Process Control : The Passive Systems Approach

passive system cannot deliver more energy than what is stored. Typically, a passive system delivers less than what is stored since useful energy is invariably and irreversibly lost through friction and other dissipative processes that convert useful work into heat. Such properties show that passivity is related to principles used to develop mathematical models for all kinds of physical systems. Applications of passivity-based control methods are found in robotics [1]–[3], systems biology [4], large-scale systems analysis [5], [6], and chemical process control [7]. One of the more intriguing aspects of passivity is that it relates to thermodynamics [8], [9]. The latter property motivates the use of passivity-based methods for chemical process control since it suggests that it may be possible to derive process control systems directly from process physics. To define the notion of passivity we consider a dynamical system with input u and output y. This system is passive if there exists a storage function W ( t ) $ 0 such that, for all t0 , t1,