一阶不确定系统的固定时间收敛扰动观测器

In this paper, non-recursive fixed-time convergent disturbance observers are proposed to deal with the total disturbance fast observation problem for a first-order uncertain system. The primary disturbance observer is designed based on the observer error amplification strategy and bi-limit homogeneous approximation theory. Due to nonlinearity of power functions, a variant of the proposed disturbance observer is presented to obtain the noise tolerance ability. The observer error amplification strategy is actually a special high gain approach, based on which the domination scope of the power functions in the correction terms is extended. At the same time, the convergence rate of the observer is accelerated, and the parameters tuning process is simplified. By choosing a reasonable amplifier and removing the low-order power functions in the correction terms, the structure of the disturbance observer is simplified, and the noise tolerance ability is enhanced. In addition, a fixed-time convergent robust disturbance observer is designed based on generalized super-twisting algorithm as well. Except the detailed theoretical derivation, numerical simulations, with or without measurement noise, are carried out to verify the feasibilities of the proposed three types of the disturbance observers. And, an typical extended state observer is employed for comparison. Finelly, the characteristics and applicability of the disturbance observers are discussed.