Dynamic Inversion Control for Performing Herbst Manoeuver with Lateral Center-of-Gravity Offset

2017 ◽  
Vol 67 (2) ◽  
pp. 198
Author(s):  
Bijoy K. Mukherjee ◽  
Manoranjan Sinha
Keyword(s):  
Reference Frames ◽  
Equations Of Motion ◽  
Computation Time ◽  
Center Of Gravity ◽  
Dynamic Inversion ◽  
Time Step ◽  
Highly Nonlinear ◽  
Dynamics And Control ◽  
Body Reference ◽  
Six Degree Of Freedom

<!--?xml version="1.0" encoding="UTF-8"?--><div class="abstract"><div class="abstract_label">The present study addresses the effects of lateral center-of-gravity (CG) movement, resulting from asymmetric firing of some of the onboard stores, on the dynamics and control of a combat aircraft while attempting the highly demanding Herbst manoeuver. The complete six degree-of-freedom equations of motion of the aircraft for such lateral CG offset are derived in two different body reference frames attached either to the symmetric nominal CG location or to the shifted asymmetric CG location. The Herbst manoeuver is first simulated using nonlinear dynamic inversion based control to handle the highly nonlinear post stall flight dynamics considering the standard equation of motion without considering any lateral CG variation. Thereafter, it is observed that if the same controller is retained, the manoeuver performance deteriorates significantly even when the CG undergoes a moderate lateral shift. To overcome this shortfall, closed loop controllers are next designed incorporating both the models of asymmetric dynamics as derived in this paper. It is validated through MATLAB simulations that both the controls, thus designed, can recover the original manoeuver performance almost completely; however, the first one requires more complex computations and hence increased computation time while the second one requires that all the measurements be transformed to the new body reference frame at every time step.</div></div>

Dynamics of Mechanisms and Machine Systems in Accelerating Reference Frames

1981 ◽  
Vol 103 (4) ◽  
pp. 395-403 ◽  
Author(s):  
R. R. Allen
Keyword(s):  
Reference Frames ◽  
Equations Of Motion ◽  
Dynamic Interactions ◽  
Generalized Variables ◽  
Highly Nonlinear ◽  
Formal Procedure ◽  
Machine Systems ◽  
External Forces ◽  
Four Bar Linkage ◽  
General Translation

Matrix equations of motion are derived for a general machine system in an accelerating reference frame. These equations are highly-nonlinear in the displacements of inertial elements and describe the dynamics of large motions. This analysis permits study of dynamic interactions between the moving elements of a machine and the motion of the machine body. The latter may undergo general translation and rotation as a result of internal and external forces. Power-conserving transformations relating inertial, kinematic, and generalized velocities provide a highly formal procedure for kinematic and dynamic analyses and produce explicit equations in generalized variables which are efficient for numerical solution. The theory is applied to study a machine with a four-bar linkage and driveshaft elasticity mounted on a spring-damper suspension. In this example, torsional oscillations in the drive are compared to those obtained with the machine body fixed in inertial space.

Parallel Co-Simulation Approach With Macro-Step Size and Order Control Algorithm

2019 ◽  
Author(s):  
Jan Kraft ◽  
Tobias Meyer ◽  
Bernhard Schweizer
Keyword(s):  
Control Algorithm ◽  
Computation Time ◽  
Simulation Approach ◽  
Step Size ◽  
Time Step ◽  
Time Points ◽  
Highly Nonlinear ◽  
Communication Time ◽  
Coupling Variables ◽  
Time Grid

Abstract This contribution deals with the parallelization of multibody systems by making use of co-simulation techniques. The overall model is split into a user-defined number of subsystems, which are coupled and computed by means of a co-simulation approach. The co-simulation methods considered here are weak coupling approaches, which implies that each subsystem is solved independently from the other subsystems within a macro-time step. Information (i.e. coupling variables) is only exchanged between the subsystems at certain communication-time points (macro-time points). Within each macro-time step, the unknown coupling variables are approximated by extrapolation polynomials. The separate integration of the subsystems is the crucial point for a parallelized computation. A main drawback of many co-simulation implementations is that they are based on a constant macro-step size. Using an equidistant communication-time grid may in many practical applications be not very efficient with respect to computation time, especially in connection with highly nonlinear models or in context with models with strongly varying quantities. Here, a co-simulation approach is presented which incorporates a macro-step size and order control algorithm. Numerical examples show the benefit of this implementation and the significant reduction in computation time compared to an implementation with an equidistant communication-time grid.

scholarly journals Numerical Integration Scheme Using Singular Perturbation Method

2013 ◽  
Author(s):  
Gibin Gil ◽  
Ricardo G. Sanfelice ◽  
Parviz E. Nikravesh
Keyword(s):  
Singular Perturbation ◽  
Perturbation Method ◽  
Numerical Integration ◽  
Equations Of Motion ◽  
Computation Time ◽  
Integration Scheme ◽  
Singular Perturbation Method ◽  
Time Step ◽  
Numerical Integration Scheme ◽  
Deformable Bodies

Some multi degree-of-freedom dynamical systems exhibit a response that contain fast and slow variables. An example of such systems is a multibody system with rigid and deformable bodies. Standard numerical integration of the resultant equations of motion must adjust the time step according to the frequency of the fastest variable. As a result, the computation time is sacrificed. The singular perturbation method is an analysis technique to deal with the interaction of slow and fast variables. In this study, a numerical integration scheme using the singular perturbation method is discussed, its absolute stability condition is derived, and its order of accuracy is investigated.

Calculation of Dynamic Tire Forces from Aircraft Instrumentation Data

2010 ◽  
Vol 38 (3) ◽  
pp. 182-193 ◽  
Author(s):  
Gary E. McKay
Keyword(s):  
System Performance ◽  
Equations Of Motion ◽  
Test Laboratory ◽  
Excellent Correlation ◽  
Friction Behavior ◽  
Aircraft Landing ◽  
Data Scatter ◽  
Tire Forces ◽  
Six Degree Of Freedom ◽  
Tire Friction

Abstract When evaluating aircraft brake control system performance, it is difficult to overstate the importance of understanding dynamic tire forces—especially those related to tire friction behavior. As important as they are, however, these dynamic tire forces cannot be easily or reliably measured. To fill this need, an analytical approach has been developed to determine instantaneous tire forces during aircraft landing, braking and taxi operations. The approach involves using aircraft instrumentation data to determine forces (other than tire forces), moments, and accelerations acting on the aircraft. Inserting these values into the aircraft’s six degree-of-freedom equations-of-motion allows solution for the tire forces. While there are significant challenges associated with this approach, results to date have exceeded expectations in terms of fidelity, consistency, and data scatter. The results show excellent correlation to tests conducted in a tire test laboratory. And, while the results generally follow accepted tire friction theories, there are noteworthy differences.

scholarly journals A new boundary element algorithm for modeling and simulation of nonlinear thermal stresses in micropolar FGA composites with temperature-dependent properties

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Modeling And Simulation ◽  
Boundary Element ◽  
Thermal Stresses ◽  
Computation Time ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Time Step ◽  
Kirchhoff Transformation ◽  
Nonlinear Temperature ◽  
Temperature Dependent Properties

AbstractThe main aim of this article is to develop a new boundary element method (BEM) algorithm to model and simulate the nonlinear thermal stresses problems in micropolar functionally graded anisotropic (FGA) composites with temperature-dependent properties. Some inside points are chosen to treat the nonlinear terms and domain integrals. An integral formulation which is based on the use of Kirchhoff transformation is firstly used to simplify the transient heat conduction governing equation. Then, the residual nonlinear terms are carried out within the current formulation. The domain integrals can be effectively treated by applying the Cartesian transformation method (CTM). In the proposed BEM technique, the nonlinear temperature is computed on the boundary and some inside domain integral. Then, nonlinear displacement can be calculated at each time step. With the calculated temperature and displacement distributions, we can obtain the values of nonlinear thermal stresses. The efficiency of our proposed methodology has been improved by using the communication-avoiding versions of the Arnoldi (CA-Arnoldi) preconditioner for solving the resulting linear systems arising from the BEM to reduce the iterations number and computation time. The numerical outcomes establish the influence of temperature-dependent properties on the nonlinear temperature distribution, and investigate the effect of the functionally graded parameter on the nonlinear displacements and thermal stresses, through the micropolar FGA composites with temperature-dependent properties. These numerical outcomes also confirm the validity, precision and effectiveness of the proposed modeling and simulation methodology.

Time suboptimal control of industrial manipulators along specified paths while keeping an end-effector orientation unchanged

Robotica ◽  
2003 ◽  
Vol 21 (2) ◽  
pp. 153-161 ◽  
Author(s):  
S. Kilicaslan ◽  
Y. Ercan
Keyword(s):  
Suboptimal Control ◽  
Time Step ◽  
End Effector ◽  
Industrial Manipulator ◽  
Industrial Manipulators ◽  
Angular Velocities ◽  
System Equations ◽  
Six Degree Of Freedom ◽  
Time Suboptimal Control

A method for the time suboptimal control of an industrial manipulator that moves along a specified path while keeping its end-effector orientation unchanged is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in a case study to verify the method developed.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

Determination of the Minimum Distance Between Moving Objects Including Velocity Information

1993 ◽  
Author(s):  
Meyer Nahon
Keyword(s):  
Minimum Distance ◽  
Moving Objects ◽  
Rapid Determination ◽  
Computation Time ◽  
Optimization Techniques ◽  
Real Time Control ◽  
Time Step ◽  
Time Control ◽  
Velocity Information

Abstract The rapid determination of the minimum distance between objects is of importance in collision avoidance for a robot maneuvering among obstacles. Currently, the fastest algorithms for the solution of this problem are based on the use of optimization techniques to minimize a distance function. Furthermore, to date this problem has been approached purely through the position kinematics of the two objects. However, although the minimum distance between two objects can be found quickly on state-of-the-art hardware, the modelling of realistic scenes entails the determination of the minimum distances between large numbers of pairs of objects, and the computation time to calculate the overall minimum distance between any two objects is significant, and introduces a delay which has serious repercussions on the real-time control of the robot. This paper presents a technique to modify the original optimization problem in order to include velocity information. In effect, the minimum distance calculation is performed at a future time step by projecting the effect of present velocity. This method has proven to give good results on a 6-dof robot maneuvering among obstacles, and has allowed a complete compensation of the lags incurred due to computational delays.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

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