Jerk Limited Input Shapers

2004 ◽  
Vol 126 (1) ◽  
pp. 215-219 ◽  
Author(s):  
Tarunraj Singh
Keyword(s):  
Time Delay ◽  
Closed Form ◽  
Transfer Functions ◽  
Filter Design ◽  
Limited Time ◽  
Design Technique ◽  
Closed Form Solutions ◽  
First Order ◽  
Damped Systems

The focus of this paper is on the design of jerk limited input shapers (time-delay filters). Closed form solutions for the jerk limited time-delay filter for undamped systems is derived followed by the formulation of the problem for damped systems. Since the jerk limited filter involves concatenating an integrator to a time-delay filter, a general filter design technique is proposed where smoothing of the shaped input can be achieved by concatenating transfer functions of first order, harmonic systems, etc.

Thermal Stresses in Compliantly Joined Materials

1990 ◽  
Vol 112 (1) ◽  
pp. 24-29 ◽  
Author(s):  
J. C. Glaser
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Thermal Stresses ◽  
Material Interface ◽  
Element Mesh ◽  
Closed Form Solutions ◽  
First Order ◽  
The Past ◽  
Compliant Layer ◽  
Analytical Relations

In the past several years there have been a number of papers published which provide closed-form solutions for the stresses in bonded layers of materials. These closed-form solutions offer a rapid method to obtain first-order stresses for materials which are joined together and the compliant layer between them. However, before using them, it is desirable to have some feeling as to the accuracy of the results from these closed-form equations. Comparisons between these analytical relations and other approaches found in published works on bonding and to finite element solutions for several example problems are given. An attempt is made to qualify these closed-form equations in terms of their accuracy, as compared to other methods of analysis. The effects of finite element mesh refinement on the material interface stress results are also given.

scholarly journals Two Integrable Classes of Emden–Fowler Equations with Applications in Astrophysics and Cosmology

2018 ◽  
Vol 73 (9) ◽  
pp. 805-814
Author(s):  
Stefan C. Mancas ◽  
Haret C. Rosu
Keyword(s):  
General Relativity ◽  
Closed Form ◽  
Nonlinear Oscillator ◽  
Reduction Method ◽  
Nonlinear Ordinary Differential Equations ◽  
Parametric Form ◽  
Closed Form Solutions ◽  
First Order ◽  
Class 1 ◽  
Elliptic Solutions

AbstractWe show that some Emden–Fowler (EF) equations encountered in astrophysics and cosmology belong to two EF integrable classes of the type ${\mathrm{d}^{2}}z/\mathrm{d}{\chi^{2}}=A{\chi^{-\lambda-2}}{z^{n}}$ for $\lambda=(n-1)/2$ (class 1), and $\lambda=n+1$ (class 2). We find their corresponding invariants which reduce them to first-order nonlinear ordinary differential equations. Using particular solutions of such EF equations, the two classes are set in the autonomous nonlinear oscillator the form ${\mathrm{d}^{2}}\nu/\mathrm{d}{t^{2}}+a\mathrm{d}\nu/\mathrm{d}t+b(\nu-{\nu^{n}})=0$, where the coefficients $a,b$ depend only on $\lambda,n$. For both classes, we write closed-form solutions in parametric form. The illustrative examples from astrophysics and general relativity correspond to two n = 2 cases from class 1 and 2, and one n = 5 case from class 1, all of them yielding Weierstrass elliptic solutions. It is also noticed that when n = 2, the EF equations can be studied using the Painlevé reduction method, since they are a particular case of equations of the type ${\mathrm{d}^{2}}z/\mathrm{d}{\chi^{2}}=F(\chi){z^{2}}$, where $F(\chi)$ is the Kustaanheimo-Qvist function.

scholarly journals Factorization method for some inhomogeneous Lienard equations

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 443
Author(s):  
O. Cornejo Perez ◽  
S. C. Mancas ◽  
H. C. Rosu ◽  
C. A. Rico-Olvera
Keyword(s):  
Differential Equations ◽  
Closed Form ◽  
Factorization Method ◽  
Closed Form Solutions ◽  
First Order ◽  
Liénard Equations ◽  
First Order Differential Equations

The factorization of inhomogeneous Li\'enard equations is performed showing that through the factorization conditions involved in the method one can obtain forcing terms for which closed-form solutions exist. Because of the reduction of order feature of factorization, the solutions are simultaneously solutions of first-order differential equations with polynomial nonlinearities. Several illustrative examples of such solutions are presented, generically having rational parts and consequently singularities.

scholarly journals Adaptive fuzzy practical tracking control for flexible-joint robots via command filter design

2020 ◽  
Vol 53 (5-6) ◽  
pp. 814-823
Author(s):  
Shuzhen Diao ◽  
Wei Sun ◽  
Wenxing Yuan
Keyword(s):  
Fuzzy System ◽  
Tracking Control ◽  
Filter Design ◽  
Limited Time ◽  
Flexible Joint ◽  
First Order ◽  
Flexible Joint Robots ◽  
Complexity Problem ◽  
Command Filter ◽  
Compensation Signal

This paper investigates the issue of finite-time tracking control for flexible-joint robots. In the design scheme, the unknown continuous function is identified by a fuzzy system. By introducing the command filter technique, “explosion of complexity” problem which arises from repeated differentiation of virtual controllers is avoided. Meanwhile, errors resulting from the first-order filters can be reduced with the introduced compensation signal. Besides, the proposed method ensures that the tracking performance could be achieved within a limited time. Eventually, the simulation is given to demonstrate the effectiveness of the proposed scheme.

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