Dynamic Model Simplification and Fuzzy Rule Control of Flexible Manipulator

The dynamic equations governing the servo system of the flexible manipulator incorporating second-order mode and two-dimensional deformation is too complicated to be used as the controlled object. To achieve accurate control, the dynamic equation must be simplified to make it accurate and easy to calculate. Firstly, the Lagrange equation is employed to establish the system dynamics equation. Four simplified methods of dynamics model are proposed, and the deformation is obtained from the original equation and four simplified dynamics equations with different parameters are compared. Then, based on fuzzy rules, an enhanced fuzzy compensation SMC strategy is introduced, aiming to enhance control performance. Through simulation analysis and physical control experiments, it has been demonstrated that utilizing the tanh function within the fuzzy compensation SMC approach can alleviate the chattering phenomenon and decrease acceleration errors. The outcomes also indicate that this control strategy exhibits low variance and standard deviation, underscoring its stability and consistency. Consequently, the combined control approach advocated in this study is deemed highly applicable to flexible manipulators, offering a substantial enhancement in control accuracy.