Prediction and Analyis of the Dynamic Behavior of Nonlinear Systems

• Main Authors: Chiang-Hsiang Fan, 范景翔
• Other Authors: Shyh-Hong Hwang
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/6yc846

碩士 === 國立成功大學 === 化學工程學系碩博士班 === 90 === High nonlinearity existing in most chemical processes could result in complicated dynamic behavior, including multiple steady states, limit cycles, period doubling, torus and chaos. This thesis analyzes a continuous stirred tank reactor system often encountered in the process industry. Generic bifurcation points of the system are explored and the dynamics in the vicinity of each bifurcation point are predicted based on center manifold projection and normal form provided by bifurcation theory. First, we analyze the linearized stability of the CSTR system under various open-loop operating ranges. Subsequently, a proportional and a proportional-integral controller are introduced, and the resulting nonlinear dynamic behavior near the controller-induced bifurcation points are observed by adjusting the controller gains. Under proportional control, the normal form model gives immediately the amplitude and stability of the limit cycle, which are consistent with the simulation results. Under proportional-integral control, we can identify the route from period doubling to chaos with changes in the controller gains. Finally, parameter values at which period doubling occurs is further confirmed by the Feigenbaum number.