高阶不确定非线性系统的线性自抗扰控制

Linear active disturbance rejection control for high-order nonlinear systems with uncertainty

针对一类具有内部动态和外部扰动未知的SISO高阶非线性系统,提出一种通用的线性自抗扰控制方案.该方案基于单参数调节的高增益观测器思想,分别设计线性跟踪微分器、线性扩张状态观测器和线性状态误差反馈控制律.利用Lagrange中值定理和Cauchy-Schwarz不等式将系统总扰动的微分值转化为关于系统估计和跟踪误差的函数,可以解决因系统控制增益未知所导致的控制量微分值难以预先确定的问题.在此基础上,基于Lyapunov稳定性定理证明闭环系统误差信号有界,并进一步分析得到系统估计和跟踪误差与控制器参数的定量关系,即都可以随观测器增益的增大而达到无限小.仿真比较结果验证了所提出方案的有效性,与韩式自抗扰控制方案相比,该方案结构简单,调节参数少,易于工程实现.

A general linear active disturbance rejection control(LADRC)approach is proposed for a class of single-input single-output(SISO)high-order nonlinear systems with subject to dynamical and external uncertainties.For every part of LADRC,the principle of high-gain observer with single parameter tuning is adopted to construct the linear tracking differentiator,the linear extended state observer and the linear state error feedback law.By using Lagrange mean value theorem and Cauchy-Schwarz inequality,the differential value of the system’s total disturbance is transformed into a function with respect to the system estimation and tracking errors,thus solving the problem that the differential value of control input is difficult to be determined in advance due to the unknown control gain.Then it is proved that the errors of the closed-loop system are bounded based on the Lyapunov stability theorem.By further analysis,the quantitative relationship between the estimation and tracking errors with the control parameters is derived,and both can be infinitely small as the observer gain increases.Numerical simulation results show the effectiveness of the proposed approach.Compared with Han’s ADRC,the proposed LADRC has simple structure,few tuning parameters and easy implementation in engineering.