旋轉倒立單擺上甩控制器設計

Abstract

本論文主要研究目的是在設計旋轉倒立單擺上甩控制器，並用三個模擬實驗來驗證其上甩控制法則。首先，第一個模擬實驗是尋找可行的上甩推力係數Sigma >0，且固定切換角在±30°，促使讓原本旋轉倒立單擺從某個初始擺放位置上甩至線性可控制區域-30°< Gamma < 30°之間。其次，在第二個模擬實驗是固定在切換角-30°< Gamma < 30°之間，試圖尋找Sigma值可行之最大Sigma-max與最小Sigma-min範圍，最後，更進一步地，第三個模擬實驗是使用最大值Sigma-max去尋找可行之不同切換角，其範圍在–Epsilon < Gamma < Epsilon。經由上述三個模擬實驗可得知Sigma值需要在Sigma-min < Sigma < Sigma-max區間，才不致於使Thetadot過大造成無法使旋轉倒立單擺上甩至垂直。

The purpose of this thesis is to design the swing-up controller of the rotary inverted pendulum, or RIP in short, and verify it by numerical simulation in three cases. The first case is to check the existence of gain Sigma >0 such that the RIP can be swung up from the initial down-right position to a desired switching region –Epsilon < Gamma < Epsilonwhere Epsilon=30°. In the second case, from the simulation results with the fixed switching region -30°< Gamma < 30°, the upper bound max and the lower bound min of the input gain Sigma are determined, i.e., to search the appropriate range Sigma-min < Sigma < Sigma-max. The third case employs the maximum gain Sigma-max to find the possibility of different switch region -Epsilon < Gamma < Epsilon. Base on above experimentation results, the Sigma value must in an appropriate range Sigma-min < Sigma < Sigma-max which make a suitable thetadot value and let RIP swing up to vertical position.