths/min. Results: APEN was significantly higher in patients in standing posture during normal as well as controlled breathing (p = 0.002 and 0.02, respectively). LLE was also significantly higher in standing posture during normal breathing (p = 0.009). Similarly, the time domain measures of standard deviations and the coefficient of variation (COV) of tidal volume (TV) were significantly higher in the patient group (p = 0.02 and 0.004, respectively). The frequency of sighs was also higher in the patient group in standing posture (p = 0.02). In standing posture, LLE (p < 0.05) as well as APEN (p < 0.01) contributed significantly toward the separation of the two groups over and beyond the linear measure, i.e. the COV of TV. Conclusion: These findings support the previously described respiratory irregularity in patients with panic disorder and also illustrate the utility of nonlinear measures such as APEN and LLE as additional measures toward a better understanding of the abnormalities of respiratory physiology in similar patient populations as the correlation between LLE, APEN and some of the time domain measures only explained up to 50-60% of the variation. Copyright (C) 2002 S. Karger AG, Basel.

Structural changes in single-walled carbon nanotubes under non-hydrostatic pressures: x-ray and Raman studies

Using in situ x-ray diffraction and Raman scattering techniques, we have investigated the behaviour of single-walled carbon nanotubes bundles under non-hydrostatic pressures. It is seen that the diffraction line corresponding to the two-dimensional triangular lattice in the bundles is not reversible for pressures beyond 5 GPa, in sharp contrast to earlier results under hydrostatic pressure conditions. Most interestingly, radial breathing and tangential Raman modes of the pressure-cycled samples from 21 and 30 GPa match very well with those of the starting sample. Raman and x-ray results put together clearly suggest that the ordering of tubes in the bundles is only marginally regained with a very short coherence length on decompression.