Partial differential equation modeling and vibration control for a nonlinear 3D rigid‐flexible manipulator system with actuator faults

2019 ◽  
Vol 29 (11) ◽  
pp. 3793-3807 ◽  
Author(s):  
Fangfei Cao ◽  
Jinkun Liu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Vibration Control ◽  
Flexible Manipulator ◽  
Equation Modeling ◽  
Actuator Faults ◽  
Partial Differential ◽  
Differential Equation Modeling

NUMERICAL SIMULATIONS OF A NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATION MODELING PHYTOPLANKTON AGGREGATION

2015 ◽  
Vol 23 (04) ◽  
pp. 1550032 ◽  
Author(s):  
NADJIA EL SAADI ◽  
ALASSANE BAH
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stochastic Partial Differential Equation ◽  
Stochastic Equation ◽  
Numerical Solutions ◽  
Equation Modeling ◽  
Partial Differential ◽  
Nonlinear Reaction ◽  
Differential Equation Modeling ◽  
Parameter Values

In this paper, we are interested in the numerical simulation of a nonlinear stochastic partial differential equation (SPDE) arising as a model of phytoplankton aggregation. This SPDE consists of a diffusion equation with a chemotaxis term and a branching noise. We develop and implement a numerical scheme to solve this SPDE and present its numerical solutions for parameter values corresponding to real conditions in nature. Further, a comparison is made with two deterministic versions of the SPDE, that are advection–diffusion equations with linear and nonlinear reaction terms, to emphasize the efficiency of the stochastic equation in modeling the aggregation behavior in phytoplankton.

scholarly journals Study of an Elliptic Partial Differential Equation Modeling the Ocean Flow in Arctic Gyres

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Susanna V. Haziot
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Elliptic Partial Differential Equation ◽  
Equation Modeling ◽  
Conformal Map ◽  
Uniqueness Of Solutions ◽  
Partial Differential ◽  
Rotating Sphere ◽  
Mercator Projection ◽  
Differential Equation Modeling

AbstractWe study the ocean flow in Arctic gyres using a recent model for gyres derived in spherical coordinates on the rotating sphere. By projecting this model onto the plane using the Mercator projection, we obtain a semi-linear elliptic partial differential equation in an unbounded domain, difficulty which is then overcome by projecting the PDE onto the unit disk via a conformal map. We then study existence, regularity and uniqueness of solutions for constant and linear vorticity functions.

scholarly journals Weighted multiple model adaptive boundary control for a flexible manipulator

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041988646
Author(s):  
Weicun Zhang ◽  
Qing Li ◽  
Yuzhen Zhang ◽  
Ziyi Lu ◽  
Cheng Nian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Control ◽  
Control Strategy ◽  
Flexible Manipulator ◽  
Multiple Model ◽  
Parameter Uncertainties ◽  
Partial Differential ◽  
Local Boundary ◽  
Adaptive Boundary Control

In this article, a weighted multiple model adaptive boundary control scheme is proposed for a flexible manipulator with unknown large parameter uncertainties. First, the uncertainties are approximatively covered by a finite number of constant models. Second, based on Euler–Bernoulli beam theory and Hamilton principle, the distributed parameter model of the flexible manipulator is constructed in terms of partial differential equation for each local constant model. Correspondingly, local boundary controllers are designed to control the manipulator movement and suppress its vibration for each partial differential equation model, which are based on Lyapunov stability theory. Then, a novel weighted multiple model adaptive control strategy is developed based on an improved weighting algorithm. The stability of the overall closed-loop system is ensured by virtual equivalent system theory. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed control strategy.

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