中文摘要：

针对阀控非对称液压缸位置伺服系统存在参数摄动和不确定外负载的问题，提出了一种鲁棒H∞自适应反步控制器的设计方法。在设计控制器时，通过对子系统选择合适的Lyapunov函数，避免了高阶系统中对虚拟控制量重复求导的问题；使系统的跟踪误差满足鲁棒日。性能指标，增强了系统的鲁棒性；考虑到控制输入前的不确定参数会导致所设计控制律和自适应律互相嵌套，把系统模型中的时变参数进行变量置换，并对整个系统构造了一个合适的Lyapunov函数，从而解决了该问题；最后对闭环系统的稳定性进行了证明。仿真结果表明，与PID控制器相比，所设计的控制器使系统的输出对给定信号的跟踪速度更快，具有更小的跟踪误差，且对参数变化有较强的鲁棒性。

英文摘要：

A robust H∞ adaptive control method based on backstepping theory was proposed for position servo system of asymmetric hydraulic cylinder in the presence of parameter uncertainties and external disturbances. In the controller design process, a proper Lyapunov function of the subsystem was selected to avoid the problem caused by repeated differentiations of high-order system. The robust control method guaranteed the output tracking error satisfied the H∞ performance. Considering the uncertain parameter in front of the control input could lead to the nesting problem caused by the mutual inclusion of the control law and parameter adaptive law, the uncertain parameter in the model of the system is replaced and a proper Lyapunov function was constructed, which solved the problem. Finally, the stability of the closed loop system was proved based on Lyapunov function approach. Simulation results verified that the proposed controller enabled the output of the closed loop to track the given signal at a faster speed, to achieve smaller tracking error and better robustness to parameter variety by contrast with PID control method.