采用李雅普诺夫函数的电液伺服系统反馈线性化控制  

Feedback Linearization Control for an Electro-Hydraulic Servo System Using Lyapunov Functions

作　　者：俞珏[1] 庄健[1] 于德弘[1] 

机构地区：[1]西安交通大学机械工程学院,西安710049

出　　处：《西安交通大学学报》2014年第7期71-76,123,共7页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51375363);西安市科技计划资助项目(CX12504)

摘　　要：针对电液伺服系统的参数时变、强非线性,致使传统控制算法难以实现高精度高稳定性的位置输出的问题,提出了一种采用李雅普诺夫函数(Lyapunov)的反馈线性化控制器。该控制器通过反馈线性化方法将电液伺服系统的位置输出控制在预定轨迹上,使系统满足准确性、快速性的要求。针对液压系统中的油液体积弹性模量参数存在着较大的不确定性且难以在线测量、不精确的参数将削弱反馈线性化的控制效果甚至导致系统失稳的问题,采用Lyapunov直接法对反馈线性化控制器进行再设计。通过系统的综合误差构建形式简单的Lyapunov函数,进而给出最优参数估计值的取值方法,且满足Lyapunov函数的导函数为非正定,从而保证了整个系统的渐进稳定性。仿真结果表明,改进的反馈线性化控制器能够很好地兼顾控制精度和系统的鲁棒性,获得较好的控制效果。A feedback linearization controller for an electro-hydraulic servo system through using Lyapunov functions is proposed to solve the problem that position output with high-precision and high-stability is difficult to obtain from traditional control algorithms due to the time-varying parameter and strong nonlinear characteristics of the system.The controller applies a feedback linearization method to drive position outputs to a predetermined trajectory,making the system response accurate and rapid.Since the bulk modulus of oil in hydraulic system is highly uncertain and its parameters cannot be measured on-line,inaccurate estimation of the parameters will weaken control performances of the controller and may even cause instability of the control system.Hence,the Lyapunov direct method is applied to redesign the feedback linearization controller.A simple Lyapunov function is constructed through system tracking errors,and a method is given to calculate the optimal value for parameter estimation.The optimal estimation of parameters meets the requirement that the derivative of the Lyapunov function is non-positive and guarantees the asymptotic stability of the system.Simulation results show that the proposedcontroller has satisfactory tracking performance with high control accuracy and strong robustness to parameter variation.

关 键 词：李雅普诺夫函数 电液伺服系统 反馈线性化 参数时变 体积弹性模量 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]