Connguration Flatness of Lagrangian Systems Underactuated by One Control
نویسندگان
چکیده
Lagrangian control systems that are diierentially at with at outputs that only depend on connguration variables are said to be connguration at. We provide a complete characterisation of connguration atness for systems with n degrees of freedom and n ?1 controls whose range of control forces only depends on connguration and whose Lagrangian has the form of kinetic energy minus potential. The method presented allows us to determine if such a system is connguration at and, if so provides a constructive method for nding all possible connguration at outputs. Our characterisation relates connguration atness to Riemannian geometry. We illustrate the method by two examples.
منابع مشابه
Configuration Flatness of Lagrangian Systems Underactuated by One Control
Lagrangian control systems that are differentially flat with flat outputs that depend only on configuration variables are said to be configuration flat. We provide a complete characterization of configuration flatness for systems with n degrees of freedom and n−1 controls whose range of control forces only depends on configuration and whose Lagrangian has the form of kinetic energy minus potent...
متن کاملExperimental control of a flexible link by the method of Controlled Lagrangian
The Controlled Lagrangian method is a branch of energy shaping methods that is designed to control underactuated mechanical systems. The method emp...
متن کاملCon guration Flatness of Lagrangian Systems Underactuated by One Control
Lagrangian control systems that are di erentially at with at outputs that only depend on con guration variables are said to be con guration at We provide a complete characterisation of con guration atness for systems with n degrees of freedom and n controls whose range of con trol forces only depends on con guration and whose Lagrangian has the form of kinetic energy minus potential The method ...
متن کاملTime-Invariant State Feedback Control Laws for a Special Form of Underactuated Nonlinear Systems Using Linear State Bisection
Linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. The specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. The basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...
متن کاملNonlinear Control and Reduction of Underactuated Systems with Symmetry I: Actuated Shape Variables Case
In this paper, we address nonlinear control and reduction of a class of high-order underactuated mechanical systems with kinetic symmetry called Class-I systems. Class-I systems are underactuated systems with actuated shape variables, decoupled inputs, and integrable normalized momentums (all to be de ned). We show that all Class-I underactuated systems can be transformed into cascade systems i...
متن کامل