(430c) Extensive, Intensive and Invariant Variable Control Systems

In the current paper we review the basics of the Legendre-Fenchel dual and how to use this concept to motivate a variety of methods proposed for process control and control of networks during the past six decades. Many of these methods have faded into the background, some have found industrial application and still in practical use and some provided basis for fruitful research that continues to this day. The objective of this paper is to seek some communality among these diverse method and provide foundations for further development and discussion.

The main idea behind the use of extensive variables and invariants for process control go back to the mass an energy balance control systems developed and applied by Buckley and Shinskey in the 1960ies. The use of process invariants (symmetries) was proposed by Fjeld et al. (1974) and the Extensive Variable Control method was proposed by Georgakis (1986) for the synthesis of multivariable and (or) nonlinear control structures. The Generic Model Control (GMC) method was proposed by Lee and Sullivan (1988), partial control by Shinnar et al. (1996) and Inventory control by Farschman et al. (1998). The latter was based on the observation that material and enenrgy balances could be viewed as special cases of passive systems. Tyreus proposed Dominant Variable Control and more recently Bonvin (2005) developed reaction and flow invariants and Adomaitis et al (2016) applied invariants to modeling and control of CVD reactors. All these papers posed the question of how to control complex chemical processes and networks of processes using only a small subset of all the variables used to model such systems. They also aim to address question such as which variables to measure and control and in this sense the methods are more focused on control strategies rather than which algorithm to use.

The main idea that emerges in all these applications is that chemical processes are governed by conservation principles (symmetries) that will hold at every length and time scale. These symmetries are in their simplest form expressed as conservation of mass, energy and mol-numbers for example. This property can also be expressed in terms of duality and the optimization of specifc potentials and ths provides a more general way of expressing dynamics and control. The main problems that emerge are the questions of how to use these principles for control and optimization, how to present convincing arguments to demonstrate that variables that are not controlled, the so-called zero dynamics, are stable and finally how to satisfy tracking objectives. These problems are by no means completely addressed at present. Some open research problems will be presented.