Complexity Measure for Block Diagrams

The concept of complexity has been widely studied in the last years in several different areas. Although many writers on the subject understand qualitatively similar things by the term ”complexity”, a transition from this qualitative understanding to a quantitative approach would be highly desirable and necessary. The lack of understanding in this area has hindered planners in deciding how much integration is beneficial and beyond which point integration is actually detrimental to system performance, since correct decisions are difficult to make due to high system complexity. The objective of this paper is to present a method to quantify the static complexity of a block diagram in a way that can be useful for process control structure selection. The method is applied in several examples. The importance of this evaluation is to help to produce good control structures with the smallest possible complexity due to the fact that the costs of implementation increase in large complex systems. Once determined a way to quantify it, it is possible to minimize the complexity of this system keeping the same control performance.