{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T14:54:55Z","timestamp":1769007295453,"version":"3.49.0"},"reference-count":23,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008,6,1]]},"abstract":"<jats:title>Extension of First Order Predictive Functional Controllers to Handle Higher Order Internal Models<\/jats:title><jats:p>Predictive Functional Control (PFC), belonging to the family of predictive control techniques, has been demonstrated as a powerful algorithm for controlling process plants. The input\/output PFC formulation has been a particularly attractive paradigm for industrial processes, with a combination of simplicity and effectiveness. Though its use of a lag plus delay ARX\/ARMAX model is justified in many applications, there exists a range of process types which may present difficulties, leading to chattering and\/or instability. In this paper, instability of first order PFC is addressed, and solutions to handle higher order and difficult systems are proposed. The input\/output PFC formulation is extended to cover the cases of internal models with zero and\/or higher order pole dynamics in an ARX\/ARMAX form, via a parallel and cascaded model decomposition. Finally, a generic form of PFC, based on elementary outputs, is proposed to handle a wider range of higher order oscillatory and non-minimum phase systems. The range of solutions presented are supported by appropriate examples.<\/jats:p>","DOI":"10.2478\/v10006-008-0021-z","type":"journal-article","created":{"date-parts":[[2008,6,26]],"date-time":"2008-06-26T01:06:32Z","timestamp":1214442392000},"page":"229-239","source":"Crossref","is-referenced-by-count":35,"title":["Extension of First Order Predictive Functional Controllers to Handle Higher Order Internal Models"],"prefix":"10.61822","volume":"18","author":[{"given":"Mohamed","family":"Khadir","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Ringwood","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","reference":[{"key":"1","author":"K. \u00c5strom","year":"1997","journal-title":"Computer-Controlled Systems: Theory and Design"},{"key":"2","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/0005-1098(87)90087-2","article-title":"Generalised predictive control - Part I. The basic algorithm","volume":"2","author":"D. Clarke","year":"1987","journal-title":"Automatica"},{"key":"3","article-title":"Dynamic matrix control \u2014 A computer algorithm","author":"C. Cutler","year":"1980"},{"key":"4","author":"C. Houpis","year":"1992","journal-title":"Digital Control Systems"},{"key":"5","unstructured":"Khadir M.T. (2002). <i>Modelling and predictive control of a milk pasteurisation plant<\/i>, Ph.D. thesis, Department of Electronic Engineering, NUI, Maynooth, Ireland."},{"key":"6","unstructured":"Khadir M.T. and Ringwood J. (2003). Higher order predictive functional control, <i>Internal report EE\/JVR\/01, Department of Electronic Engineering, NUI Maynooth.<\/i>"},{"key":"7","first-page":"459","article-title":"Self tuning generalised predictive control with input constraints","volume":"2","author":"A. Kr\u00f3likowski","year":"2001","journal-title":"International Journal of Applied Mathematics and Computer Science"},{"key":"8","first-page":"53","article-title":"Analytical design of stable continuous time generalised predictive control","volume":"1","author":"Z. Kowalczuk","year":"1999","journal-title":"International Journal of Applied Mathematics and Computer Science"},{"key":"9","author":"J. Maciejowski","year":"2002","journal-title":"Predictive Control with Constraints"},{"key":"10","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TAC.1981.1102568","article-title":"Principal component analysis in linear systems: Controlability, observability, and model reduction","volume":"1","author":"B. Moore","year":"1981","journal-title":"IEEE Transactions on Automatic Control"},{"key":"11","first-page":"667","article-title":"Model predictive control: Past, present and future","volume":"4","author":"M. Morari","year":"2000","journal-title":"Computers and Chemical Engineering"},{"key":"12","first-page":"1119","article-title":"Algorithmic control of industrial processes","author":"J. Richalet","year":"1976"},{"key":"13","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/0005-1098(78)90001-8","article-title":"Model predictive heuristic control: Application to industrial processes","volume":"5","author":"J. Richalet","year":"1978","journal-title":"Automatica"},{"key":"14","author":"J. Richalet","year":"1993","journal-title":"Pratique de la commande predictive"},{"key":"15","unstructured":"Richalet J. (1998). La commande predictive, <i>Techniques de l'Ingenieur Traite Mesure et Control<\/i>, R7 423, pp. 1-17."},{"key":"16","doi-asserted-by":"crossref","unstructured":"Rossiter J.A. and Richalet J. (2001a). Predictive functional control of unstable processes, <i>Internal report 807, Department of Automatic Control and Systems Engineering, Sheffield University, UK.<\/i>","DOI":"10.1109\/ACC.2002.1025409"},{"key":"17","first-page":"63","article-title":"Realigned models for prediction in MPC: A good thing or not?","author":"J. Rossiter","year":"2001b"},{"key":"18","unstructured":"Rossiter J.A. (2001). Stable predictive for unstable independent models, <i>Internal report 812, Department of Automatic Control and Systems Engineering, Sheffield University, UK.<\/i>"},{"key":"19","first-page":"4746","article-title":"Handling constraints with predictive functional control of unstable processes","author":"J. Rossiter","year":"2002"},{"key":"20","first-page":"9","article-title":"Some issues in the design of predictive control","volume":"1","author":"R. Scattolini","year":"1999","journal-title":"International Journal of Applied Mathematics and Computer Science"},{"key":"21","first-page":"705","article-title":"Predictive functional control based on fuzzy model for heat-exchanger pilot plant","volume":"6","author":"I. Skrjank","year":"2000","journal-title":"IEEE Transactions on Fuzzy Systems"},{"key":"22","author":"P. Tatjewski","year":"2007","journal-title":"Advanced Control of Industrial Processes: Structures and Algorithms"},{"key":"23","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/S0967-0661(02)00186-7","article-title":"A survey of industrial model predictive control technology","volume":"7","author":"S. 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