scholarly journals Asymptotically Convergent Higher-Order Switching Differentiator

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 185
Author(s):  
Jang-Hyun Park ◽  
Tae-Sik Park ◽  
Seong-Hwan Kim
Keyword(s):  
Time Derivative ◽  
Higher Order ◽  
Time Varying ◽  
Tracking Errors ◽  
Order Tracking ◽  
Barbalat’S Lemma ◽  
Derivatives Of

A novel switching-differentiator (SD) that can asymptotically track the time derivative of time-varying signal was previously proposed. This paper extends the previous SD to estimation of higher-order time derivatives. This study shows that higher-order time-derivatives can be estimated by connecting multiple SDs in cascade form. By successive applying the generalized Barbalat’s lemma, all higher-order tracking errors also approach zeros asymptotically. To illustrate the performance of the proposed higher-order switching differentiator, simulations were performed for estimating higher-order time-derivatives of a signal.

Trajectory and Vibration Control of a Single-Link Flexible-Joint Manipulator Using a Distributed Higher-Order Differential Feedback Controller

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
John T. Agee ◽  
Zafer Bingul ◽  
Selcuk Kizir
Keyword(s):  
Trajectory Tracking ◽  
Higher Order ◽  
Feedback Controller ◽  
Step Response ◽  
Position Measurement ◽  
Tracking Errors ◽  
Flexible Joint ◽  
Nonminimum Phase ◽  
Step Input ◽  
Flexible Joint Manipulator

The trajectory tracking in the flexible-joint manipulator (FJM) system becomes complicated since the flexibility of the joint of the FJM superimposes vibrations and nonminimum phase characteristics. In this paper, a distributed higher-order differential feedback controller (DHODFC) using the link and joint position measurement was developed to reduce joint vibration in step input response and to improve tracking behavior in reference trajectory tracking control. In contrast to the classical higher-order differential (HOD), the dynamics of the joint and link are considered separately in DHODFC. In order to validate the performance of the DHODFC, step input, trajectory tracking, and disturbance rejection experiments are conducted. In order to illustrate the differences between classical HOD and DHODFC, the performance of these controllers is compared based on tracking errors and energy of control signal in the tracking experiments and fundamental dynamic characteristics in the step response experiments. DHODFC produces better tracking errors with almost same control effort in the reference tracking experiments and a faster settling time, less or no overshoot, and higher robustness in the step input experiments. Dynamic behavior of DHODFC is examined in continuous and discontinues inputs. The experimental results showed that the DHODFC is successful in the elimination of the nonminimum phase dynamics, reducing overshoots in the tracking of such discontinuous input trajectories as step and square waveforms and the rapid damping of joint vibrations.

A C0 three-node triangular element based on preprocessing approach for thick sandwich plates

2017 ◽  
Vol 21 (6) ◽  
pp. 1820-1842
Author(s):  
Wu Zhen ◽  
Ma Rui ◽  
Chen Wanji
Keyword(s):  
Transverse Shear ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Higher Order ◽  
Triangular Element ◽  
Shear Stresses ◽  
Sandwich Plates ◽  
Transverse Shear Stress ◽  
Transverse Shear Stresses ◽  
Derivatives Of

This paper will try to overcome two difficulties encountered by the C0 three-node triangular element based on the displacement-based higher-order models. They are (i) transverse shear stresses computed from constitutive equations vanish at the clamped edges, and (ii) it is difficult to accurately produce the transverse shear stresses even using the integration of the three-dimensional equilibrium equation. Invalidation of the equilibrium equation approach ought to attribute to the higher-order derivations of displacement parameters involved in transverse shear stress components after integrating three-dimensional equilibrium equation. Thus, the higher-order derivatives of displacement parameters will be taken out from transverse shear stress field by using the three-field Hu–Washizu variational principle before the finite element procedure is implemented. Therefore, such method is named as the preprocessing method for transverse shear stresses in present work. Because the higher-order derivatives of displacement parameters have been eliminated, a C0 three-node triangular element based on the higher-order zig-zag theory can be presented by using the linear interpolation function. Performance of the proposed element is numerically evaluated by analyzing multilayered sandwich plates with different loading conditions, lamination sequences, material constants and boundary conditions, and it can be found that the present model works well in the finite element framework.

Expansions of the mildly relativistic dispersion function for nearly perpendicular electron cyclotron ray tracing

1999 ◽  
Vol 61 (1) ◽  
pp. 121-128 ◽  
Author(s):  
I. P. SHKAROFSKY
Keyword(s):  
Ray Tracing ◽  
Computer Programs ◽  
Higher Order ◽  
Electron Cyclotron ◽  
Dispersion Function ◽  
Relativistic Dispersion ◽  
Plasma Dispersion ◽  
Derivatives Of ◽  
Cyclotron Harmonic ◽  
Experienced Difficulty

To trace rays very close to the nth electron cyclotron harmonic, we need the mildly relativistic plasma dispersion function and its higher-order derivatives. Expressions for these functions have been obtained as an expansion for nearly perpendicular propagation in a region where computer programs have previously experienced difficulty in accuracy, namely when the magnitude of (c/vt)2 (ω−nωc)/ω is between 1 and 10. In this region, the large-argument expansions are not yet valid, but partial cancellations of terms occur. The expansion is expressed as a sum over derivatives of the ordinary dispersion function Z. New expressions are derived to relate higher-order derivatives of Z to Z itself in this region of concern in terms of a finite series.

On the use of jerk and snap in condition monitoring of machinery – review and case studies

2021 ◽  
Vol 63 (8) ◽  
pp. 457-464
Author(s):  
S Lahdelma
Keyword(s):  
Condition Monitoring ◽  
Large Scale ◽  
Early Stage ◽  
Time Derivative ◽  
Additional Insight ◽  
Rolling Bearings ◽  
Monitoring Applications ◽  
Derivatives Of ◽  
Insight Into ◽  
Peak Value

The time derivatives of acceleration offer a great advantage in detecting impact-causing faults at an early stage in condition monitoring applications. Defective rolling bearings and gears are common faults that cause impacts. This article is based on extensive real-world measurements, through which large-scale machines have been studied. Numerous laboratory experiments provide additional insight into the matter. A practical solution for detecting faults with as few features as possible is to measure the root mean square (RMS) velocity according to the standards in the frequency range from 10 Hz to 1000 Hz and the peak value of the second time derivative of acceleration, ie snap. Measuring snap produces good results even when the upper cut-off frequency is as low as 2 kHz or slightly higher. This is valuable information when planning the mounting of accelerometers.

scholarly journals Mathematical modelling of the mass-spring-damper system - A fractional calculus approach

2012 ◽  
Vol 22 (5) ◽  
pp. 5-11 ◽  
Author(s):  
José Francisco Gómez Aguilar ◽  
Juan Rosales García ◽  
Jesus Bernal Alvarado ◽  
Manuel Guía
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Mathematical Modelling ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Time Derivative ◽  
System A ◽  
Fractional Differential ◽  
Mass Spring ◽  
Derivatives Of

In this paper the fractional differential equation for the mass-spring-damper system in terms of the fractional time derivatives of the Caputo type is considered. In order to be consistent with the physical equation, a new parameter is introduced. This parameter char­acterizes the existence of fractional components in the system. A relation between the fractional order time derivative and the new parameter is found. Different particular cases are analyzed

Open Higher Order Continuous-Time Dynamic Model with Mixed Stock and Flow Data and Derivatives of Exogenous Variables

1991 ◽  
Vol 7 (3) ◽  
pp. 404-408 ◽  
Author(s):  
K. Ben Nowman
Keyword(s):  
Continuous Time ◽  
Higher Order ◽  
Flow Data ◽  
Continuous Time Model ◽  
Exogenous Variables ◽  
Time Model ◽  
Time Dynamic ◽  
Mixed Stock ◽  
Gaussian Estimation ◽  
Derivatives Of

This paper is concerned with deriving formulae for higher order derivatives of exogenous variables for use in estimating the parameters of an open secondorder continuous time model with mixed stock and flow data and first and second order derivatives of exogenous variables which are not observable. This should provide the basis for the future estimation of continuous time models in a range of applied areas using the new Gaussian estimation computer program developed by Nowman [4].

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