伺服电机驱动的连铸结晶器振动位移系统反步滑模控制
Backstepping sliding mode control for continuous cast mold oscillation displacement system driven by servo motor

针对伺服电机通过偏心轴连杆机构驱动的连铸结晶器振动位移系统中存在减速比加工误差、偏心轴机械 零位初始偏差和负载转矩扰动等问题, 本文设计了一种基于双幂次趋近律和扩张状态观测器(ESO)的反步滑模控 制器. 首先, 针对偏心轴转角到结晶器位移非线性关系逆解的非唯一性, 可通过分段函数法建立结晶器位移到偏心 轴转角一一对应的映射函数关系; 其次, 针对不可测的减速比加工误差和负载转矩扰动可采用扩张状态观测器来 实时估计, 以削弱扰动对系统跟踪性能的影响; 最后, 采用一种具有二阶滑模特性且有限时间收敛的双幂次趋近律 以提高收敛速度和削弱抖振. 仿真对比结果表明, 本文所设计的控制器能有效实现连铸结晶器位移的渐近跟踪, 并 对系统扰动具有较强的鲁棒性.
In this paper, a backstepping sliding mode controller based on the double power reaching law and extended state observer (ESO) is designed for the problems of the machining error of reduction ratio, the initial deviation of the eccentric shaft mechanical zero and load torque disturbance, which exist in oscillation displacement system of the continuous casting mold driven by servo motor through the eccentric shaft linkage. Firstly, for the non-uniqueness of the nonlinear inverse relationship from the position angle of eccentric shaft to the displacement of continuous casting mold, the correspondence nonlinear mapping function from the displacement of mold to the position angle of eccentric shaft is established by piecewise function. Secondly, for the non measurable machining error of reduction ratio and the load torque disturbances the ESO is designed to weaken the influence of disturbance on the system tracking performance. Finally, double exponential reaching law with second-order sliding mode characteristics and finite time convergence characteristics is used to improve the convergence speed and weaken the chattering. The Simulation results show that the controller designed in this paper can achieve asymptotic tracking to the displacement of continuous casting mold and have robustness to the disturbance of system.