Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control...

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Bibliographic Details
Published in:Nonlinear dynamics Vol. 102; no. 3; pp. 1611 - 1626
Main Authors: Dabiri, Arman, Poursina, Mohammad, Machado, J. A. Tenreiro
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.11.2020
Springer Nature B.V
Subjects:
Acceleration
Algorithms
Automotive Engineering
Canonical forms
Chains
Classical Mechanics
Computing time
Control
Control methods
Control stability
Control systems
Control theory
Dynamic models
Dynamic stability
Dynamical Systems
Engineering
Inverse dynamics
Mechanical Engineering
Multibody systems
Nonlinear control
Optimal control
Original Paper
Stability criteria
System dynamics
Torque
Tracking errors
Vibration
Parallel computing
Optimal control
Multibody dynamics
Open-chain system
Fractional control
PID
LQR
Closed-chain system
Computed-torque control
Divide and conquer algorithm
ISSN:0924-090X, 1573-269X
Online Access:Get full text
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Summary:In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-05954-3