带有非匹配扰动的连铸结晶器振动位移系统自适应反步滑模控制

Adaptive backstepping sliding mode control for oscillation displacement system of continuous casting mold with unmatched perturbations

针对伺服电机驱动的连铸结晶器振动位移系统中存在非匹配的参数不确定性、干扰等问题,提出一种基于非线性扩张状态观测器(ESO)的自适应反步滑模控制方法.首先,基于双曲正切函数和高增益构造ESO对系统中的非匹配扰动进行估计.然后,利用反步法将非匹配扰动视为匹配扰动进行处理,并在每一步设计自适应积分滑模控制器,以消除非匹配扰动对系统的影响.另外,在反步设计的后两步引入了积分滑模滤波器用于估计前一步虚拟控制律的导数.理论分析表明,所设计的ESO能够保证估计误差收敛到原点附近的小邻域内;所设计的控制器能够保证闭环系统所有信号有界,并且,通过选取适当的参数能够保证系统状态可渐近收敛到原点.最后,通过仿真结果验证了所提出方法的有效性.

An adaptive backstepping sliding mode control algorithm based on the nonlinear extended state observer(ESO)is proposed for an oscillation displacement system of continuous casting mold driven by servo motor,in which there exists unmatched perturbations including parameter uncertainties and disturbances.Firstly,based on the hyperbolic tangent function and a high gain,two nonlinear ESOs are constructed to estimate the unmatched perturbations.Then,by means of the backstepping technique,the unmatched perturbations can be viewed as the matched ones to be handled,and the adaptive integral sliding mode controller is designed in each step of the backstepping procedure to eliminate the effect of the unmatched perturbations.In addition,two integral sliding mode filters are introduced to estimate the time derivatives of the previous step virtual controllers in the last two steps.It can be proved that the estimation errors of the ESO are convergent to a small neighborhood of the origin,and all of the signals of the closed-loop system are bounded,and the system states can be asymptotically stable under the conditions of selecting appropriate parameters.Finally,simulation results show the effectiveness of the proposed method.