反應/分離迴流程序之設計與控制(1/3)

在本研究中針對一個兩階不可逆反應（A+B=2C ）的 多入料迴流系統，探究了這個系統在不同穩態設計下的 動態情形以及控制上的問題。 首先由質量平衡式出發，得到了以系統設計參數為 函數的轉移函數(zC,λ=zA/zB)，此轉移函數能夠清楚的描 繪出在組成三角圖上任一點的迴流程序動態情形，這讓 我們發現了多入料的迴流工廠存在內部流不穩定的特性 (一個極點在原點)，只有兩股進料相等時系統才能穩定， 在此證明了Luyben 所提的迴流工廠進料必須滿足化學計 量平衡，這個發現也讓我們瞭解到前饋控制結構在實務 中是不能使用的，必須使用回饋控制來確保兩股進料相 等。在除去不可使用的前饋控制之後，我們還提出了幾 個控制結構，對於這些結構使用非線性分析（bifurcation analysis ）的方式，此方式提供了我們一個全面性的視野， 讓我們瞭解使用各控制結構的穩定區域。另外線性轉移 函數讓我們看到了在各個穩態設計點上各控制結構所得 到的動態響應情形，也可經由極點的位置來選擇適用的 控制結構，對於所選擇的控制結構更可以導入一個動態 補償器來改善得到完美產控制。 最後使用一個反應器加上兩根蒸餾塔的真實嚴謹系 統來印證線性分析方式的可靠度，結果顯示不只控制結 構的選擇無誤，也能夠達到近乎完美產能控制的響應。In this work we explore dynamics and control of recycle plants with multiple feed streams under different process designs. Without loss of generality, a ternary system with second order irreversible reaction, A+B=2C, is used to illustrate the dynamics and control of such multiple-feed systems. Given design parameters, process transfer function matrices can be derived analytically (design parameters are expressed in terms of reactor composition, i.e., zA, zB, and zC in the triangular composition space). Therefore, we are able to evaluate recycle dynamics for different designs (e.g., different conversion, zC, and reactant distribution, zA/zB). The results show that, irrespective of design parameters, recycle plants with multiple feeds are internally unstable system (a pole at the origin). The recycle plant can be stabilized only if the feed flows are exactly the same at steady-state. This proves Luyben’s conjecture that we have to balance the reactants down to the last molecule. This also implies feed-ratio control scheme will not work in practice and one of the feed flows should be adjusted via feedback. After eliminating unworkable control structures, remaining candidate control structures are evaluated next. Globally, for a given control structure, the bifurcation diagram is used to identify unstable region (if exist) in the composition space and, subsequently, a stability boundary can be drawn. Locally, the speed of recycle flows (pole location from transfer function matrix) is used select the preferable one. Finally, dynamical compensation to the feed flow is devised according to the transfer function matrix such that almost perfect production rate control can be achieved. A nonlinear recycle process with one reactor and two columns (programmed in FORTRAN) is used to illustrate the usefulness of the proposed analysis. Simulation results clearly indicate that correct control structure is selected and almost perfect production rate changes can be achieved