In the hydraulic systems, the non-structural uncertainties such as the nonlinear friction will reduce the tracking accuracy for the hydraulic servo system. In this paper, an incomplete differential-based improved adaptive backstepping integral sliding mode control (ID-BIABISMC) is proposed to realize the position control for the hydraulic servo system based on the friction compensation. The backstepping-based control being integrated the integral sliding mode surface-based sliding mode control with the friction compensation are used to solve the problem of non-structural uncertainty of the hydraulic system. The incomplete differential is introduced to the adaptive update law, by which the low-pass filtering behavior in the incomplete differential is capable of effectively suppressing the interference caused by the pure differential mutation signal. Compared with the traditional adaptive backstepping control (ABC), adaptive sliding mode control (ASMC), the adaptive backstepping sliding mode control (ABSMC) and the proposed adaptive backstepping integral sliding mode control (IABISMC), the experimental results verify the high accuracy tracking performance of the proposed the incomplete differential-based improved adaptive backstepping integral sliding mode control (ID-BIABISMC). For the responses of the sinusoidal signal $40sin(0.2\pi \mathrm{t}+1.5\pi )+40mm$ and step signal with 30 mm, the corresponding tracking accuracy for ID-BIABISMC are 0.005 mm and 2.15 mm, respectively.

在液压系统中，非结构性不确定性（例如非线性摩擦）会降低液压伺服系统的跟踪精度。本文提出了一种基于不完全差分的改进自适应反步积分滑模控制（ID-BIABISMC），以实现基于摩擦补偿的液压伺服系统位置控制。将基于后推的控制与集成的基于滑模的基于表面的滑模控制与摩擦补偿集成在一起，用于解决液压系统的非结构不确定性问题。将不完全差分引入到自适应更新定律中，由此不完全差分中的低通滤波行为能够有效地抑制纯差分突变信号引起的干扰。与传统的自适应反步控制（ABC），自适应滑模控制（ASMC），自适应反步滑模控制（ABSMC）和拟议的自适应反步积分滑模控制（IABISMC）相比，实验结果验证了高精度跟踪性能提出的基于不完全差分的改进的自适应反步积分滑模控制（ID-BIABISMC）。对于正弦信号的响应 实验结果验证了所提出的基于不完全差分的改进的自适应反步积分滑模控制（ID-BIABISMC）的高精度跟踪性能。对于正弦信号的响应 实验结果验证了所提出的基于不完全差分的改进的自适应反步积分滑模控制（ID-BIABISMC）的高精度跟踪性能。对于正弦信号的响应$40罪（0。2\pi \mathrm{Ť}+\mathrm{1个}。5\pi ）+40米米$ 和30 mm的步进信号，ID-BIABISMC的相应跟踪精度分别为0.005 mm和2.15 mm。