Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model

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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Adaptive vibration control of a flexible marine riser via the backstepping technique and disturbance adaptation

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331216684010 ◽

2017 ◽

Vol 40 (5) ◽

pp. 1407-1416 ◽

Cited By ~ 5

Author(s):

Fang Guo ◽

Yu Liu ◽

Zhijia Zhao ◽

Fei Luo

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Boundary Control ◽

Vibration Suppression ◽

Original Position ◽

Backstepping Technique ◽

Marine Riser ◽

Partial Differential ◽

Disturbance Adaptation ◽

Adaptive Boundary Control

This paper proposes an adaptive boundary control for vibration suppression of a flexible marine riser system. The dynamic model of the riser system is described in the form of a nonlinear nonhomogeneous hyperbolic partial differential equation and four ordinary differential equations. In a proper mathematical manner, the backstepping technique, Lyapunov’s direct method, and the adaptive technique are utilized to design an adaptive boundary control for the vibration suppression of the riser system, and also for the global stabilization of the riser within a small neighbourhood of its original position. In addition, a parameter adaptive law is designed to compensate for the system parametric uncertainties and a disturbance adaptation law is proposed to eliminate the effects of boundary disturbance. The uniformly bounded stability of the closed-loop riser system is achieved through rigorous Lyapunov analysis with no discretization or simplification of the partial differential equation dynamics model of the system. Simulation results are presented to illustrate the effectiveness of the proposed control.

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The Boundary Proportion Differential Control Method of Micro-Deformable Manipulator with Compensator Based on Partial Differential Equation Dynamic Model

Micromachines ◽

10.3390/mi12070799 ◽

2021 ◽

Vol 12 (7) ◽

pp. 799

Author(s):

Xiangli Pei ◽

Ying Tian ◽

Minglu Zhang ◽

Ruizhuo Shi

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Dynamic Model ◽

Control Method ◽

System Modeling ◽

Working Environment ◽

Partial Differential ◽

External Interference ◽

Differential Control ◽

Differential Control Method

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.

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