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Mixed H2/H(subscript ∞) Cruise Control of High Speed Train via Linear Matrix Inequalities
以線性矩陣不等式設計高速鐵路列車之混合H2/H(下標 ∞)巡弋控制器
摘要
本文探討推挽式(push-pull driven type)高速鐵路列車，當其車廂間之連接器存在非線性軟彈簧(nonlinear softening spring)之特性時，其巡弋控制器的設計。對於具有此非線性連結器的高速鐵路列車縱向動力學模型，可將其線性化爲標稱質量彈簧系統(nominal mass-spring system)並且考慮彈簧係數真有在某一限制範圍內變化的不確定性，再應用線性矩陣不等式以求得混合H2/H(下標 ∞)巡弋控制器。最後的電腦數值模擬是在整合控制器與高速列車以軟彈簧連接之非線性動態系統中所進行，其結果顯示，混合H(下標 ∞)巡弋控制器允許設計者在也與H(下標 ∞)佳能間彈性地作取捨，藉著適當選擇H(下標 ∞)範數的要求，設計者可以得到兼顧命令追蹤(command tracking)性能與陣風衰減(wind gust attenuation)性能的巡弋控制器。
並列摘要
In this paper we consider the cruise control problem of the push-pull driven type high speed train in which the couplers are characteristic of nonlinear softening spring. The longitudinal dynamics of high speed train with the nonlinear couplers is linearized as the nominal mass-spring system with an variation of stiffness coefficient so that we may apply the Linear Matrix Inequalities (LMI) approach to synthesize the mixed H2/H(subscript ∞) cruise controller, Nonlinear simulation results show that this mixed H2/H(subscript ∞) optimal design lead designers into a flexible trade-off between H2/H(subscript ∞) objectives. By choosing the H2/H(subscript ∞) performance bound, properly, designers can determine the desired cruise controller that gives satisfactory performances of command tracking as well as wind gust attenuation for high speed train.