Robust D-partition analysis for parametric uncertain systems

• Main Authors: Li-fong Hwang, 黃立方
• Other Authors: Chyi Hwang
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/11117201917997369366

碩士 === 國立中正大學 === 化學工程研究所 === 92 === In this session, we discuss the stability analisys of systems with parametric uncertainty by using robust D-partition. Among several parametric space methods, D-partition is an applicable method in the analysis of system stability. Many people proposed some theorem in the domain of D-partition. With the characteristic polynomial of systems, D-partition subdivides controller parametric space into several subdomain. Each subdomain includes the difference kind of poles, called D-partition areas. The lines which subdivide the subdomains was called D-partition boundary. If the system has uncertain parameters, D-partition boundary will expanse to band. It is called D-partition border. To locate the boundary of the border is the key to analyze the stability of systems. The formation of the boundary of the D-partition border is enslaved to the characteristic polynomial of system. In this paper, we will derive the form of robust D-partition. It is important that how to locate the D-partition boundary rapidly. After deciding the polynomial of the boundary by using D-partition method, it could be located precisely with locus tracking methods. The kind of methods must make a choose on a starting point before tracking. If the boundary does not lap over the starting point, it can not be found. Therefore, the locus tracking method can not provide a guarantee of locating all boundary in the parametric space. To be sure that, we quote the concept of branch and bound. The concept is that the controller parametric space is subdivided into several subdomain, and exclude the subdomain which does not include the boundary. The remain subdomain repeat the procedure until the subdomain is small enough. Finally, the remain subdomain is the set of D-partition boundary. For checking whether the boundary is included in subdomain rapidly, we will use the Bernstein expansion. This kind of method specified a set of base function to make a transformation with the object function. Because of the properties of the base function, it help us to evaluate the value of object function. At last, we link up the theorem and technology of D-partition for the application of parametric uncertainty of general systems, and prove the D-partition is applicable and realizable.