自由基型聚合反应在连续搅拌釜反应器中的稳定性分析

STABILITY ANALYSIS OF FREE RADICAL POLYMERIZATION IN A CONTINUOUS STIRRED TANK REACTORS

产品质量稳定是生产过程中最重要的控制指标之一,即希望工况条件发生扰动时,操作状态(又称定态点)将偏离在指定的范围内;一旦扰动消除,操作状态能够逐渐回复原样。实际操作状态能否满足上述要求,即为稳定性分析之范畴。稳定性分析的结果可以作为反应器设计、控制及工艺参数设置的理论依据,有重要的现实意义。聚合反应系统有其本身的复杂性和特殊性,往往难以控制,其数学模型通常是非线性的,给稳定性分析带来一定的难度。本文应用李亚普诺夫直接法分析自由基型聚合反应系统在连续搅拌釜反应器中的稳定性,利用克拉索夫斯基定理构造李亚普诺夫函数来判别聚合反应过程的稳定性,并且还计算了工况条件允许的变动范围。

To assure the uniformity of any industrial product, the production processes should be kept as stable as possible. However, disturbances of various nature are unavoidable which make the operation states deviate from the expected values. A system is considered as stable where the operation state can return to the original point after the disturbances diappear. So the stability analysis is extremely important in the design of any production process and its control. Polymerization is a rather complex system and its control is quite difficult. The stability analysis of the polymerization system is also very troublesome since the mathematical model of the system is always nonlinear. In this paper, stability of free radical polymerization in a C. S. T. R. is analyzed by Lyapunov's direct method. An approach based on the Krasovskii technique for generating a Lyapunov function is used to determine the nature of the stability of a steady state and to estimate regions of asymptotic stability (RAS).