Abstract
AbstractThis article investigates underactuated systems' energy shaping control by controlled Lagrangian (CL) method. The existence of CL based control depends on a set of matching conditions, which are usually in terms of partial differential equations (PDEs). In this work, the matching conditions are derived and simplified for underactuation‐degrees‐two systems. Moreover, the solvability conditions are provided for a class of systems satisfying Assumptions 1 and 2, based on which the controlled energy could be explicitly solved. By the proposed matching solution method, the desired equilibrium can be effectively assigned. The proposed matching controller is implemented for a strongly coupled single rigid body system with six degrees of freedom for the first time. Smooth state feedback control laws guaranteeing asymptotic stability of the system are presented. The range of the control parameters could be obtained based on the positive definiteness of reshaped closed‐loop energy. Simulations for comparison with relate work show the effectiveness of the theoretical results.
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