Dynamic modeling and adaptive fuzzy terminal sliding mode controller with nonlinear observer of a 2-(PUU)2R hybrid mechanism

Abstract

This article proposes a new spatial 2-(PUU)2R hybrid mechanism that can perform the three degrees of freedom translation and one degree of freedom rotation and presents an analysis of the dynamics of the mechanism. An adaptive fuzzy terminal sliding mode controller with nonlinear observer for the hybrid mechanism is proposed to achieve a precise trajectory tracking, which could be utilized in solving the problems of the hybrid mechanism caused by model uncertainties, varying payloads, and external disturbances. Firstly, through the interrelation between the constraints, the 6 × 6 Jacobian matrix and 6 × 6 × 6 Hessian matrix for the mechanism are derived. Furthermore, dynamic modeling is established based on the virtual work principle, through which the characteristics of dynamic modeling can be proved. To achieve high-precision position tracking, a nonlinear observer was introduced to feed into the terminal sliding mode control which had improved the mechanism’s ability to resist the external disturbances. In addition, the chattering caused by the terminal sliding mode control was eliminated by approximating the switching gain with the usage of adaptive fuzzy logic in a finite time. Finally, a series of numerical simulations are carried out to prove the validity of the proposed approach, and the results verify better robustness and higher precision for the trajectory tracking than proportional–integral–derivative and sliding mode control.