为了提高伺服电机系统的动态响应速度、抗干扰能力,解决输入饱和的问题,课题组基于扩张状态观测器(extended state observer,ESO)和抗饱和输入(anti-saturation input,ASI)辅助系统设计了伺服电机的运动控制方案.首先,建立了伺服电机的数学模型,将系统阻尼和系统不确定性归为扰动,将扰动设为系统的扩张状态;然后在等效反步滑模控制(backstepping sliding mode control,BSMC)的基础上,引入了ASI辅助系统和ESO,解决输入饱和问题,并抑制内、外干扰;采用双曲正切饱和函数替换符号函数以减小滑模控制的抖振;通过李雅普诺夫稳定性方法检验所提出控制器的稳定性.最后,将基于ESO和ASI的等效反步滑模控制与比例积分微分(proportional integral differential,PID)控制、滑模控制(sliding mode control,SMC)进行仿真对比.结果表明:相较于传统PID和SMC控制器,课题组所设计的控制器可以实现伺服电机的无超调快速响应,解决了输入饱和问题,并具有较好的抗干扰能力和减小输入冲击的作用.
Equivalent Backstepping Sliding Mode Control of Servo Motors Based on Extended State Observer and Anti-Saturation Input
In order to improve the dynamic response speed of the servo motor system,anti-disturbance ability and solve the input saturation problem,the group designed the motion control of the servo motor based on the expanded state observer(ESO)and anti-saturation input(ASI)auxiliary system.Firstly,the mathematical model of the servo motor was established,and the system damping and system uncertainty are categorized as perturbations,and the perturbation was set to be the expansion state of the system;then the ASI auxiliary system and the ESO were introduced on the basis of equivalent backstepping sliding mode control(BSMC)to solve the input saturation problem and suppress the internal and external disturbances;the hyperbolic tangent saturation function was used to replace the sign function to reduce the jitter of the sliding mode control;the stability of the proposed controller was proved by the Lyapunov stability method.Finally,the equivalent backstepping sliding mode control based on ESO and anti-saturation input was simulated and compared with proportional integral differential(PID)and sliding mode control(SMC).The results show that compared with the traditional PID and SMC controllers,the designed controller can realize the fast response of the servo motor without overshooting,solve the input saturation problem,as well as have better disturbance rejection ability and reduce the input shock.
servo motorESO(extended state observer)ASI(anti-saturation input)assist systemBSMC(backstepping sliding mode control)Lyapunov stability
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