Unknown Moments Research Articles

Fast and Saturating Thrust Direction Control for a Quadrotor Helicopter

Abstract In this paper we design a continuous, nonlinear state feedback controller that aligns the body-fixed thrust direction of a quadrotor helicopter with a constant desired direction given in an inertial coordinate system. The controller is designed based on an energy shaping approach and is able to saturate the control torques. Almost global asymptotic stability of the desired thrust direction is proven for arbitrary unknown moment of inertia matrices. Performance of the closed loop system is verified by simulations.

Finite element method solution of the simplified P3 equations for general geometry applications

The method and performance of a finite element method based simplified P3 code developed for generalized geometry applications are presented. The code takes the mesh data produced by an external general-purpose mesh generator. The weighted residual method with Galerkin weighting is directly applied to the two SP3 equations which were slightly modified to attain symmetry. The linear system for the global problem involving two unknown flux moments per node is obtained by summing up the elementwise weighted residual equations. The solution accuracy is examined for a suite of benchmark problems consisting of typical thermal and fast reactor problems together with the comparisons against the corresponding diffusion theory solutions. The effectiveness of the quadratic basis function is assessed as well against the linear function. It is demonstrated that the SP3 formulation is particularly beneficial for fast neutron systems.

Bending analysis of laminated sector plates with polar and rectilinear orthotropy

Abstract Bending of sector plates with both polar and rectilinear orthotropy is investigated using generalized differential quadrature (GDQ) method. The governing equations are written in polar coordinate system within the framework of the first-order shear deformation theory (FSDT). In polar orthotropic sector plates variation of thickness along radial direction due to moving out radial fibers, is considered. In rectilinear cases the variation of stiffness along circumferential direction due to variation of fiber angle with radial line, is considered. The governing equations are based on the FSDT which consists of thirteen first-order partial differential equations in terms of unknown displacements, rotations, forces and moments. Governing equations are discretized at whole domain grid points and boundary conditions are implemented exactly at boundary grid points using the GDQ method. Application of the GDQ technique to the governing equations, solution domain and boundary conditions leads to a system of algebraic equations. To compare the results of this study, the problems are also analyzed using commercial finite element software Abaqus. Various combinations of clamped, simply supported and free boundary conditions are implemented. It is found that the present method can analyze accurately sector plates with both polar and rectilinear orthotropy.

Closed-form solutions for stepped Timoshenko beams with internal singularities and along-axis external supports

The Timoshenko beam model in presence of internal singularities causing deflection and rotation discontinuities and resting on external concentrated supports along the span is studied in a static context. The internal singularities are modelled as concentrated reductions in the flexural and the shear stiffness by making use of the distribution theory. Along-axis supports are treated as unknown concentrated loads and moments. An exact integration procedure of the proposed model, not requiring continuity conditions at all, is presented. Closed-form solutions are provided for both cases of homogeneous and stepped Timoshenko beams. The so-called static Green’s functions are also obtained by the proposed procedure and their explicit expressions are provided.

Attitude Coordination Control for a Group of Spacecraft Without Velocity Measurements

This paper investigates the problem of velocity-free attitude coordination control for a group of spacecraft with attitude represented by modified Rodrigues parameters. The communication flow among neighbor spacecraft is described by an undirected connected graph. Two velocity-free attitude coordination control schemes are proposed. By employing linear reduced-order observers, robust control and Chebyshev neural networks, the first velocity-free control scheme allows a group of spacecraft to simultaneously align their attitude and track a time-varying reference attitude even in the presence of unknown mass moment of inertia matrix and external disturbances, where all spacecraft have access to the common reference attitude. The second control law guarantees a group of spacecraft to track a time-varying reference attitude without requiring velocity measurements even when the common reference attitude is available only to a subset of the group members. Furthermore, the stability of the overall closed-loop system for both control laws is guaranteed by a Lyapunov-based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controllers.

Analytical solution of piezolaminated rectangular plates with arbitrary clamped/simply-supported boundary conditions under thermo-electro-mechanical loadings

This paper extends an analytical method for static analysis of general cross-ply piezolaminated rectangular plates with any combination of clamped/simply-supported boundary conditions under uncoupled thermo-electro-mechanical loadings. This method is based on the novel superposition method and the first-order shear deformation theory (FSDT). The FSDT enables this expanded method to consider the effect of shear deformation of the plate. The process of applying electrical and thermal resultants causes some advantages due to its simplicity and less computational process. In this analysis displacement components are written in terms of unknown force and moment resultants. Using Fourier series for displacement components, mechanical, thermal, and/or electrical stress resultants, the complex governing differential equations of the plate are reduced to a set of linear algebraic equations with non-trivial solution. The obtained equations may be solved analytically to determine the unknown stress resultants. Several examples are proposed, and their obtained numerical results are compared with those available in the literature to verify the convergence, high accuracy, and the capability of the present method to analyze the static behavior of piezolaminated plates. It is found that there is high agreement between the present results with those obtained by other investigators.

Robust Attitude Coordination Control for Spacecraft Formation Flying Under Actuator Failures

This paper examines attitude coordination control for spacecraft formation flying. A class of distributed adaptive fault-tolerant attitude coordination control laws is proposed. The proposed control laws do not require online identification of failures. Using the Lyapunov approach and graph theory, it is shown that the control laws guarantee a group of spacecraft that simultaneously track a common time-varying reference attitude, even when the reference attitude is available only to a subset of the members of a group. Finally, numerical simulation is presented to show that the distributed controller is successful in achieving high-attitude tracking and synchronization performance, even in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, actuator failures, and control saturation limits.

Non‐linear analysis of moderately thick laminated plates and shell panels under thermo‐mechanical loadings

AbstractNon‐linear bending analysis of moderately thick laminated plates and cylindrical panels with various thermo‐mechanical loadings and boundary conditions is presented using generalized differential quadrature (GDQ) method together with the Newton‐Raphson iterative scheme. Different symmetric and asymmetric lamination sequences together with various combinations of clamped, simply supported and free boundary conditions are considered. Assuming the effects of shear deformation and initial curvature, based on the first‐order shear deformation theory (FSDT) and von Kármán‐type of geometric non‐linearity, the governing system of equations is obtained. This system includes thirteen non‐linear partial differential equations (PDEs) in terms of unknown displacements, rotations, forces and moments. The solution domain, governing equations and related boundary conditions are then discretized based on the GDQ technique. It is observed that the method provides reasonably accurate results with relatively small number of grid points. Comparisons of the predictions with results of finite element analyses show very good agreement. More results for panels with particular boundary conditions are presented for future references.

Quadrupole moments of odd-odd near-magic nuclei

Ground state quadrupole moments of odd-odd near double magic nuclei are calculated in the approximation of no interaction between odd particles. Under such a simple approximation, the problem is reduced to the calculations of quadrupole moments of corresponding odd-even nuclei. These calculations are performed within the self-consistent Theory of Finite Fermi Systems based on the Energy Density Functional by Fayans et al. with the known DF3-a parameters. A reasonable agreement with the available experimental data has been obtained for odd-odd nuclei and odd near-magic nuclei investigated. The self-consistent approach under consideration allowed us to predict the unknown quadrupole moments of odd-even and odd-odd nuclei near the double-magic $^{56,78}$Ni, $^{100,132}$Sn ones.

Bending analysis of moderately thick laminated conical panels with various boundary conditions

Bending analysis of moderately thick laminated conical panels with various boundary conditions is presented using the generalized differential quadrature (GDQ) method. Different combinations of clamped, simply supported, and free boundary conditions are considered. General lay up of laminates including symmetric and asymmetric panels is considered. Assuming the effects of shear deformation and initial curvature, the governing partial differential equations (PDEs) of the problem consist of 15 first-order PDEs in terms of unknown displacements, rotations, moments, and forces. Solution domain, governing equations and related boundary conditions are then discretized based on the GDQ technique. Results revealed that convergence of the method is very fast as it provides reasonably accurate results with a relatively small number of grid points. It is also demonstrated that a similar formulation and solution technique can be used to obtain predictions for sector plates by assuming appropriate geometrical parameters. Comparison of the predictions with results of other analytical and numerical methods shows very good agreement. Further results for symmetric and asymmetric laminated conical panels with various boundary conditions are also presented and validated using the commercial finite-element code ABAQUS for future references.

Reissner–Sagoci problem for a homogeneous coating on a functionally graded half-space

This paper is concerned with the axisymmetric elastostatic problem related to the rotation of a rigid punch which is bonded to the surface of a nonhomogeneous half-space. The half-space is composed of an isotropic homogeneous coating in the form of layer, which is attached to the functionally graded half-space. The shear modulus of the FGM is assumed to vary in the direction of axis O z normal to the boundary as μ 1( z) = μ 0(1 + αz) β , where μ 0, α, β are positive constants. The punch undergoes rotation due to the action of the internal loads. By using Hankel's integral transforms, the mixed boundary value problem is reduced to dual integral equations, and next, to a Fredholm's integral equation of the second kind, which is solved numerically for the case of β = 2. The final results show the effect of non-homogeneity on the shear stresses and an unknown moment of punch rotation.

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

Robust attitude control of helicopters with actuator dynamics using neural networks

In this study, attitude control is proposed for helicopters with actuator dynamics. For the nominal helicopter dynamics, model-based control is firstly presented to keep the desired helicopter attitude. To handle the model uncertainty and the external disturbance, radial basis function neural networks are adopted in the attitude control design. Using neural network approximation and the backstepping technique, robust attitude control is proposed with full state feedback. Considering unknown moment coefficients and the mass of helicopters, approximation-based attitude control is developed for the helicopter dynamics. In all proposed attitude control techniques, multi-input and multi-output non-linear dynamics are considered and the stability of the closed-loop system is proved via rigorous Lyapunov analysis. Extensive numerical simulation studies are given to illustrate the effectiveness of the proposed attitude control.

Adaptive fuzzy fault-tolerant attitude control of spacecraft

This paper investigates the attitude control of spacecraft in the presence of unknown mass moment of inertia matrix, external disturbances, actuator failures, and control input constraints. A robust adaptive controller is proposed with the utilization of fuzzy logic and backstepping techniques. The unit quaternion is employed to describe the attitude of spacecraft for global representation without singularities. The system uncertainty is estimated by introducing a fuzzy logic system. The adaptive mechanism has only two parameters to be adapted on-line because the adaptive law of the proposed controller is derived from the norm of the weight matrix. The stability of the closed-loop system is guaranteed by Lyapunov direct approach. Results of numerical simulations state that the proposed controller is successful in achieving high attitude performance in the presence of parametric uncertainties, external disturbances, actuator failures, and control input constraints.

Generalized invariant-unbiased masking and estimation of informational processes with multistructural noise

We develop a method of masking informational processes and estimating their various numerical characteristics after measurements that contain multistructural piecewise continuous noise with unknown structure switching moments.

Estimating the source parameters for the M W 7.6 April 20, 2006 Olyutorskii earthquake from long period P-wave records made by the worldwide network

The source parameters of the MW = 7.6 Olyutorskii earthquake were estimated using the moments of the slip rate function with degrees 1 and 2. The moments were estimated from broadband P-wave records at 52 stations of the worldwide network. The first step was to find a function S(t) for each station; this function is an apparent source time function, i.e., the P-wave slip as radiated by the source toward a station under consideration. The method of empirical Green’s functions was used to estimate S(t). The next step was to calculate the moments of S(t) of degrees 1 and 2 over time and to set up relevant equations to be solved by least squares for the unknown source moments. The horizontal linear source was used as a nonparametric model for calculating the source moments. Haskell’s parametric model was used for further interpretation of the source moments. The resulting estimates are as follows: the source centroid was 13–25 km southwest of the epicenter, the source was 105–120 km long, the source strike was 222°–228°, the rupture velocity was 2.7–3.0 km/s, and the total radiation duration was 24–27 s. These estimates indicate a bilateral rupture dominated by a southwestward sense of rupture propagation. The source characteristics are consistent with the aftershock area geometry and with the focal mechanism, as well as with surface breakage as observed by geologists in the field.

Adaptive attitude control of spacecraft without velocity measurements using Chebyshev neural network

This paper proposes an adaptive neural controller for the attitude tracking control of a rigid spacecraft without angular velocity measurements and in the presence of an unknown mass moment of inertia matrix and external disturbances. The modified Rodrigues parameters are employed for the representation of spacecraft attitude. The system uncertainty, which may include unknown mass moment of inertia matrix and external disturbances, is estimated by introducing a Chebyshev neural network. The controller is designed by incorporating a filtering technique to generate a pseudo-velocity tracking error signal from attitude angle measurements into the exiting adaptive neural network control scheme using the Chebyshev neural network. The uniform ultimate boundedness of all signals in the closed-loop system is guaranteed by the Lyapunov approach. The proposed controller is robust not only to structured uncertainty such as unknown mass moment of inertia matrix but also to understructured uncertainty such as external disturbances. Results of the numerical simulations state that the proposed controller is successful in achieving high attitude performance in presence of system parameter uncertainties and external disturbances.

A New Neuroadaptive Control Architecture for Nonlinear Uncertain Dynamical Systems: Beyond $\sigma $- and $e$-Modifications

This paper develops a new neuroadaptive control architecture for nonlinear uncertain dynamical systems. The proposed framework involves a novel controller architecture involving additional terms in the update laws that are constructed using a moving time window of the integrated system uncertainty. These terms can be used to identify the ideal system weights of the neural network as well as effectively suppress and cancel system uncertainty without the need for persistency of excitation. A nonlinear parametrization of the system uncertainty is considered and state and output feedback neuroadaptive controllers are developed. To illustrate the efficacy of the proposed approach we apply our results to a spacecraft model with unknown moment of inertia and compare our results with standard neuroadaptive control methods.

Non-linear bending analysis of laminated sector plates using Generalized Differential Quadrature

Non-linear static analysis of laminated sector plates with any combination of clamped, simply supported and free edges is presented using Generalized Differential Quadrature (GDQ) method. Particular interest of this study is large deformation of asymmetric sector plates with free edges. Based on the first-order shear deformation theory and von Kármán type non-linearity, the governing system of equations include a system of 13 partial differential equations (PDEs) in terms of unknown displacements, forces and moments. Successive application of the GDQ technique to the governing equations resulted in a system of non-linear algebraic equations. The Newton–Raphson iterative scheme is then employed to solve the system of non-linear equations. Illustrative examples are presented to demonstrate accuracy and rapid convergences of the method with small number of grid points. Predictions of the presented method show very good agreement with other numerical studies available in the literature. Further results for asymmetric laminated sector plates with free edges are also presented for future references.

Écrire (traduire). Hugo Claus traducteur

This article analyses the importance of translation in the work of the Flemish writer Hugo Claus (1929-2008). Notwithstanding Claus’s success in both the Dutch-speaking world and on the international scene, the heterolinguistic hybridity of his work – especially as far as translation is concerned – has so far been relatively disregarded compared to the intertextual aspects of his creative work. Since Claus’ death, however, his translation activity has provoked a renewed interest and has been considered as an inherent part of his authorial production. Nonetheless, this somewhat hagiographic apprehension does not account for the specific derivative and second nature of Claus’ literary production, which corresponds to an interlinguistic response to other forms of textual production. By reformulating the problem, this paper endeavors to envisage Claus’s translations as a relatively unknown moment of signifying practice of his own and to illustrate which collateral – among others epistemological – questions it raises for the process of writing. It will deepen the understanding of the way translation deals with a multitude of international literary manifestations on the one hand, while it is itself constituted by Claus’s singular poetics, on the other hand. It goes without saying that Claus’s poetics of translation is likely to be pervaded by some of the “original” work’s aesthetic principles. From this point of view, the question of Claus’s translation practice sheds a light on the elaboration of Claus’ “library” and on the relationship to his own creative trajectory. Furthermore, the study of recent editions of his translations, manuscripts and avant-textes enables us to situate translations as dynamic variables and inter-texts within the authorial process of text writing.