Nonlinear variable damping integral sliding mode control for electro-hydrostatic actuator
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摘要:
对于电动静液作动器(EHA)，传统滑模控制器存在加速度信息难以获取，参数不易整定和控制信号抖振等问题，从而造成控制器很难应用于实际。针对以上问题，利用奇异摄动理论对EHA数学模型进行合理的降阶，从而使控制器设计避免了使用加速度信息。在此基础上，利用降阶模型设计了一种新型非线性变阻尼积分滑模控制器(NSMC)，该控制器可根据位置控制误差实现系统阻尼比由欠阻尼到过阻尼的自适应调节，能有效提高位置阶跃调节性能。设计了一种基于滤波器的不确定项估计器对EHA中存在的参数不确定性和外部扰动进行实时估计并补偿。滑模面积分项的引入和不确定项估计器的使用，一方面使控制器中无需使用切换函数，实现了EHA的无抖振滑模控制，另一方面使系统整个动态过程完全表现为滑动模态，从而可根据EHA控制指标直接整定滑模面参数，大大简化了参数整定过程。同时利用Lyapunov 稳定性理论对整个闭环系统和滑模面的稳定性进行了详细分析。分别与PI控制器、传统滑模控制器(SMC)和传统变阻尼滑模控制器(DVSMC)进行了详细的仿真分析比较，仿真结果表明NSMC能有效提高EHA位置跟踪性能和增强对参数不确定性和外部扰动的鲁棒性。
Abstract:For electro-hydrostatic actuator (EHA), the traditional sliding mode controller has many defects, such as control signal chattering, difficulty in acceleration information acquirement and controller parameters tuning, which make the controller difficult to be applied in practice. To solve the above problems, the reduced order mathematical model of EHA is obtained reasonably by using singular perturbation theory, which result in avoiding the use of acceleration information. On this basis, a novel nonlinear variable damping integral sliding mode controller (NSMC) is synthesized by employing the reduced order model. NSMC can adaptively adjust the system damping ratio from underdamping to overdamping according to the position control error, and can effectively improve the position step performance. Besides, filter-based uncertainty estimator is designed to estimate and compensate the parameter uncertainties and external disturbances of EHA in real time. Due to the introduction of sliding mode surface integral term and uncertainty estimator, switching function is unnecessary, on the one hand, the free-chattering sliding control can be achieved. On the other hand, the whole dynamic process is determined directly by the dynamic of sliding mode surface, so that sliding mode surface parameters can be tuned directly according to EHA’s control performance index, which greatly simplifies the parameters tuning process. Meanwhile, the stability of the whole closed-loop system and sliding mode surface is proved via Lyapunov stability theory. Finally, by comparing respectively with PI, conventional sliding mode (SMC) and damping variable sliding mode controller (DVSMC), the simulation results indicated that NSMC can effectively improve EHA position tracking performance and enhance the robustness of parameter uncertainty and external disturbance.
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图 3 $ {x_{\rm{d}}} = 0.01\;{\rm{m}} $时位置阶跃响应对比曲线
Figure 3. Position step response comparison curves with $ {x_{\rm{d}}} = 0.01\;{\rm{m}} $
图 4 $ {x_{\rm{d}}} = 0.01\;{\rm{m}} $时NSMC变阻尼与定阻尼位置阶跃响应对比曲线
Figure 4. Position step response comparison curves under NSMC variable damping and constant damping with $ {x_{\rm{d}}} = 0.01\;{\rm{m}} $
图 5 $ {x_{\mathrm{d}}} = 0.1\;{\mathrm{m}} $，1000 N阶跃外负载力时位置阶跃性能对比曲线
Figure 5. Position step performance comparison curves under 1000 N step external load force with $ {x_{\mathrm{d}}} = 0.1\;{\mathrm{m}} $
图 6 $ {x_{\rm{d}}} $为时变信号，存在复杂时变扰动时位置跟踪性能对比曲线
Figure 6. Position step performance comparison curves under complex time-varying disturbance when $ {x_{\rm{d}}} $ is time-varying sinusoidal signal
表 1 仿真参数
Table 1. Simulation parameters
参 数 数 值 液压缸活塞直径/$ \mathrm{m} $ 0.066 活塞杆直径/$ \mathrm{m} $ 0.045 活塞行程/$ \mathrm{m} $ 0.2 液压缸和IEHP总泄漏系数/$ {({10}^{-11}\mathrm{m}}^{3} $·s−1·Pa−1) 2.1 油液弹性模量/(108 N·m−2) 6.86 液压缸初始总体积$ /({10}^{-4}\;{\mathrm{m}}^{3}) $ 3 液压缸和负载总黏性摩擦系数/(N·m−1·s) 1100 活塞、活塞杆和负载质量/$({10}^{-6}\;\mathrm{k}\mathrm{g})$ 60 IEHP排量/(m−3·rad−1) 1.59 IEHP总粘性摩擦系数/(N·m·rad−1·s) 0.002 IEHP定子电阻$ /\mathrm{\Omega } $ 0.2 IEHP d、q轴等效电感/H 0.00187 IEHP 极对数 2 IEHP 永磁体磁链$ / $Wb 0.25 IEHP 转动惯量/kg·m2 0.0012 IEHP最高转速/(rad$ \cdot $s−1) 314 
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