The Problem of Robust Compensation for Systems with Unmodeled Dynamics

1989 ◽  
Author(s):  
J. D. Cobb
Keyword(s):  
Unmodeled Dynamics ◽  
Robust Compensation

Adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics

2021 ◽  
pp. 014233122098563
Author(s):  
Fei Shen ◽  
Xinjun Wang ◽  
Xinghui Yin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Dead Zone ◽  
Small Neighborhood ◽  
Unmodeled Dynamics ◽  
Stochastic Nonlinear Systems ◽  
Dynamic Surface ◽  
Barrier Lyapunov Function ◽  
Full State

This paper investigates the problem of adaptive control based on Barrier Lyapunov function for a class of full-state constrained stochastic nonlinear systems with dead-zone and unmodeled dynamics. To stabilize such a system, a dynamic signal is introduced to dominate unmodeled dynamics and an assistant signal is constructed to compensate for the effect of the dead zone. Dynamic surface control is used to solve the “complexity explosion” problem in traditional backstepping design. Two cases of symmetric and asymmetric Barrier Lyapunov functions are discussed respectively in this paper. The proposed Barrier Lyapunov function based on backstepping method can ensure that the output tracking error converges in the small neighborhood of the origin. This control scheme can ensure that semi-globally uniformly ultimately boundedness of all signals in the closed-loop system. Two simulation cases are proposed to verify the effectiveness of the theoretical method.

The Design of a Chain of Spherical Stephenson Mechanisms for a Gearless Robotic Pitch-Roll Wrist

2005 ◽  
Vol 128 (2) ◽  
pp. 422-429 ◽  
Author(s):  
S. Hernandez ◽  
S. Bai ◽  
J. Angeles
Keyword(s):  
Unmodeled Dynamics ◽  
Manufacturing Cost ◽  
Interference Avoidance ◽  
Dimensional Synthesis ◽  
Bevel Gears ◽  
Industrial Manipulators ◽  
Differential Mechanism ◽  
Gear Trains ◽  
Robot Performance ◽  
A Chain

Although bevel-gear robotic wrists are widely used in industrial manipulators due to their simple kinematics and low manufacturing cost, their gear trains function under rolling and sliding, the latter bringing about noise and vibration. Sliding is inherent to the straight teeth of the bevel gears of these trains. Moreover, unavoidable backlash introduces unmodeled dynamics, which mars robot performance. To alleviate these drawbacks, a gearless pitch-roll wrist is currently under development for low backlash and high stiffness. The wrist consists of spherical cam-rollers and spherical Stephenson linkages, besides two roller-carrying disks that drive a combination of cams and Stephenson mechanisms, the whole system rotating as a differential mechanism. The paper focuses on the design of the chain of spherical Stephenson mechanisms. The problem of the dimensional synthesis is addressed, and interference avoidance is discussed. An embodiment of the concept is also included.

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