Modified ILMI algorithm for practical PID/PD implementation on a Micro Air Vehicle

This paper extends the iterative linear matrix inequality algorithm (ILMI) for systems having non-ideal PI, PD and PID implementations. The new algorithm uses the practical implementation of the feedback blocksto form the equivalent static output feedback plant. The LMI based synthesis techniques are used in the algorithm to design a multi-loop, multi-objective fixed structure control. The benefits of such a control design technique are brought out by applying it to the lateral stabilizing and tracking feedback control problem of a 30cm wingspan micro air vehicle.

Star Camera Calibration Combined with Independent Spacecraft Attitude Determination

A methodology for determining spacecraft attitude and autonomously calibrating star camera, both independent of each other, is presented in this paper. Unlike most of the attitude determination algorithms where attitude of the satellite depend on the camera calibrating parameters (like principal point offset, focal length etc.), the proposed method has the advantage of computing spacecraft attitude independently of camera calibrating parameters except lens distortion. In the proposed method both attitude estimation and star camera calibration is done together independent of each other by directly utilizing the star coordinate in image plane and corresponding star vector in inertial coordinate frame. Satellite attitude, camera principal point offset, focal length (in pixel), lens distortion coefficient are found by a simple two step method. In the first step, all parameters (except lens distortion) are estimated using a closed-form solution based on a distortion free camera model. In the second step lens distortion coefficient is estimated by linear least squares method using the solution of the first step to be used in the camera model that incorporates distortion. These steps are applied in an iterative manner to refine the estimated parameters. The whole procedure is faster enough for onboard implementation.

Positional Consensus in Multi-Agent Systems using a Broadcast Control Mechanism

In this paper a strategy for controlling a group of agents to achieve positional consensus is presented. The proposed technique is based on the constraint that every agents must be given the same control input through a broadcast communication mechanism. Although the control command is computed using state information in a global framework, the control input is implemented by the agents in a local coordinate frame. We propose a novel linear programming formulation that is computationally less intensive than earlier proposed methods. Moreover, we introduce a random perturbation input in the control command that helps us to achieve perfect consensus even for a large number of agents, which was not possible with the existing strategy in the literature. Moreover, we extend the method to achieve positional consensus at a pre-specified location. The effectiveness of the approach is illustrated through simulation results.

Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

FSK bursts for efficient clutter rejection

The clutter-rejection properties of compact f.s.k. bursts with amplitude modulation are investigated. A procedure for computer-aided design of such signals is given. The loss of clutter performance on constraining the individual pulse amplitudes to be equal is evaluated.

Rapid distortion of axisymmetric turbulence

A generalization of the isotropic theory of Batchelor & Proudman (1954) is developed to estimate the effect of sudden but arbitrary three-dimensional distortion on homogeneous, initially axisymmetric turbulence. The energy changes due to distortion are expressed in terms of the Fourier coefficients of an expansion in zonal harmonics of the two independent scalar functions that describe the axisymmetric spectral tensor. However, for two special but non-trivial forms of this tensor, which represent possibly the simplest kinds of non-isotropic turbulence and specify the angular distribution but not the wavenumber dependence, the energy ratios have been determined in closed form. The deviation of the ratio from its isotropic value is the product of a factor containing R, the initial value of the ratio of the longitudinal to the transverse energy component, and another factor depending only on the geometry of the distortion. It is found that, in axisymmetric and large two-dimensional contractions, the isotropic theory gives nearly the correct longitudinal energy, but (when R > 1) over-estimates the increase in the transverse energy; the product of the two intensities varies little unless the distortion is very large, thus accounting for the stress-freezing observed in rapidly accelerated shear flows.Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement. The different ansatzes predict results in broad qualitative agreement with a simple strategem suggested by Reynolds & Tucker (1975), but the quantitative differences are not always negligible.

Analysis of vibration of clamped square plates by the Rayleigh-Ritz method with asymptotic solutions from a modified Bolotin method

Estimates of flexural frequencies of clamped square plates are initially obtained by the modified Bolotin's method. The mode shapes in “each direction” are then determined and the product functions of these mode shapes are used as admissible functions in the Rayleigh-Ritz method. The data for the first twenty eigenvalues in each of the three (four) symmetric groups obtained by the (i) Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are reported here. The Rayleigh estimates are found to be much closer to the true eigenvalues than the Bolotin estimates. The present product functions are found to be much superior to the conventional beam eigenmodes as admissible functions in the Rayleigh-Ritz method of analysis.

A study of the deformation slip lines in quenched and aged Al-2% Ge alloy

Optical microscopy has been employed to observe the slip lines in deformed Al-2% Ge alloy samples. Slip lines have been observed in the as-quenched, partially-aged, fully-aged and over-aged states. The lines tend to traverse fairly straight paths in the case of quenched and partially-aged conditions. Fully-aged samples also reveal such straight running lines when tested at low-temperatures. However, the density of the lines generally decreases as the peak-aged state is approached. These results are in agreement with the idea that thermally activated shearing of the precipitates is occurring in the alloy aged up to peak-hardness. The irregular lines for the over-aged specimens support the view that the moving dislocations by-pass the precipitates during deformation. The influence of test-temperature on the appearance of slip traces has been briefly examined.

Rotational cut-off and anharmonicity effects on thermodynamic properties of gases at high temperatures

The exact expressions for the partition function (Q) and the coefficient of specific heat at constant volume (Cv) for a rotating-anharmonic oscillator molecule, including coupling and rotational cut-off, have been formulated and values of Q and Cv have been computed in the temperature range of 100 to 100,000 K for O2, N2 and H2 gases. The exact Q and Cv values are also compared with the corresponding rigid-rotator harmonic-oscillator (infinite rotational and vibrational levels) and rigid-rotator anharmonic-oscillator (infinite rotational levels) values. The rigid-rotator harmonic-oscillator approximation can be accepted for temperatures up to about 5000 K for O2 and N2. Beyond these temperatures the error in Cv will be significant, because of anharmonicity and rotational cut-off effects. For H2, the rigid-rotator harmonic-oscillator approximation becomes unacceptable even for temperatures as low as 2000 K.

The structure of turbulent boundary layers along mildly curved surfaces

This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers. (Published Online April 12 2006)

Theoretical gain optimization studies in 10.6 µm CO2-N2 gasdynamic lasers. IV. Further results of parametric study

Based on a method proposed by Reddy and Shanmugasundaram, similar solutions have been obtained for the steady inviscid quasi-one-dimensional nonreacting flow in the supersonic nozzle of CO2-N2-H2O and CO2-N2-He gasdynamic laser systems. Instead of using the correlations of a nonsimilar function NS for pure N2 gas, as is done in previous publications, the NS correlations are computed here for the actual gas mixtures used in the gasdynamic lasers. Optimum small-signal optical gain and the corresponding optimum values of the operating parameters like reservoir pressure and temperature and nozzle area ratio are computed using these correlations. The present results are compared with the previous results and the main differences are discussed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Determination of optimal trajectory under design constraints for a satellite launch vehicle

An optimal pitch steering programme of a solid-fuel satellite launch vehicle to maximize either (1) the injection velocity at a given altitude, or (2) the size of circular orbit, for a given payload is presented. The two-dimensional model includes the rotation of atmosphere with the Earth, the vehicle's lift and drag, variation of thrust with time and altitude, inverse-square gravitational field, and the specified initial vertical take-off. The inequality constraints on the aerodynamic load, control force, and turning rates are also imposed. Using the properties of the central force motion the terminal constraint conditions at coast apogee are transferred to the penultimate stage burnout. Such a transformation converts a time-free problem into a time-fixed one, reduces the number of terminal constraints, improves accuracy, besides demanding less computer memory and time. The adjoint equations are developed in a compact matrix form. The problem is solved on an IBM 360/44 computer using a steepest ascent algorithm. An illustrative analysis of a typical launch vehicle establishes the speed of convergence, and accuracy and applicability of the algorithm.

Optimal iterative schemes for computing the Moore-Penrose matrix inverse

Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A Fortran programme for these schemes is provided.

Non-linear vibrations of non-unifo with concentrated masses

Large amplitude oscillations of cantilevered beams of variable cross-section, with concentrated masses along the span, are studied in this paper. The governing non-linear ordinary differential equation is solved by an averaging technique to obtain approximate solutions. Stability boundaries of the response are also investigated.