Sharif Digital Repository

This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative motion of spacecraft. Specially, the feasibility problem of the position norm constraints is considered in this paper. Under assumptions, it is proved that if a position vector be reachable, then the reach time and the corresponding time of impulses are unique. The trajectory boundedness of the spacecraft between adjacent impulses are analyzed using the Gerschgorin and the Rayleigh-Ritz theorems as well as a finite form of the Jensen's inequality. Some... 

A system is called prescribed-time attractive if its solution converges at an arbitrary user-defined finite time. In this note, necessary and sufficient conditions are developed for the prescribed-time attractivity of linear time-varying (LTV) systems. It is proved that the frozen-time eigenvalues of a prescribed-time attractive LTV system have negative real parts when the time is sufficiently close to the convergence moment. This result shows that the ubiquitous singularity problem of prescribed-time attractive LTV systems can be avoided without instability effects by switching to the corresponding frozen-time system at an appropriate time. Consequently, it is proved that the time-varying... 

A fault detection and isolation method for satellite rate gyros is proposed based on using the satellite-to-satellite measurements such as relative position beside orbit parameters of the primary satellite. By finding a constant of motion, it is shown that the dynamic states in a relative motion are restricted in such a way that the angular velocity vector of primary satellite lies on a quadratic surface. This constant of motion is then used to detect the gyroscope faults and estimate the corresponding scale factor or bias values of the rate gyros of the primary satellite. The proposed algorithm works even in time variant fault situations as well, and does not impose any additional... 

This article introduces a class of time-varying controllers for Euler-Lagrange systems such that the convergence occurs at an arbitrary finite time, independently of initial conditions, and free of chattering. The proposed controller is based on a mapping technique and is designed in two steps: First, a conventional (obstacle avoidance) asymptotically stable controller is specified for the nominal system; then, by a simple substitution, a prescribed-time (obstacle avoidance) controller is achievable for the perturbed system. It is proved that the proposed scheme is uniformly prescribed-time stable for unperturbed systems and prescribed-time attractive for perturbed systems as it rejects... 

This letter presents a unified framework for the design of prescribed-time controllers under time-varying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a time-domain mapping method by which any infinite-time system can be corresponded to a prescribed-time system and vice versa. It is shown that the design of a constrained nonasymptotic prescribed-time controller can be reduced to the asymptotic control design for an associated constrained infinite-time system. Faà di Bruno’s formula and Bell polynomials are used for a constructive representation of the associated infinite-time system. The presented results... 

This paper introduces a class of time-varying controllers for Euler-Lagrange systems such that the convergence occurs at an arbitrary finite time, independently of initial conditions, and free of chattering. The proposed controller is based on a mapping technique and is designed in two steps: First, a conventional (obstacle avoidance) asymptotically stable controller is specified for the nominal system; then, by a simple substitution, a prescribed-time (obstacle avoidance) controller is achievable for the perturbed system. It is proved that the proposed scheme is uniformly prescribed-time stable for unperturbed systems and prescribed-time attractive for perturbed systems as it rejects... 

In this letter, a new notion of stability is introduced, which is called triangular stability. A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its intersection point with the time axis can be arbitrarily commanded by the user. Triangular stability implies prescribed-time stability, which means that the nonlinear system is converged to zero equilibrium at an arbitrary finite time. A prescribed-time controller with guaranteed triangular stability is developed for normal form nonlinear systems with uncertain input gain, which is able to reject the disturbances and unmodeled dynamics. Numerical simulations are... 

This letter presents a unified framework for the design of prescribed-time controllers under time-varying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a time-domain mapping method by which any infinite-time system can be corresponded to a prescribed-time system and vice versa. It is shown that the design of a constrained nonasymptotic prescribed-time controller can be reduced to the asymptotic control design for an associated constrained infinite-time system. Faà di Bruno's formula and Bell polynomials are used for a constructive representation of the associated infinite-time system. The presented results... 

Natural frequencies and mode shapes of two joined isotropic conical shells are presented in this study. The joined conical shells can be considered as the general case for joined cylindrical-conical shells, joined cylinder-plates or cone-plates, conical and cylindrical shells with stepped thicknesses and also annular plates. Governing equations are obtained using thin-walled shallow shell theory of Donnell and Hamilton's principle. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved assuming trigonometric response in circumferential and series solution in meridional directions and all... 

In this study, the buckling of two joined isotropic conical shells under axial compression and simply supported boundary conditions is investigated. The governing equations are obtained using thin-walled shallow shell theory of Donnell-type and theorem of minimum potential energy. The continuity conditions at the joining section of the cones are appropriate expressions among stress resultants and deformations. The equations are solved by assuming trigonometric response in circumferential and series solution in meridional direction. The results are validated in comparison with the available results in the literature. Effects of semi-vertex angles and meridional lengths on the buckling load... 

In the present study, a simple analytical method is introduced for determination of natural frequencies of generally laminated conical and cylindrical shells with arbitrary boundary conditions. The governing equations of motion employed are those of thin-walled shell theory of Donnell. The free-vibration equations are solved using state space method and series solution in meridional direction. The results are compared and validated with the available especial results in the literature. The effects of bending-stretching coupling, semi-vertex angle, meridional length, shell thickness, fiber directions of composite plies, and lamination sequences on the natural frequency of conical and... 

A new test specimen for a tensile test of industrial graphite is introduced using experiment and finite element results. The most influencing factors on the tensile strength of the test specimens are considered and the number of tests, which are necessary to optimize the tensile strengths are reduced based on the design of experiment using the Taguchi method and the effects of all factors on strength of test samples are studied. Comparison of the predicted strengths based on the Taguchi approach with the measured experimental results and finite element analysis shows a good correlation between them. In addition, results show that the new introduced specimen makes a 33% increase in the... 

Design and performance of a beam shaping device based on a simple flexible plastic fiber-bundle stripe and a prism duct is described in this study. Such a system offers practical means to modify and change the output beam shape and also provides quantitative information concerning the transmitted power. It is possible to measure transmitted power signal by using a precise photodetector and also analyze beam images taken by a digital camera. The photograph picture of the illuminating LED beam just at its output point shows a circular shape with a radius of about 4 mm and the fiber-bundle output beam is rectangular shape with a dimension of 22.5×2 mm. A regular duct is tested in this study and... 

Elastic stability of shell structures under certain loading conditions is characterized by a dramatically unstable postbuckling behavior. The presence of simultaneous 'competing' buckling modes (corresponding to the same critical buckling load) is understood to be largely responsible for such behavior. In this paper, within the framework of linear bifurcation eigenvalue analysis and Donnell shallow shell theory, the presence of simultaneous buckling modes in axially compressed isotropic cones is determined using the semi-analytical method of Galerkin. The results are presented in the plane of the dimensionless reciprocal meridional and circumferential buckling half wavelengths, and are... 

The buckling analysis of cross-ply laminated conical shell panels with simply supported boundary conditions at all edges and subjected to axial compression is studied. The conical shell panel is a very interesting problem as it can be considered as the general case for conical shells when the subtended angle is set to 2π and also cylindrical panels and shells when the semi-vertex angle is equal to zero. Equations were derived using classical shell theory of Donnell type and solved using generalized differential quadrature method. The results are compared and validated with the known results in the literature. The effects of subtended angle, semi-vertex angle, length, thickness and radius of... 

This paper describes a systematic numerical investigation into the nonlinear elastic behavior of conical shells, with various types of initial imperfections, subject to a uniformly distributed axial compression. Three different patterns of imperfections, including first axisymmetric linear bifurcation mode, first non-axisymmetric linear bifurcation mode, and weld depression are studied using geometrically nonlinear finite element analysis. Effects of each imperfection shape and tapering angle on imperfection sensitivity curves are investigated and the lower bound curve is determined. Finally, an empirical lower bound relation is proposed for hand calculation in the buckling design of conical... 

Buckling of generally laminated conical shells under uniform torsion with simply-supported boundary conditions is investigated. The Donnel type strain displacement relations are used to obtain potential strain energy of the shell and membrane stability equation is applied to acquire the external work done by torsion. The Ritz method is used to solve the governing equations and critical buckling loads are obtained. The accuracy of the results is validated in comparison of with other investigations and finite element method. The effects of lamination sequence, semi-vertex angle and length to radius ratio of the cone are evaluated and mode shapes are presented for two types of lamination... 

This paper presents an orbit estimation using non-simultaneous horizon detector measurements in the presence of uncertainties in the celestial body rotational velocity and its geometrical characteristics. The celestial body is modeled as a tri-axial ellipsoid with a three-dimensional force field. The non-simultaneous modelling provides the possibility to consider the time gap between horizon measurements. An unscented Kalman filter is used to estimate the spacecraft state variables and the geometric characteristics as well as the rotational velocity vector of the celestial body. A Monte-Carlo simulation is implemented to verify the results. Simulations showed that using non-simultaneous... 

A novel trajectory design methodology is proposed in the current work to minimize the state uncertainty in the crucial mission of spacecraft rendezvous. The trajectory is shaped under constraints utilizing a multiple-impulse approach. State uncertainty is characterized in terms of covariance, and the impulse time as the only effective parameter in uncertainty propagation is selected to minimize the trace of the covariance matrix. Furthermore, the impulse location is also adopted as the other design parameter to satisfy various translational constraints of the space mission. Efficiency and viability of the proposed idea have been investigated through some scenarios that include constraints on...