In order to suppress the nonlinear vibration during the motion of a flexible manipulator,a model-free hybrid control strategy of trajectory tracking and vibration suppression based on a novel online observation of disturb forces is proposed. The Lagrange equation and singular perturbation method are employed to model and decouple the dynamics of the manipulator,which are decomposed into a slow subsystem representing rigid motion and a fast subsystem representing flexible vibration. Considering the complexity of modeling and uncertainty of model parameters,PD control method is adopted to realize trajectory tracking,and model-free adaptive control algorithm is proposed to realize nonlinear vibration control of flexible links. To solve the control divergence problem caused by unknown external disturb forces,a modified extended state observer is proposed to online estimate and real-time compensate the disturb force,which can improve the convergence performance of model-free vibration control algorithm effectively. The simulation results show that the proposed method can effectively suppress the vibration of the flexible manipulator in the presence of disturb force,and has good dynamic performance and robustness.
| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |