Multiobjective Control Structure Design: A Branch and Bound Approach

Abstract

Control structure design traditionally involves two steps of 
selections, namely the selection of controlled and manipulated variables 
and the selection of pairings interconnecting these variables. The 
available criteria for both selections require enumeration of every 
alternative. Hence, an exhaustive search can be computationally forbidding 
for large-scale processes. On the other hand, owing to the computational 
complexity, variables and pairings are often selected sequentially, which 
may result in suboptimal control structures. In this paper, an efficient 
branch and bound (BAB) method is proposed to select the variables and pairings 
together in a multiobjective optimization framework. As an illustration of the 
proposed multiobjective BAB framework, the minimum singular value rule and the 
p-interaction measure are used as the criteria for selection of controlled 
variables and pairings, respectively. Numerical tests using randomly generated 
matrices and the large-scale case study of hydrodealkylation of toluene (HDA) 
process show that the BAB method is able to reduce the solution time by several 
orders of magnitude in comparison with exhaustive search.