论文标题
关于平面离散时间系统的确切线性化和控制
On the Exact Linearization and Control of Flat Discrete-time Systems
论文作者
论文摘要
本文通过通用的静态或动态反馈来解决平面非线性离散时间系统的确切线性化，这也可能取决于新输入的前移。我们首先研究一个问题，可以原理选择给定平面输出的前移，并随后如何通过合适的反馈来实际引入新的输入。对于可行输入的选择，得出了易于验证的条件。引入这样的新输入需要反馈，这通常可能不仅取决于此新输入本身，还取决于其前移。这类似于连续的时间案例，在这种情况下，依赖于闭环输入的时间衍生物（尤其是准静态）的反馈已经成功地用于自上世纪90年代以来平面系统的确切线性化。对于不取决于输入的前移的平面输出的系统，它显示了如何系统地构建新输入的系统，以使平面输出的相应前向偏移的总数很小。此外，可以表明，在这种情况下，线性化反馈的计算特别简单，并讨论了基于离散时间平坦的跟踪控制的随后设计。呈现的理论通过轮式移动机器人和3DOF直升机的离散模型进行了说明。
The paper addresses the exact linearization of flat nonlinear discrete-time systems by generalized static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts of a given flat output can be chosen in principle as a new input, and subsequently how to actually introduce the new input by a suitable feedback. With respect to the choice of a feasible input, easily verifiable conditions are derived. Introducing such a new input requires a feedback which may in general depend not only on this new input itself but also on its forward-shifts. This is similar to the continuous-time case, where feedbacks which depend on time derivatives of the closed-loop input - and in particular quasi-static ones - have already been used successfully for the exact linearization of flat systems since the nineties of the last century. For systems with a flat output that does not depend on forward-shifts of the input, it is shown how to systematically construct a new input such that the total number of the corresponding forward-shifts of the flat output is minimal. Furthermore, it is shown that in this case the calculation of a linearizing feedback is particularly simple, and the subsequent design of a discrete-time flatness-based tracking control is discussed. The presented theory is illustrated by the discretized models of a wheeled mobile robot and a 3DOF helicopter.
