平行式雙倒單擺相較於一般傳統的倒單擺，除同樣為非極小相位和不穩定系統外，因單擺長度相異，具不同自然頻率特性，尚須考慮軌道長度限制，在所有倒單擺類型中，控制難度相對較高，且因線性馬達滑軌上摩擦力非均勻分佈，單以狀態回授控制無法達到良好的定位性能。本論文提出一串級控制之架構（Cascade Control），內迴路使用狀態回授穩定系統、外迴路採用模型預測控制（Model Predictive Control）來加強線性馬達之定位控制。除此之外，本研究從機構設計開始，完成平行式雙倒單擺系統的建立並推導出系統之動態模型，提出一平行式雙倒單擺之甩上控制方法，將長短單擺分別甩至上平衡點，最後再利用模型預測控制進行平衡控制與定位控制。模擬與實驗結果和傳統狀態回授控制結果相比，使用模型預測控制能明顯降低定位誤差，克服了使用狀態回授需建立足夠精準摩擦力模型的問題。

The aim of this paper is to apply Model Predictive Control (MPC) to the Parallel-type Double Inverted Pendulum (PDIP). Control of the PDIP is more difficult among the inverted pendulum family. Because the different lengths of the two pendulums give them distinct natural frequencies and the stoke length is limited. Besides, friction is not homogenously distributed on the track. Please bear in mind that one cannot achieve good performance if only state feedback is used. Therefore, we proposed a cascade structure where the inner loop was formed via state feedback and MPC directed the outer loop to enhance position control of the linear motor. In this work, a positive feedback control combined with energy-based control is adopted to swing up the PDIP sequentially, and then is switched to balance control. From simulation and experimental results, the proposed control scheme was successfully applied to the PDIP. Compared with conventional state feedback control, position errors could be reduced by MPC, which overcome the requirement of precise friction model needed in state feedback applications.

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