非最小相位系统的极点配置设计详解.docVIP

非最小相位系统的极点配置设计 摘要 具有非最小相位环节的系统称为非最小相位系统，非最小相位环节会对控制系统的稳定性和其他性能指标产生不利的、有时是非常严重的影响，因此对非最小相位系统的研究具有十分重要的理论意义和实际工程应用价值。 极点配置方法是一种有效的设计控制器的方法，特别适用于非最小相位系统的设计。但对于具有不稳定极点的非最小相位系统，这种方法鲁棒性较差，其应用也受到限制。本文对常规极点配置方法进行了改进，应用了一种新的极点配置方法。指出非最小相位系统不符合Bode的幅-相定理，带宽不能反映系统的动态特性，故不宜再用带宽来作为设计指标，而应该采用穿越频率作为性能指标，应小于非最小相位的零点。对不稳定非最小相位系统,提出了一种新的极点配置方法,将极点配置问题转换为正实性问题,用线性矩阵不等式求解控制器,并指出将是鲁棒性设计时的极限值。 本文将非最小相位环节与系统的其余部分结合在一起进行讨论，将对象分为稳定的和不稳定对象，并给出鲁棒性设计的范围。 首先，建立倒立摆系统的数学模型。倒立摆系统稳定效果非常明了，可以通过摆动角度、位移和稳定时间直接度量，控制好坏一目了然。理论是工程的先导，倒立摆的研究具有重要的工程背景。 然后，推导小车倒立摆归一化模型，确定小车倒摆系统无量纲处理后的传递函数。由于其是有一个不稳定零点和一个不稳定极点，是非最小相位系统里最经典，又较为简单的例子，所以用研究不稳定非最小相位系统最为合适。 最后，设计非最小相位控制器。先后设计非最小相位零点a=1.414，a=3.317，a=7.14时对应的的图线，并给出本文结论。 关键词 Pole placement design of non minimum phase systems Abstract System with non minimum phase system are called non minimum phase system, non minimum phase system will have on the stability of the control system and other performance indicators of adverse, sometimes very serious impact, so it has very important theory significance and practical application value for the study of non minimum phase systems. The pole placement method is an effective method to design the controller, the design is particularly applicable to non minimum phase systems. But for non minimum phase systems with unstable poles, this method has poor robustness, its application is restricted. This paper improves the conventional pole placement method, using a new method of pole placement. Points out that the non minimum phase system does not meet the Bode amplitude phase theorem, bandwidth can not reflect the dynamic characteristics of the system, so it should not be reused bandwidth as a design index, and should use the crossover frequency as the performance index, should be less than the non minimum phase zeros. On unstable non minimum phase system, proposes a new method of pole placement, converting the pole assignment problem for positive realness, controller for solving linear matrix inequalities, and that will be the