Journal ArticleDOI
Constraint-following Servo Control Design for Mechanical Systems:
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TLDR
In this article, the servo control design problem for constraint-following is thoroughly discussed in an algebraic setting in which a second order constraint is adopted, and the complete solution to this problem is provided in analytical form.Abstract:
A mechanical system is required to obey a set of constraints. The tools to accomplish this performance requirement are a set of servo controls1 that is, the servo controls are to generate the appropriate constraint force. In this article, the servo control design problem for constraint-following is thoroughly discussed. The problem is formulated as an algebraic setting in which a second order constraint is adopted. The control is a solution to the problem, whose projection to a subspace is used to ensure conformation to the constraint. The complete solution to this problem is provided in analytical form. It is shown that the environmentally constrained system simply adopts the minimum form of the complete solution. The setting presented here helps to broaden the scope of traditional Lagrangian mechanics.read more
Citations
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Journal ArticleDOI
Adaptive robust approximate constraint-following control for mechanical systems
Ye-Hwa Chen,Xinrong Zhang +1 more
TL;DR: The objective is to design control which renders approximate constraint following, and it is able to demonstrate guaranteed system performance, regardless of the uncertainty.
Journal ArticleDOI
Application of the Udwadia–Kalaba approach to tracking control of mobile robots
TL;DR: The control torques required to control the mobile robot so that it precisely satisfies the trajectory requirements which are represented by an arbitrary function of time are obtained explicitly and in closed form by solving Udwadia–Kalaba equation.
Journal ArticleDOI
Adaptive robust control methodology for active roll control system with uncertainty
TL;DR: An adaptive robust control scheme based on the Udwadia and Kalaba’s approach is proposed to drive the active roll control system to follow the pre-specified constraint approximately, which renders the ARCS practically stable and achieves constraints following maneuvering.
Journal ArticleDOI
Optimal Design of Constraint-Following Control for Fuzzy Mechanical Systems
TL;DR: An adaptive robust control for the mechanical system for approximate constraint-following is proposed and it is proved that the global solution to the resulting optimization problem always exists and is unique.
Journal ArticleDOI
Adaptive robust control for dual avoidance–arrival performance for uncertain mechanical systems
TL;DR: It is proved that, with the proposed control input, the avoidance constraint is completely followed and the arrival constraint is closely followed; hence, the dual avoidance–arrival problem is carried out.
References
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Book
Robust and Optimal Control
TL;DR: This paper reviewed the history of the relationship between robust control and optimal control and H-infinity theory and concluded that robust control has become thoroughly mainstream, and robust control methods permeate robust control theory.
Book
Manifolds, tensor analysis, and applications
TL;DR: In this paper, the authors provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists, including manifolds, dynamical systems, tensors, and differential forms.
Journal ArticleDOI
Stabilization of constraints and integrals of motion in dynamical systems
J. Baumgarte,J. Baumgarte +1 more
TL;DR: In this article, it is shown how the analytical relations can be satisfied in a stabilized manner in order to improve the numerical accuracy of the solution of the differential equations, which leads to a modified differential system which is often stable in the sense of Ljapunov.