一类非线性系统的一阶D型迭代学习控制

First-order D-type iterative learning control for a class of nonlinear systems

传统的D型迭代学习控制的控制律设计方案依赖于被控系统的相对度.为解决该问题以及相对度增益与高阶微分运算的问题,针对一类具有任意高阶相对度的非线性系统,提出了基于虚拟模型的一阶D型迭代学习控制设计方法.该方法的主要思想是与具有任意高阶相对度的非线性被控系统并联一个一阶子系统,构造一个相对度为1、相对度增益可以任意设计的虚拟模型,在此基础上设计一个一阶D型迭代学习控制律,使得虚拟模型能够实现期望轨迹的完全跟踪,从而实际被控系统在一定误差范围内实现期望轨迹的跟踪.仿真实例验证了所提方法的可行性与有效性.

The design scheme of the classical D-type iterative learning control law depends on the relative degree of the controlled systems. In order to solve this problem and the problems of the gain of relative degree, and of the higher-order differential operation, a first-order D-type iterative learning control design scheme was presented for a class of nonlinear systems with arbitrary higher relative degree based on the dummy model. The main idea of the method was constructing a dummy model with relative degree one and with gain of relative degree that can be designed arbitrary by connecting in parallel with a first-order subsystem for the nonlinear controlled systems with arbitrary higher relative degree. A first-order D-type iterative learning control law was designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example illustrates the feasibility and validity of the presented scheme.