基于脉冲描述的复位控制系统频域建模
Frequency-Domain Modelling of Reset Control Systems using an Impulsive Description
摘要：
不断增长的工业需求，以提高性能，使线性控制器的设计遇到了根本的限制。需要诸如复位控制（RC）的非线性控制方法来克服这些。RC是一个很有前途的候选人，因为与其他非线性方法不同，它很容易集成到行业首选的PID设计框架中。到目前为止，RC已分析在频域中通过描述函数分析或直接闭环数值计算。前者通过假设足够的低通特性来计算简化的闭环RC响应。在这样做的时候，它忽略了所有的谐波，文献发现这会导致显着的建模预测误差。后者给出了一个精确的解决方案，但其直接闭环计算并没有清楚地显示开环RC设计如何转化为闭环性能。这项工作的主要贡献是为了克服这些限制，考虑一种替代方法建模RC使用状态相关的脉冲输入。这允许从底层线性系统开始精确计算闭环RC行为，从而提高对系统的理解。闭环RC的频域描述，这是通过使用几个定义良好的假设解析求解。使用模拟的高精度阶段，严格检查建模误差的来源，验证了这种分析解决方案。所提出的方法的准确性进一步证实使用控制器设计的各种规格。
英文摘要：
The ever-increasing industry desire for improved performance makes linear controller design run into fundamental limitations. Nonlinear control methods such as Reset Control (RC) are needed to overcome these. RC is a promising candidate since, unlike other nonlinear methods, it easily integrates into the industry-preferred PID design framework. Thus far, RC has been analysed in the frequency domain either through describing function analysis or by direct closed-loop numerical computation. The former computes a simplified closed-loop RC response by assuming a sufficient low-pass behaviour. In doing so it ignores all harmonics, which literature has found to cause significant modelling prediction errors. The latter gives a precise solution, but by its direct closed-loop computation does not clearly show how open-loop RC design translates to closed-loop performance. The main contribution of this work is aimed at overcoming these limitations by considering an alternative approach for modelling RC using state-dependent impulse inputs. This permits accurately computing closed-loop RC behaviour starting from the underlying linear system, improving system understanding. A frequency-domain description for closed-loop RC is obtained, which is solved analytically by using several well-defined assumptions. This analytical solution is verified using a simulated high-precision stage, critically examining sources of modelling errors. The accuracy of the proposed method is further substantiated using controllers designed for various specifications.
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