Guidelines for Computing Longitudinal Dynamic Stability Characteristics of a Subsonic Transport

A systematic study is presented to guide the selection of a numerical solution strategy for URANS computation of a subsonic transport configuration undergoing simulated forced oscillation about its pitch axis. Forced oscillation is central to the prevalent wind tunnel methodology for quantifying aircraft dynamic stability derivatives from force and moment coefficients, which is the ultimate goal for the computational simulations. Extensive computations are performed that lead in key insights of the critical numerical parameters affecting solution convergence. A preliminary linear harmonic analysis is included to demonstrate the potential of extracting dynamic stability derivatives from computational solutions

Dynamic characterisation of a damaged composite structure with stiffeners employing fibre bragg gratings

One of the key issues in composite structures for aircraft applications is the early detection and localisation of damage. Often service induced damage does not involve visible plastic deformation, but internal matrix related damage, like transverse cracks and delaminations. Their detection imposes costly maintenance techniques. Vibration based damage identification methods are promising as an alternative for the time consuming and costly Non-Destructive Testing methods currently available. These methods also offer the potential to be used in a real-time health monitoring system. The measured change of the dynamic properties is employed to identify damage such as delaminations.\ud Earlier performed research [1] showed that the Modal Strain Energy Damage Index algorithm [2] is a suitable method to identify impact induced damage in a fibre reinforced composite plate structure with stiffeners using laser vibrometer measurements. The damage identification algorithm requires the computation of the second derivative of the displacement mode shapes.\ud The goal is to extent this research by applying fibre Bragg gratings since they can be valuable. Firstly, optical fibre sensors are suitable for integration, which is required in a Structural Health Monitoring environment. Secondly, measured strain mode shapes could be advantageous with respect to the numerical errors induced by the computation of second derivatives of the displacement mode shapes.\ud Before applying the damage identification algorithm, it is a challenge to accurately extract the dynamic properties. The dynamic properties of a damaged composite T-shaped stiffener section, shown in figure 1, are investigated in this work using fibre Bragg gratings

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control

A new method for nonlinear circuit simulation in time domain: NOWE

Cataloged from PDF version of article.A new method for the time-domain solution of general nonlinear dynamic circuits is presented. In this method, the solutions of the state variables are computed by using their time derivatives up to some order at the initial time instant. The computation of the higher order derivatiws b equivalent to solving the same linear circuit for various sets of dc excitations. Once the time derivatives of the state variables are obtained, an approximation to the solution can be found as a polynomial rational function of time. The time derivatives of the approximation at the initial time instant are matched to those of the exact solution. This method is promising in terms of execution speed, since it can achieve the same accuracy as the trapezoidal approximation with much smaller number of matrix inversions

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning