Systematic techniques for determining modelling requirements for SISO and MIMO feedback control

This paper presents a fundamental methodology for assessing modelling requirements of SISO and MIMO linear control problems. The main result is the formulation of a control-relevant parameter estimation problem (CRPEP), which suitably captures the interplay that occurs between controller sophistication, speed and shape of the closed-loop response, and set-point/disturbance directions affecting the closed-loop system. The CRPEP is used to explain the apparent dilemma between emphasis on low-frequency, steady-state behaviour versus high-frequency, initial time behaviour in modelling for SISO feedback control. For multivariable systems, solutions to the CRPEP are presented using prefiltered estimation of MIMO ARX models (model reduction case) and a state-space frequency-weighted estimation method (system identification case). The superior performance of reduced order and model predictive controllers obtained from control-relevant models is demonstrated on a subset of the Shell heavy oil fractionator problem.