Practical solutions to multivariate feedback control performance assessment problem: reduced a priori knowledge of interactor matrices Biao Huang a, * ,1 , Steven X. Ding b , Nina Thornhill c a Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G6 b University of Duisburg-Essen, Inst. Auto. Cont. and Comp. Sys./Faculty 5, Bismarckstrasse 81, BB511, 47048 Duisburg, Germany c Department of E&E Engineering, University College London, Torrington Place, London, UK Received 5 April 2004; received in revised form 7 September 2004; accepted 22 October 2004 Abstract The research on control loop performance monitoring and diagnostics has been and remains to be one of the most active research areas in process control community. Despite of numerous developments, it remains as a considerably challenging problem to obtain a minimum variance control benchmark from routine operating data for multivariable process since the solution relies on the inter- actor matrix (or inverse time delay matrix). Knowing the interactor matrix is tantamount to knowing a complete knowledge of pro- cess models that are either not available or not accurate enough for a meaningful calculation of the benchmark. However, the order of an interactor matrix (OIM) for a multivariable process, a scalar measure of multivariate time delay, is a relatively simple para- meter to know or estimate a priori. This paper investigates the possibility to estimate a suboptimal multivariate control benchmark from routine operating data if the OIM is available. The relation between this suboptimal benchmark and the true multivariate min- imum variance control benchmark is investigated. Analytical expressions for the lower and upper bounds of the true multivariate minimum variance are derived. Although not minimum variance control, this benchmark answers important practical questions like ‘‘at least how much potential of the improvement does the control have by tuning or redesigning?’’ It is further shown that the proposed suboptimal benchmark is achievable by a practical control provided that the system of interest is minimum phase. Simulation examples illustrate the feasibility of the proposed approach. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Performance monitoring; Performance assessment; Control monitoring; Multivariate systems; Interactor matrices 1. Introduction The research on control loop performance monitor- ing and diagnostics has been and remains to be one of the most active research areas in process control com- munity. It is estimated that several hundreds of papers have published in this or related direction [5]. In practi- cal side, Eastman Kodak recently reported regular loop monitoring on over 14,000 PID loops. Some commercial control performance assessment software including mul- tivariate performance assessment has also been avail- able. Despite of the success in the research and the applications of univariate control performance assess- ment, applications of multivariate control performance assessment remain as a challenge. In the editorial for the special issue on control loop performance monitor- ing [5], it is pointed out that ‘‘Various methods to handle the multivariable case have been published in recent years; however, hardly any of them has been successfully 0959-1524/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jprocont.2004.10.006 * Corresponding author. Tel.: +1 780 492 9016; fax: +1 780 492 2881. E-mail addresses: biao.huang@ualberta.ca (B. Huang), s.x.ding@ uni-duisburg.de (S.X. Ding), n.thornhill@ee.ucl.ac.uk (N. Thornhill). 1 Currently visiting University of Duisburg-Essen, Germany. www.elsevier.com/locate/jprocont Journal of Process Control 15 (2005) 573–583