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Extension of PID Regulators to Dynamical Systems on Smooth Manifolds (M-PID)
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2021-01-07 , DOI: 10.1137/19m1307743
Simone Fiori

SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 78-102, January 2021.
This paper outlines possible extensions of a classical proportional-integral-derivative (PID) scheme to abstract systems whose state-spaces are smooth manifolds (i.e., state-manifolds). In particular, we first present a “direct” extension of a PID controller for first-order systems where the control actions are direct translations to manifolds, via canonical identifications. We show that one such direct extension is, however, unfeasible. Next, we suggest a specific extension, which arises as a nonstraightforward and careful definition of error terms, which leads to a consistent definition of M-PID controller. On the basis of the successful, novel definition of PID controller, we proceed in extending its design from first-order to second-order systems in two different versions, namely, position and velocity control. To complete this endeavor, we prove analytically that both position and velocity control may be achieved through the proposed approach.


中文翻译:

将PID调节器扩展到平滑流形(M-PID)上的动态系统

SIAM控制与优化杂志,第59卷,第1期,第78-102页,2021年1月。
本文概述了经典比例积分微分(PID)方案可能扩展到状态空间为光滑流形(即状态流形)的抽象系统。特别是,我们首先针对一阶系统提出PID控制器的“直接”扩展,在该系统中,控制动作是通过规范标识直接转换为歧管的。我们表明,这样的直接扩展是不可行的。接下来,我们建议一个特定的扩展名,该扩展名是错误项的非直截了当的仔细定义,从而导致了M-PID控制器的一致定义。在成功,新颖地定义PID控制器的基础上,我们将其设计从一阶系统扩展到二阶系统,并采用了两种不同的版本,即位置和速度控制。为了完成这项工作,
更新日期:2021-01-07
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