Abstract
Since the loops in multivariable control systems can be coupled, a multivariable control strategy can further reduce process variations, thus, only multivariable assessment can provide the right measure of performance improvement potential in the general case. In this chapter, methods for multivariable minimum-variance benchmarking are presented: it is shown how to use the interactor matrix to derive the multivariable variant of MVC; then the FCOR algorithm as the most known algorithm for assessing MIMO control systems based on routine operating data and the knowledge of the interactor matrix is presented. As the interactor matrix is hard to determine, and thus control assessment based on it is difficult, an assessment procedure that does not require the interactor matrix is proposed. Numerous examples are given to illustrate how the methods work.
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The basic algorithms were implemented by Martina Thormann and Heinrich Ratjen, see Ratjen (2006).
References
Bittanti S, Colaneri P, Mongiovi M (1994) The spectral interactor matrix for the singular Riccati equation. In: Proc IEEE confer decision control, Orlando, USA, vol 3, pp 2165–2169
Ettaleb L (1999) Control loop performance assessment and oscillation detection. PhD thesis, University of British, Columbia, Canada
Goodwin GC, Sin K (1984) Adaptive filtering, prediction and control. Prentice Hall, New York
Harris T, Boudreau F, MacGregor JF (1996a) Performance assessment using of multivariable feedback controllers. Automatica 32:1505–1518
Huang B, Shah SL (1998) Practical issues in multivariable feedback control performance assessment. J Process Control 8:421–430
Huang B, Shah SL (1999) Performance assessment of control loops. Springer, Berlin
Huang B, Shah SL, Kwok EK (1997a) Good, bad or optimal? Performance assessment of multivariable processes. Automatica 33:1175–1183
Huang B, Shah SL, Kwok EK, Zurcher J (1997b) Performance assessment of multivariate control loops on a paper-machine headbox. Can J Chem Eng 75:134–142
Huang B, Ding SX, Qin J (2005a) Closed-loop subspace identification: an orthogonal projection approach. J Process Control 15:53–66
Huang B, Ding SX, Thornhill N (2005b) Practical solutions to multivariable feedback control performance assessment problem: reduced a priori knowledge of interactor matrices. J Process Control 15:573–583
Huang B, Ding SX, Thornhill N (2006) Alternative solutions to multi-variate control performance assessment problems. J Process Control 16:457–471
Ko B-S, Edgar TF (2001b) Performance assessment of multivariable feedback control systems. Automatica 37:899–905
Paplinski A, Rogozinski M (1990) Right nilpotent interactor matrix and its application to multivariable stochastic control. In: Proc Amer control confer, San Diego, USA, vol 1, pp 494–495
Peng Y, Kinnaert M (1992) Explicit solution to the singular lq regulation problem. IEEE Trans Autom Control 37:633–636
Ratjen H (2006) Entwicklung und Untersuchung von Verfahren zur Bewertung der Regelgüte bei Regelkreisen für MIMO-Systeme. Internal Tech report, University of Cologne/Germany, Subcontractor of BFI within the EU Project AUTOCHECK
Rogozinski M, Paplinski A, Gibbard M (1987) An algorithm for calculation of nilpotent interactor matrix for linear multivariable systems. IEEE Trans Autom Control 32:234–237
Shah SL, Mohtadi C, Clarke D (1987) Multivariable adaptive control without a priori knowledge of the delay matrix. Syst Control Lett 9:295–306
Tsiligiannis C, Svoronos S (1989) Dynamic interactors in multivariable process control. Chem Eng Sci 44:2041–2047
Wolovich W, Falb P (1976) Invariants and canonical forms under dynamic compensation. SIAM J Control 14:996–1008
Xia H, Majecki P, Ordys A, Grimble MJ (2006) Performance assessment of MIMO systems based on I/O delay information. J Process Control 16:373–383
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Jelali, M. (2013). Minimum-Variance Assessment of Multivariable Control Systems. In: Control Performance Management in Industrial Automation. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-4546-2_6
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DOI: https://doi.org/10.1007/978-1-4471-4546-2_6
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