基于新型趋近律的柔性机械臂滑模-最优组合控制

Sliding Mode and Optimal Combined Control of Flexible Manipulator Based on New Reaching Law

为提高柔性机械臂的控制精度,提出一种基于滑模控制与最优控制相结合的组合控制方式。通过Lagrange法和假设模态法构建其动力学模型,进而运用奇异摄动理论对柔性臂进行解耦,获得慢变和快变子系统。对于慢变子系统,采用滑模控制实现轨迹跟踪,提出一种新型趋近律,该趋近律在幂次趋近律基础上加入变速趋近项,引入系统状态变量,动态调整趋近速率,同时增加指数项提高趋近速度,使用双曲正切函数替代符号函数以抑制抖振;对于快变子系统,采用最优控制进行振动抑制。MATLAB仿真结果表明,该组合控制方法相比于纯滑模控制,具有更好的动态性能和鲁棒性能。

In order to improve the control accuracy of flexible manipulator,a combined control method based on sliding mode control and optimal control was proposed.The dynamic model was constructed by Lagrange method and hypothetical mode method,and then the flexible arm was decoupled by singular perturbation theory to obtain slow and fast varying subsystems.For the slowly varying subsystem,the sliding mode control was used to realize trajectory tracking,a new reaching law was proposed.Based on the power reaching law,the variable speed reaching term was added,the system state variable was introduced,the reaching rate was dynamically adjusted,the exponential term was added to improve the reaching speed,and the hyperbolic tangent function was used to replace the symbolic function to suppress chattering.For the fast varying subsystem,the optimal control was used to suppress the vibration.MATLAB simulation results show that the combined control method has better dynamic performance and robustness than pure sliding mode control.