Controller design for 2-DOF underactuated mechanical systems based on controlled Lagrangians and application to Acrobot control

作     者：Maoqing LI 

作者机构：The Seventh Research DivisionBeihang UniversityBeijing 100191China 

出 版 物：《Frontiers of Electrical and Electronic Engineering in China》 (中国电气与电子工程前沿（英文版）)

年 卷 期：2009年第4卷第4期

页      面：417-439页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：60334030 Ministry of Education of the People's Republic of China, MOE: 20050006024 

主　　题：underactuated mechanical systems controlled Lagrangians(CL)method gyroscopic forces matching condition stabilization Acrobot 

摘      要：On the basis of controlled Lagrangians,a controller design is proposed for underactuated mechanical systems with two degrees of freedom.A new kinetic energy equation(K-equation)independent of the gyroscopic forces is found due to the use of their *** a result,the necessary and sufficient matching condition comprises the new K-equation and the potential energy equation(P-equation)cascaded,the regular condition,and the explicit gyroscopic ***,for two classes of input decoupled systems that cover the main benchmark examples,the new K-equation,respectively,degenerates from a quasilinear partial differential equation(PDE)into an ordinary differential equation(ODE)under some choice and into a homogeneous linear PDE with two kinds of explicit general *** from one of the general solutions,the obtained smooth state feedback controller for the Acrobots is of a more general ***,a constant fixed in a related paper by the system parameters is converted into a controller parameter ranging over an open interval along with some new nonlinear terms *** what is mentioned in the related paper,some categories of the Acrobots cannot be stabilized with the existing interconnection and damping assignment passivity based control(IDA-PBC)*** a contribution,the system can be locally asymptotically stabilized by the selection of the new controller parameter except for only one special case.