Robustness Analysis Based on Approximating Nonlinear Systems with Parametric Models of Successive Linearization

• Main Authors: Ting-Fang Liu, 劉婷方
• Other Authors: Shyh-Hong Hwang
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/18229389457724981898

碩士 === 國立成功大學 === 化學工程學系 === 88 === In general, when dealing with nonlinear process control problems, one usually obtains an approximate linear model around a nominal equilibrium point and designs a linear control system based on the linear model. However, the dynamic characteristics of a nonlinear system vary with the equilibrium points, and hence the parameters in the approximate linear model cannot be the same over the whole dynamic regime. In addition, the linearization procedure often ignores the higher-order terms of a nonlinear system. Consequently, the error between the real system and the linear model may result, which forms the so-called model uncertainty. In order to describe the above model uncertainty more accurately, this thesis introduces the concept of successive linearization. First, parameterize a set of equilibrium points of the nonlinear plant. Second, derive a family of linearized models that are successively parameterized by the system's equilibrium points. Though this approach does not account for the effects of the higher-order terms, it does accommodate the variations of the first-order terms with respect to the operating points. We then use the successive linearization models to analyze the model uncertainty resulting from the linearization procedure of a nonlinear plant in the framework of linear internal model control. We also develop a method that uses the structure singular value to test the robust stability of the closed-loop system. Finally, the method is tested on several nonlinear flow and reactor systems and compared with some available methods based on global multiple models. It appears that the present approach is able to describe rather accurately the structure of the model uncertainty produced by nonlinear dynamics and determine an appropriate controller parameter.