Finite-Iteration Learning Error-Tracking Control for a Class of Uncertain Discrete-Time Systems
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摘要: 本文针对一类在有限时间内执行重复任务的不确定离散时间系统轨迹跟踪问题, 提出一种有限次迭代学习误差跟踪控制方法. 首先, 构造不依赖于参考轨迹的期望误差轨迹, 放宽传统迭代学习控制中的初值一致条件, 且离散形式的期望误差轨迹设计仅需已知每次迭代的误差初值, 简化设计要求. 其次, 通过在迭代轴上构建饱和迭代吸引律, 设计带有干扰补偿的迭代学习控制器, 并推导出跟踪误差的稳态误差带和满足精度要求所需的最大迭代次数表达式, 根据期望精度选择控制器参数, 在参数设计阶段保证系统鲁棒性, 实现跟踪误差有限次迭代收敛. 最后, 通过数值仿真和实验结果验证所提控制方法的有效性.Abstract: In this paper, a finite-iteration learning error-tracking control method is proposed for the trajectory tracking problem of a class of uncertain discrete-time system that perform repetitive tasks in finite time. Firstly, a desired error-trajectory that is independent of the reference trajectory is constructed to relax the strict initial condition requirement in traditional iterative learning control. Moreover, the design of the discrete form of the expected error trajectory only requires the initial error values for each iteration, simplifying the design requirements. Secondly, by constructing a saturated iterative attraction law along the iterative axis, an iterative learning controller with disturbance compensation is designed, and the steady-state error band of the tracking error and the expression of the maximum number of iterations required to meet the accuracy requirements are derived. The controller parameters are selected based on the expected accuracy, and the robustness of the system is guaranteed in the parameter design stage to achieve finite-iterative convergence of the tracking error. Finally, the effectiveness of the proposed control method is verified through numerical simulation and experimental results.
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图 2 不同初始状态下输出角速度$y_{15} $和参考角速度$y_{r} $
Fig. 2 Output angular velocity $y_{15} $ and reference angular velocity $y_{r} $ under different initial conditions
图 3 不同初始状态下误差轨迹$e_{15} $和期望误差轨迹$ e_{15}^{\ast }$
Fig. 3 Error trajectory $e_{15} $ and desired error trajectory $e_{15}^{\ast } $ under different initial conditions
图 5 期望误差轨迹$e_{k}^{\ast } $和跟踪误差$e_{k} $
Fig. 5 Expected error trajectory $e_{k}^{\ast } $ and tracking error $e_{k} $
图 7 输出跟踪$ y_k$、误差跟踪$e_{k} $和性能指标
Fig. 7 Output tracking $ y_k$, error tracking $e_{k} $ and performance index
表 1 永磁同步电机参数
Table 1 Permanent magnet synchronous motor parameters
物理量 参数 值 惯性系数 $ J/({\rm{kg}}\cdot {\rm{m}}^{2}) $ 0.0275 负载转矩 $ T_{L}/({\rm{N}}\cdot {\rm{m}}) $ $ 0.5\sin x_{1} $ 磁通 $ \psi _{f} /{\rm{Wb}} $ 0.109 极对数 $ n_{p} $ 4 摩擦系数 $ B / ({\rm{Nm/rad/s}}) $ 0.0012 
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