在本篇論文中,我們首先介紹一個新的機械元件「慣質」的觀念,這個新發明的被動式元件是從機械與電子網路系統中彼此的不完美對稱性中發現。由於慣質的出現,使得電子系統之網路實現理論可以應用至機械系統。接著利用線性矩陣不等式理論,對單輪火車懸吊系統做各種性能指標的最佳化,再將各個最佳化模型利用網路實現理論實現出來。至於最佳化的結果,因為我們只有指定懸吊系統之階數,因此懸吊系統轉移函數之係數自由度很大,不像固定結構式的懸吊系統被限制住了,所以可以得到令人滿意的結果,也藉此驗證慣質的確可以有效改進傳統的懸吊系統。未來可以更進一步將線性矩陣不等式理論應用至兩輪、四輪及全車的火車系統,並可以測試更多的性能指標。
This thesis first discusses the concepts of a newly-developed mechanical network element, called Inerter. This passive element was invented in 2001 from the imperfect analogy between mechanical and electrical networks. Due to the invention of inerter, we can apply electrical network synthesis theory to mechanical systems. Furthermore, we apply linear matrix inequalities (LMI) to the synthesis of passive suspensions for the optimization of certain performance measures for a one-wheel train model. The characterization of the passive constraint using matrix inequalities and the use of inerter permits the optimization over the entire class of passive admittances and the realization of the resulting admittance using passive elements. The optimization results are compared with previous optimization over fixed-structure admittances. It is shown from the results that the proposed method can potentially achieve better performance.