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迭代学习控制律可以为重复执行的控制过程提供合适的控制输入以实现零误差跟踪。该文从优化的角度给出了2类迭代学习控制律,一类以未来时刻跟踪误差最小作为优化目标,按目标函数的最速下降方向进行迭代,也称为压缩映射迭代学习控制律;另一类以全部时刻跟踪误差以及迭代控制增量最小作为优化目标,最优解即为迭代学习控制增量,也称为最小二次型迭代学习控制律。在第二类迭代学习控制律的基础上,充分考虑反馈闭环内作动器的饱和约束,将其转化为控制系统输入增量的约束,因此构成凸规划问题,进而用二次规划方法求解。基于一类既有连续信号又有离散信号的混合受限闭环反馈控制系统,针对作动器的饱和特性,搭建了在饱和和非饱和阶段相互切换的系统动态模型。仿真验证了上述算法的有效性,并对比了两类算法的收敛性能,同时也表明压缩映射迭代学习控制律对系统饱和非线性具有一定的鲁棒性能,而二次规划方法可以充分考虑作动器约束,避免饱和发生,同时具有很好的误差收敛特性。
Iterative learning control laws can provide suitable control inputs for repetitively executed control processes to achieve zero error tracking. In this paper, two kinds of iterative learning control laws are given from the perspective of optimization. One type of iterative learning control law is to minimize the tracking error in the future and iterate in the direction of steepest descent of the objective function. The class aims at optimizing the tracking error and the minimum increment of iterative control. The optimal solution is iterative learning control increment, also known as the least-quadratic iterative learning control law. On the basis of the second type of iterative learning control law, the saturation constraints of feedback closed-loop actuators are fully considered and converted into constraints of input increment of control system, so convex programming problem is formed and then solved by quadratic programming method. Based on a class of hybrid closed-loop closed-loop feedback control systems with both continuous and discrete signals, a dynamic model of the system switching between saturation and non-saturation phases is established for the saturation characteristics of the actuator. The simulation results verify the effectiveness of the above algorithm and compare the convergence performance of the two algorithms. At the same time, it shows that the Iterative Learning Control Law of Compression Mapping has certain robustness to the system nonlinearity, while the quadratic programming method can fully consider the action Constraints, to avoid saturation occurs, while having good error convergence characteristics.