Multivariable time delay approximations for analysis and control

Abstract Time delays form a fundamental part of many chemical engineering systems. They cause considerable analysis and control difficulties in part because they represent infinite-dimensional elements. This paper explores the use of finite-dimensional Pade approximations in system analysis and control. For analysis, the concern is whether two systems can be compared and quality of control assessed, based on analyses of their corresponding approximations. This paper demonstrates that analysis in terms of integral square error to unit step can be performed on Pade approximations rather than delay systems. For control, the concern is how a system with delays can be controlled by a controller without explicit delays. Pade approximations were found to be useful since their rational controller designs generally work quite well for delay systems. For MIMO systems, preliminary work indicates it is necessary to factor the shortest response time of each output before applying the Pade approximation.