Case Study of Controller Design Limitations of an Ill-Conditioned System Using t1 and /i Design Concepts

The focus of this paper is a comprehensive case study of the fundamental limitations of and controller design for the ill-conditioned high purity distillation column problem. As a result of the work on this problem, general ideas are presented concerning the design of robust controllers using norm-based methods. The case study of the distillation column problem includes three main components. The first component is a study of the physical plant including performance objectives, singular value analysis, and uncertainty description. It is shown that the relationship between the plant singular value directions and the input uncertainty makes this control problem dif-ficult. The second component is the application of i-synthesis, a design methodology for robust performance incorporating the concept of structured uncertainty in an H, setting, on the distillation column. The results of the designs are analyzed and conclusions are made concerning tradeoffs for controller design and frequency domain characteristics of the re-sulting controllers. The third component of the study is the application of the 4f design methodology. Since only within the past year was a computationally stable algorithm fo