倒單擺在傳統控制理論上，乃是一經典的非穩定系統模式，但在推導倒單擺數學模型時，為了數學推導上之便利，常會進行線性化之假設。此一假設的之數學模型，與原有之數學模型之間會有所誤差，致使所得之控制參數在實際應用時，出現效能降低或耗能變高，甚至超出系統本身的負載之問題。本研究探討其線性化造成之誤差，其誤差與角度之間的成長關係以PID控制法為例，對於所得的線性化允許角度進行驗證。
Invert pendulum system is a classical model in the traditional control theory. In order to facilitate the mathematical analysis, linear hypothesis often is used in the derivation of inverted pendulum mathematical model. But the hypothesis will create the error between linear with original non-linear mathematical model and result in performance decreasing. The discussion of this article obtains the specific quantitative data to provide the weight of abnormal response factors by comparing the models. This article focused on finding the relation between control error and the linear angle zero, by comparing and using PID control method to verify the estimated max linear angle zero range and the tolerance of the simplified model.
