Modeling of Continuous-Discrete Processes

Abstract

Models of industrial processes often contain discrete phenomena superimposed on the continuous system behavior. Simulation of batch processes, start-up and shutdown procedures, fault diagnosis and alarms fall under this category. Models for such processes require a mathematical framework for both its continuous and discrete state transitions. A key problem in hybrid simulation lies in the detection and exact location of discontinuities that delineate state changes. Hence, hybrid systems require special numerical procedures, which are not available in conventional integration methods. In this paper, important issues pertaining to the numerical aspects in hybrid simulation will be discussed. We will demonstrate a new approach to event handling. The main target of this new approach is enhanced computational performance without loss of rigor. The authors anticipate the significance of high speed in the advent of new challenges in optimal control and dynamic optimization problems. The improvements are due to the exploiting local monotonicity and smooth function properties observed in varaible step-size integration algorithms.