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| 基于李雅普诺夫直接法的电液力控制系统稳定性研究 |
| Study on stability of electro-hydraulic force control system based on Lyapunov direct method |
| 投稿时间：2019-01-25 |
| DOI： |
| 中文关键词: 电液力控制系统 李雅普诺夫直接法 二阶液压补偿器 系统稳定性 负载刚度 液压弹簧刚度 |
| 英文关键词: electro-hydraulic force control system Lyapunov direct method second-order hydraulic compensator system stability load stiffness hydraulic spring stiffness |
| 基金项目:国家自然科学基金资助项目(51675387). |
| 作者 | 单位 | E-mail | | 陈帅杰 | 武汉科技大学冶金装备及其控制教育部重点实验室,湖北 武汉,430081 | 956149398@qq.com | | 金晓宏 | 武汉科技大学冶金装备及其控制教育部重点实验室,湖北 武汉,430081
武汉科技大学机械传动与制造工程湖北省重点实验室,湖北 武汉,430081 | | | 黄浩 | 武汉科技大学冶金装备及其控制教育部重点实验室,湖北 武汉,430081
武汉科技大学机械传动与制造工程湖北省重点实验室,湖北 武汉,430081 | | | 张邵峰 | 武汉科技大学冶金装备及其控制教育部重点实验室,湖北 武汉,430081 | |
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| 中文摘要: |
| 电液力控制系统是一种高度非线性的时变复杂系统,其传递函数的分子中存在振荡频率较低的二阶微分环节,导致系统状态趋于振荡甚至不稳定,尤其是在系统负载刚度远小于液压弹簧刚度的情况下。针对上述问题,本文运用流量连续性方程和系统动力学方程,建立了适用于全工作范围的阀控缸系统的数学模型,在此基础上得出与输出变量相关的三阶微分方程。然后利用李雅普诺夫直接法的反演方式求解系统稳定条件,将其转变为二阶液压补偿器,并给出了具体的推导过程和构造方案。通过Simulink仿真对比分析了系统分别加入传统双惯性环节和二阶液压补偿器的校正效果,讨论了液压弹簧刚度与负载刚度的变化对系统特性的影响。结果表明,二阶液压补偿器能有效提高系统的稳定性并抑制谐振峰值；对于不同频率的正弦输入信号,系统可在0.12 s内达到稳态,最大稳态误差不超过3.7%；当负载刚度远小于液压弹簧刚度时,随着负载刚度的减小,系统响应速度变慢,稳态误差增大；在液压缸活塞接近于行程终端位置的工况条件下,与双惯性环节校正效果相比,系统在二阶液压补偿器作用下的上升时间、峰值时间和调整时间分别缩短68%、59%和37%,稳态误差减小。 |
| 英文摘要: |
| Electro-hydraulic force control system is a highly nonlinear and time-varying complex system. The numerator of its transfer function has second-order differential element with low oscillation frequency, which causes oscillation and even instability of the system state, particularly in the case of system’s load stiffness being much smaller than the hydraulic spring stiffness. To address this problem, flow continuity equation and system dynamics equations were used to establish a mathematical model of the valve-controlled cylinder system for the full working range, and a third-order differential equation related to the output variable was deduced. The inversion technique of Lyapunov direct method was used to solve the system’s stability condition which was then transformed into a second-order hydraulic compensator, and the specific derivation process and construction scheme were given. The correction effects of traditional double inertial element and the designed second-order hydraulic compensator applied to the electro-hydraulic force control system respectively were compared by means of Simulink simulation, and how the changes of load stiffness and hydraulic spring stiffness affect the system characteristics was also discussed. The results show that the second-order hydraulic compensator can improve system stability and suppress resonance peak effectively. For sinusoidal input signals with different frequencies, the system can reach its steady state within 0.12 s and the maximum steady-state error is no more than 3.7%. When the load stiffness is far less than the hydraulic spring stiffness, with the decrease of load stiffness, the system response speed becomes slower and the steady-state error increases. Under the condition that piston of the hydraulic cylinder is close to terminal position of its stroke, compared with those of the system corrected by the traditional double inertial element, the rise time, peak time and settling time of the system with the second-order hydraulic compensator are shortened by 68%, 59% and 37%, respectively, and the steady-state error is also reduced. |
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