基于双曲正切函数的二阶时变参数扩张状态观测器
Time-varying parameter second-order extended state observer based on hyperbolic tangent function

当传统扩张状态观测器(ESO)的状态初值与系统的状态初值相差较大时, 普遍存在微分峰值现象. 为了消 除这种现象, 本文给出了用双曲正切非线性函数构造ESO的一般形式, 并且用Lyapunov 函数证明了二阶ESO的误差 系统为渐近稳定. 然后又利用双曲正切函数自身饱和的特性, 设计出一种时变ESO, 可以实现微分峰值的有效抑制. 最后, 把这种ESO的仿真结果与经典ESO的仿真结果进行对比, 表明这里提出的ESO能够有效抑制微分峰值现象, 并可以获得系统状态变量和非线性扰动的精确估计.
The derivative peaking phenomenon in the traditional extended state observer (ESO) usually occurs when the initial difference between the initial value of the traditional ESO and the initial value of the system state variable is large. To deal with this phenomenon, we derive the general form of the ESO based on the nonlinear hyperbolic tangent function, and use Lyapunov functions to prove the asymptotic stability of the second-order ESO error system. Then, we make use of the self saturation characteristic of the hyperbolic tangent function to design a second-order ESO with time-varying parameters, which can effectively suppress the derivative peaking phenomenon. Comparing the simulation result of this type of ESO with that of the traditional ESO, we find that the proposed ESO can effectively inhibit the derivative peaking phenomenon, and obtain the accurate estimation for both system state variables and nonlinear disturbances.