Adaptive filtered control for uncertain electro-hydraulic servo systems with time-varying output constraints
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摘要:
针对电液伺服系统位置跟踪控制中存在的输出约束和不确定性问题，提出一种基于正切型时变障碍Lyapunov函数的输出约束自适应滤波控制方法。构造具有时变约束边界的正切型时变障碍Lyapunov函数，通过时变边界函数的参数设置，使系统输出具有较好的瞬态和稳态性能；设计径向基函数（ RBF ） 神经网络及权重自适应学习律，在线逼近由模型不确定性和未知干扰组成的复合干扰，并将逼近值用于反馈控制；采用二阶指令滤波反步法设计状态反馈控制律和误差补偿机制, 避免反步设计中“计算爆炸”的问题，同时消除滤波误差，提高系统位置跟踪精度；依据Lyapunov稳定性理论证明闭环系统中所有误差信号的收敛性。仿真结果表明：系统的稳态误差在所提方法下约为3.48×10−8 m，相比于其他控制方法，跟踪误差始终约束在时变的约束边界内，跟踪精度和控制性能均得到提升。
Abstract:To address such problems as output constraints and uncertainties in the position tracking control of electro-hydraulic servo systems, an adaptive filter control method with output constrained was proposed based on the time-varying tangent barrier Lyapunov function. Firstly, a tangent barrier Lyapunov function with a time-varying constrained boundary was derived. By setting the parameters of the time-varying boundary function, the output of the system achieved good transient and steady performance.Secondly, a radial basis function (RBF) neural network and a weight adaptive learning law were designed to approximate the compound disturbance composed of model uncertainties and unknown disturbances online, and the approximate value was used for feedback control.Then, a second-order command filter backstepping method was used to design a state feedback control law and an error compensation mechanism, so as to avoid“computation explosion”in the backstepping design and eliminate the filtering error so that the position tracking accuracy of the system could be improved. Finally, the convergence of all error signals in a closed-loop system was proven by the Lyapunov stability theory. The simulation results show that the steady-state tracking error of the system under the proposed method is about 3.48×10−8 m.Compared with other control methods, the tracking error is always constrained within the time-varying constraint boundary, and control performance and tracking accuracy are both improved.
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图 3 电液伺服系统的时变输出约束自适应滤波控制系统结构
Figure 3. Structure of adaptive filtered control system with time-varying output constraints of electro-hydraulic servo system
表 1 某650 mm轧机电液伺服系统标称参数
Table 1. Nominal parameters of an electro-hydraulic servo system of 650 mm rolling mill
参数 数值 $ {{{K_{\text{a}}}} / {({{\text{A}} \mathord{\cdot {\vphantom {{\text{A}} {\text{V}}}} } {\text{V}}}}} ^{-1})$ 0.0125 ${C_{\mathrm{d}}}$ 0.61 $ {\omega \mathord{\left/ {\vphantom {\omega {\text{m}}}} \right. } {\text{m}}} $ 0.025 $ {\rho /{\left( {{\text{kg}}\cdot{{\text{m}}^{{-3}}}} \right)}} $ 850 ${{{K_{{\text{sv}}}}}/{( {{{\text{m}} \cdot {\text{A}}}} }}^{-1})$ 0.01 ${{{m_0}} / {{\text{kg}}}}$ 1500 $ {{{P_{\text{S}}}} \mathord{\left/ {\vphantom {{{P_{\text{S}}}} { {{\text{MPa}}} }}} \right. } { {{\text{MPa}}} }} $ 24 $C_{\mathrm{t}}/({\mathrm{m}}^5\cdot({\mathrm{N}}\cdot{\mathrm{s}})^{-1} )$ 5×10−16 $ {V / {{{\text{m}}^{\text{3}}}}} $ 3.768×10−3 $ {{{K_0}} / {\left( {{ { {{\text{N}} \cdot{\text{m}^{-1}}}} {}}} \right)}} $ 1.25×109 $ {{{A_{\text{p}}}} / {{{\text{m}}^{\text{2}}}}} $ 0.01256 ${{{\beta _{\text{e}}}} \mathord{\left/ {\vphantom {{{\beta _{\text{e}}}} {{\text{P}}{{\text{a}}_{}}}}} \right. } {{\text{P}}{{\text{a}}_{}}}}$ 7×108 $ {{{B_{{\text{p0}}}}} / {\left( {{\text{N}} \cdot {{\text{s}} \cdot {\text{m}^{-1}}}} \right)}} $ 2.25×106 ${{{F_{{\text{L0}}}}} \mathord{\left/ {\vphantom {{{F_{{\text{L0}}}}} {\text{N}}}} \right. } {\text{N}}}$ 2×106 
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