scholarly journals Deflection Reduction Shaping Commands with Asymmetric First-Order Actuators

2019 ◽  
Vol 9 (19) ◽  
pp. 3982
Author(s):  
Yoon-Gyung Sung ◽  
Chang-Lae Kim
Keyword(s):  
Flexible Structures ◽  
Closed Form Solution ◽  
Form Solution ◽  
Real Time Control ◽  
Pendulum System ◽  
Command Shaping ◽  
First Order ◽  
Time Control ◽  
Input Shaper ◽  
Vector Approach

In this paper, two approaches for generating deflection reduction shaping commands are proposed to reduce the transient and residual deflections of flexible systems subject to asymmetric first-order actuators. The commands are limited-state in that they consist of two positive actuations of different magnitudes and one negative actuation, similar to on-off-on commands. Standard on–off commands that are commonly used in robots, cranes, and spacecrafts can degrade the control performance of conventional input-shaped commands and cause detrimental damage resulting from large transient deflections of flexible structures due to asymmetric first-order actuators. Therefore, to cope with the performance degradation resulting from the effects of first-order actuators, an approximated closed-form solution and a numerically optimized approach for deflection reduction shaping commands are presented with an exponential function, final impulse magnitude modification of an input shaper is determined by a transient deflection constraint and a phasor vector approach. The performance assessment showed that the approximated analytical approach has an advantage in real-time control applications. The characteristics of the proposed deflection reduction shaping commands are analyzed with respect to system parameters, deflection reduction ratios, and actuator time constants. The proposed command shaping techniques are numerically evaluated using a pendulum system and are experimentally validated on a mini-bridge crane.

On the Kinematics of the UPS Wrist for Real Time Control

1992 ◽  
Author(s):  
Jason J. Lee ◽  
Sun-Lai Chang
Keyword(s):  
Real Time ◽  
High Speed ◽  
Closed Form Solution ◽  
Direct Analysis ◽  
Form Solution ◽  
Parallel Structure ◽  
Forward Kinematics ◽  
Real Time Control ◽  
Spatial Mechanism ◽  
Time Control

Abstract A parallel structure is used in the design of the UPS wrist to allow for a large payload, high speed, high repeatability, and a large workspace. Because of the inherent design and machining difficulties involved with spherical mechanisms, a spatial mechanism has been adopted. In creating such a 3-DOF spatial mechanism, many practical design problems are unavoidable, and direct analysis of the mechanism becomes extremely difficult. In this paper, we discuss the concept of using an equivalent mechanism to simplify the kinematic analysis. By using this method, we have derived a closed-form solution for the inverse kinematics, as well as a formulation for the forward kinematics. We have also developed a numerical algorithm for the forward kinematics, and a methodology for implementing the results of the analysis. The results of this study have enabled real time control and force control to become feasible for the UPS wrist.

Order-Tuned Vibration Absorbers for Cyclic Rotating Flexible Structures

2005 ◽  
Author(s):  
Brian J. Olson ◽  
Steve W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Equations Of Motion ◽  
Flexible Structures ◽  
Closed Form Solution ◽  
Nonlinear Effects ◽  
Form Solution ◽  
Vibration Absorbers ◽  
Bladed Disk ◽  
Tuned Vibration Absorbers ◽  
Engine Order ◽  
Bladed Disk Assembly

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly over- or under-tuned relative to n) can be implemented to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances near the excitation order of interest and that the resulting system is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-tuned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections and nonlinear effects are considered, and multi-DOF and general-path absorbers are employed.

scholarly journals Local Convergence of Solvers with Eighth Order Having Weak Conditions

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 70
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Closed Form Solution ◽  
Nonlinear Problems ◽  
Form Solution ◽  
Fréchet Derivative ◽  
Not Given ◽  
Eighth Order ◽  
Iterative Schemes ◽  
Frechet Derivative ◽  
First Order ◽  
Lipschitz Constants

In particular, the problem of approximating a solution of an equation is of extreme importance in many disciplines, since numerous problems from diverse disciplines reduce to solving such equations. The solutions are found using iterative schemes since in general to find closed form solution is not possible. That is why it is important to study convergence order of solvers. We extended the applicability of an eighth-order convergent solver for solving Banach space valued equations. Earlier considerations adopting suppositions up to the ninth Fŕechet-derivative, although higher than one derivatives are not appearing on these solvers. But, we only practiced supposition on Lipschitz constants and the first-order Fŕechet-derivative. Hence, we extended the applicability of these solvers and provided the computable convergence radii of them not given in the earlier works. We only showed improvements for a certain class of solvers. But, our technique can be used to extend the applicability of other solvers in the literature in a similar fashion. We used a variety of numerical problems to show that our results are applicable to solve nonlinear problems but not earlier ones.

Theory for Multilayered Anisotropic Plates With Weakened Interfaces

1996 ◽  
Vol 63 (4) ◽  
pp. 1019-1026 ◽  
Author(s):  
Zhen-qiang Cheng ◽  
A. K. Jemah ◽  
F. W. Williams
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Layer Model ◽  
General Representation ◽  
Anisotropic Plates ◽  
First Order ◽  
Multilayered Plates ◽  
Interface Parameters ◽  
Zigzag Theory ◽  
Special Case

Rigorous kinematical analysis offers a general representation of displacement variation through thickness of multilayered plates, which allows discontinuous distribution of displacements across each interface of adjacent layers so as to provide the possibility of incorporating effects of interfacial imperfection. A spring-layer model, which has recently been used efficiently in the field of micromechanics of composites, is introduced to model imperfectly bonded interfaces of multilayered plates. A linear theory underlying dynamic response of multilayered anisotropic plates with nonuniformly weakened bonding is presented from Hamilton’s principle. This theory has the same advantages as conventional higher-order theories over classical and first-order theories. Moreover, the conditions of imposing traction continuity and displacement jump across each interface are used in modeling interphase properties. In the special case of vanishing interface parameters, this theory reduces to the recently well-developed zigzag theory. As an example, a closed-form solution is presented and some numerical results are plotted to illustrate effects of the interfacial weakness.

scholarly journals Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
M. P. Markakis
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous Systems ◽  
Closed Form Solution ◽  
First Integrals ◽  
Form Solution ◽  
Second Order ◽  
Two Dimensional ◽  
First Order ◽  
Abel Equations

Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1) equations). Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1) equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form) have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.

scholarly journals Analysis of Real-Time Control Systems using First-Order Continuization

10.29007/8nq6 ◽  
2020 ◽  
Author(s):  
Maximilian Gaukler
Keyword(s):  
Control Systems ◽  
Real Time ◽  
Continuous Time ◽  
Real Time Control ◽  
Control Loops ◽  
Time Dynamics ◽  
First Order ◽  
Time Control ◽  
Formal Framework ◽  
Continuous Time System

Experience Report: Real-Time control systems can be difficult to analyze due to the mixture of discrete-time and continuous-time dynamics. This difficulty is particularly pronounced if the timing is non-periodic, e.g., due to network or execution effects. Still, most control loops behave similar to a purely continuous-time system disturbed by a small discretization error, which is exploited by Bak and Johnson (2015) in the method of Continuization. This paper uncovers limitations of that work and presents an extension, First-Order Continuization, based on a new formal framework that recovers previous results and eases future development.

Mechanical Buckling of Functionally Graded Cylindrical Shells Based on the First Order Shear Deformation Theory

2007 ◽  
Author(s):  
Ramin Narimani ◽  
Mehdi Karami Khorramabadi ◽  
Payam Khazaeinejad
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Form Solution ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
First Order

Buckling analysis of simply supported functionally graded cylindrical shells under mechanical loads is presented in this paper. The Young’s modulus of the shell is assumed to vary as a power form of the thickness coordinate variable. The shell is assumed to be under three types of mechanical loadings, namely, axial compression, uniform external lateral pressure, and hydrostatic pressure loading. The equilibrium and stability equations are derived based on the first order shear deformation theory. Resulting equations are employed to obtain the closed-form solution for the critical buckling load. The influences of dimension ratio, relative thickness and the functionally graded index on the critical buckling load are studied. The results are compared with the known data in the literature.

Lyapunov-based missile terminal guidance with short time convergence considering seeker’s first-order lag

2016 ◽  
Vol 231 (10) ◽  
pp. 1935-1950 ◽  
Author(s):  
Duo Zheng ◽  
Defu Lin ◽  
Xinghua Xu ◽  
Zhenxuan Cheng
Keyword(s):  
Lyapunov Method ◽  
Closed Form Solution ◽  
Form Solution ◽  
Guidance System ◽  
First Order ◽  
Guidance Law ◽  
Higher Order Derivative ◽  
Kalman Filter Algorithm ◽  
Short Time ◽  
Terminal Guidance

This paper presents a novel guidance law considering the seeker dynamics for manoeuvring targets to achieve short homing time guidance using the Lyapunov method. Based on linear and nonlinear kinematics, a Lyapunov-based guidance law is synthesised to compensate for the seeker’s first-order lag. The closed-form solution of the proposed guidance system is also derived analytically. To implement the proposed guidance law, a Kalman filter algorithm is presented to extract the line-of-sight rate and its higher order derivative. Numerical simulations are carried out to demonstrate the effectiveness of the proposed guidance law under various conditions. Monte Carlo simulations are also performed to test the robustness against measurement noise.

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