自适应线性自抗扰控制器的设计

自抗扰控制器对于抑制不确定的扰动有良好的效果,但其控制器参数较多且整定困难。为了实现自适应的线性自抗扰控制器,对线性自抗扰控制器的参数整定策略展开了研究。首先,设计了基于观测误差的线性扩张观测器参数自适应整定算法。接着,设计了自抗扰控制器线性反馈环节的参数的自适应整定算法。最后,利用李雅普诺夫方法,证明上述自适应整定算法得到的参数可以保证扩张状态观测器的观测误差和被控系统最终输出误差都收敛至零。实验结果表明:精密气浮运动平台低速工况下,自适应线性自抗扰控制器的参数在0.8s内即可迅速完成整定计算;线性扩张观测器观测误差绝对值小于2nm;被控精密气浮运动平台的速度波动不大于5%。自适应线性自抗扰控制器实现了控制器参数在线整定,控制器的性能表现满足要求。

Design of an adaptive linear active disturbance rejection controller

An Active Disturbance Rejection Controller (ADRC) can suppress uncertain disturbances effectively; however, its parameter tuning is difficult. In order to develop an adaptive linear ADRC, the parameter tuning strategy of a linear ADRC was studied. First, an adaptive tuning algorithm based on observational errors was designed for a linear extended state observer. Then, an adaptive tuning algorithm for the parameters of the ADRC linear feedback component was designed. Finally, by using the Lyapunov method, it was proved that the parameters obtained by the above adaptive tuning algorithms ensure that both the observation errors of the extended state observer and the output errors of the controlled system converge to zero. Experimental results indicate that, under low velocity conditions, the parameters of the proposed linear ADRC can be quickly tuned within 0.8 s; the observational errors of the linear extended state observer are less than 2 nm, and the velocity fluctuations of the precision air-bearing platform are within 5%. The proposed adaptive linear ADRC performs online tuning of the controller parameters, and the controller performance is satisfactory.