Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

scholarly journals DOA estimation based on sum–difference coarray with virtual array interpolation concept

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yarong Ding ◽  
Shiwei Ren ◽  
Weijiang Wang ◽  
Chengbo Xue
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Doa Estimation ◽  
Superior Performance ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Virtual Array ◽  
Simulation Results ◽  
The Difference ◽  
Coprime Array

AbstractThe sum–difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum–difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.

Contrastive Analysis between Shifosi Reservoir Impoundment Test and Numerical Simulation Results

2013 ◽  
Vol 353-356 ◽  
pp. 2600-2603
Author(s):  
Jun Pan ◽  
Te Leng ◽  
Yang Liu
Keyword(s):  
Numerical Simulation ◽  
Model Prediction ◽  
Simulation Method ◽  
Measured Data ◽  
Water Levels ◽  
Model Parameters ◽  
Contrastive Analysis ◽  
Reservoir Impoundment ◽  
Simulation Results ◽  
Sensitive Parameters

Using numerical simulation method for project simulating prediction, the built mathematical models of actual conditions often need to be generalized, consequently, there are some inevitably deviations between model prediction results and the measured data, which requires the adjustment of model parameters to improve the model. This paper made a comparative analysis of Shifosi reservoir impoundment test observation water levels and model prediction water levels, adjust the model parameters and boundary conditions, then it would get the sensitive parameters that affect the accuracy and stability of numerical model and boundary condition and improve the fitting degree of measured data and simulation results.

scholarly journals DOA Estimation Based on Sum-Difference Coarray with Virtual Array Interpolation Concept

2021 ◽  
Author(s):  
Yarong Ding ◽  
Shiwei Ren ◽  
Weijiang Wang ◽  
Chengbo Xue
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Doa Estimation ◽  
Superior Performance ◽  
Norm Minimization ◽  
Atomic Norm ◽  
Virtual Array ◽  
Simulation Results ◽  
The Difference ◽  
Coprime Array

Abstract The sum-difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum-difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.

PERMANENCE AND COMPLEXITY OF THE ECO-EPIDEMIOLOGICAL MODEL WITH IMPULSIVE PERTURBATION

2008 ◽  
Vol 01 (02) ◽  
pp. 121-132 ◽  
Author(s):  
SHULIN SUN ◽  
LANSUN CHEN
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Perturbation Method ◽  
Analytical Method ◽  
Small Amplitude ◽  
Floquet Theory ◽  
Epidemiological Model ◽  
Asymptotically Stable

In this paper, we investigate the eco-epidemiological model with impulsive perturbation. Using Floquet theory and small amplitude perturbation method, we prove that the boundary periodic solution is asymptotically stable if the impulsive parameter satisfies some conditions. Moreover, the permanence of the system is discussed by analytical method. Finally, the complexity of the system is verified by numerical simulation.

scholarly journals Calibration of nonlocal damping model based on numerical simulation results

2019 ◽  
Vol 6 (3) ◽  
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Least Squares Method ◽  
Element Model ◽  
Model Parameters ◽  
3D Finite Element ◽  
Distributed Load ◽  
Vibration Process ◽  
Simulation Results ◽  
Damping Model

The paper is devoted to polymer composite beams dynamic behavior simulation. The nonlocal damping model is used as a model of the internal friction. The vibration process is considered in this paper using the beam with fixed ends as an example. Equation of beam motion considering nonlocal damping is solved by Galerkin method to develop the model. The required number of eigenmodes is obtained for the beam under an instantly applied distributed load. The influence of nonlocal damping model parameters variation on the beam vibration process simulation results is considered under a periodic deterministic distributed load. The calibration of nonlocal damping model consists of defining its parameter known as influence distance which characterize the level of the nonlocal properties in material. Calibration is carried out with the least squares method using the numerical simulation data. For this purpose the results of 3D finite element modeling of thermoset vinyl ester fiber reinforced plastic beam vibrations under the instantly applied load were used. The 3D finite element model of the beam was created in SIMULIA Abaqus taking into account the orthotropic properties of the material. The calibrated model was justified for the beams with changed geometry. The results presented in this paper were obtained during the research for the PhD thesis.

scholarly journals Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

2021 ◽  
Vol 5 (1) ◽  
pp. 193
Author(s):  
Nurmaini Puspitasari ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Trisilowati Trisilowati
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Parasite Population ◽  
Asymptotically Stable ◽  
Population Extinction ◽  
Simulation Results ◽  
Extinction Point

This article discussed about a dynamic analysis of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.This article discussed about a dynamic analysis of the symbiotic model of The dynamics of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. is the main focus of this study. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination begins by identifying the conditions for the existence of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.[VM1]  [VM1]To add a mathematical effect to the article. There can be added mathematical models produced in the study at the end of this section.

scholarly journals Evolution of disturbance wavepackets in an oscillatory Stokes layer

2014 ◽  
Vol 752 ◽  
pp. 543-571 ◽  
Author(s):  
Christian Thomas ◽  
Christopher Davies ◽  
Andrew P. Bassom ◽  
P. J. Blennerhassett
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Floquet Theory ◽  
Nonlinear Evolution ◽  
Family Tree ◽  
Temporal Development ◽  
Stokes Layer ◽  
Linear And Nonlinear ◽  
Simulation Results ◽  
Successive Generations

AbstractNumerical simulation results are presented for the linear and nonlinear evolution of disturbances in a flat Stokes layer. The response to a spatially localised impulsive forcing is investigated and it is found that the spatial–temporal development of the flow displays an intriguing family-tree-like structure, which involves the birth of successive generations of distinct wavepacket components. It is shown that some features of this unexpected structure can be predicted using the results of a linear stability analysis based on Floquet theory.

Avalanche Features in Silicon Schottky-FETs in Accordance with Numerical Simulation Results

2006 ◽  
Vol 65 (16) ◽  
pp. 1533-1546
Author(s):  
Yu. Ye. Gordienko ◽  
S. A. Zuev ◽  
V. V. Starostenko ◽  
V. Yu. Tereshchenko ◽  
A. A. Shadrin
Keyword(s):  
Numerical Simulation ◽  
Simulation Results

Tail shapes lead to different propulsive mechanisms in the body/caudal fin undulation of fish

2020 ◽  
pp. 095440622096768
Author(s):  
Jialei Song ◽  
Yong Zhong ◽  
Ruxu Du ◽  
Ling Yin ◽  
Yang Ding
Keyword(s):  
Numerical Simulation ◽  
Aspect Ratio ◽  
High Efficiency ◽  
The Body ◽  
Caudal Fin ◽  
Fish Model ◽  
Swimming Efficiency ◽  
Simulation Results ◽  
Propulsive Mechanism ◽  
High Depth

In this paper, we investigate the hydrodynamics of swimmers with three caudal fins: a round one corresponding to snakehead fish ( Channidae), an indented one corresponding to saithe ( Pollachius virens), and a lunate one corresponding to tuna ( Thunnus thynnus). A direct numerical simulation (DNS) approach with a self-propelled fish model was adopted. The simulation results show that the caudal fin transitions from a pushing/suction combined propulsive mechanism to a suction-dominated propulsive mechanism with increasing aspect ratio ( AR). Interestingly, different from a previous finding that suction-based propulsion leads to high efficiency in animal swimming, this study shows that the utilization of suction-based propulsion by a high- AR caudal fin reduces swimming efficiency. Therefore, the suction-based propulsive mechanism does not necessarily lead to high efficiency, while other factors might play a role. Further analysis shows that the large lateral momentum transferred to the flow due to the high depth of the high- AR caudal fin leads to the lowest efficiency despite the most significant suction.

Sign in / Sign up

Export Citation Format

Share Document