This paper proposes a new methodology for the design of multivariable controllers with a reduced structure. The structure of a multivariable controller may be defined in several ways. In this paper it is defined as the number of the input to output connections of the controllers. Based on this structure definition, a generic cost function is determined where both the structure of the controller and the performance of the resulting closed loop system appear as minimization terms. It has been shown that there exists an optimal weighting such that the optimization of the weighted sum of these two terms will always result in a unique reduced structure controller. The methodology is then successfully applied to the model of the ALSTOM (ALSTOM Power Technology Centre, formerly GEC ALSTHOM) gasifier challenge problem, which is a difficult multivariable system to control.
BristolE. H.An introduction to process industry multivariable control. Proceedings of the International Conference on Cybernetics and society, IEEE, 1972, pp. 341–342.
2.
BristolE. H.On a new measure of interaction for multivariable process controlIEEE Trans. Automatic control, January 1966, pp. 43–44.
3.
BristolE. H.A paradox in multivariable control analysisIn Proceedings of the 4th UKACC Control convention on multivariable control system design and applications, IEE, 1971, pp. 50–58.
4.
NettC. N.A quantitative approach to the selection and partitioning of measurements and manipulations for the control of complex systemsCaltech control workshop, Pasadena, USA, Jan 1989.
5.
MorariM.ArkunY.StephanopoulosG.Studies in the synthesis of control structures for chemical process, part i: Formulation of the problem, process decomposition and the classification of the control tasks. analysis of the optimizing control structuresAlChE J., 1980, 26 (2), 220–232.
6.
StephanopoulosG.Chemical process control. International Series in the Physical and Chemical Engineering Sciences. 1984 (Prentice Hall).
7.
KookosI.PerkinsJ.Heuristic-based mathematical programming framework for control structure selectionInd. Eng. Chem. Res., 2001, 40, 2079–2088.
8.
KookosI.PerkinsJ.An algorithmic method for the selection of multivariable process control structuresJ. Process Control, 2002, 12, 85–99.
9.
YeungL. F.ChanA. Wu.Experimental design theoretic genetic algorithm for input-output block assignment problemIEEE Conference of Decision and control, 2001, 5, 4049–4050.
10.
SkogestadS.PostlethwaiteI.Multivariable feedback control: analysis and design.1996 (Wiley).
PatelR. V.MunroN.Multivariable system theory and design.1982 (Pergamon Press, Oxford).
13.
AsmarB. N.JonesW. E.WilsonJ. A.A process engineering approach to the alsotm gasifier problemProc. Instn Mech. Engrs, Part I: J. Systems and Control Engineering, 2000, 214 (16), 441–452(12).
14.
KocisG. R.GrossmannI. E.Global optimisation of nonconvex mixed-integer nonlinear programming (minlp) problems in process synthesisInd. Engng Chemistry Res., 1988, 27, 1407–1421.
15.
CardosoM. F.SalcedoR. L.AzevedoS. F.BarbosaD.A simulated annealing approach to the solution of minlp problemsComputers and Chemical Engng, 1997, 21 (12), 1349–1364.
16.
GuptaO. K.RavindranA.Branch and bound experiments is convex nonlinear integer programmingManage Sci., 1985, 31 (12), 1533–1546.
17.
GeorffionA.M.Generalized benders decompositionJ. Optimisation and Theory Applic., 1972, 10, 237–260.
18.
QuesadaI.GrossmannI. E.An lp/nlp based branch and bound algorithm for convex minlp optimisation problemsComputers and Chemical Engng, 1992, 16, 937–947.
19.
CostaL.OliveiraP.Evolutionary algorithms approach to the solution of mixed integer non-linear programming problemsComputers and Chemical Engng, 2001, 25, 257–266.
StornR.PriceK.Differential evolution simple and efficient adaptive scheme for global optimization over continuous spaces. Technical Report TR-95-012, 1995, Int. Comput. Sci. Inst., Berkeley, CA.
22.
DixonR.PikeA. W.DonneM. S.The alstom benchmark challenge on gasifier controlProc. Instn Mech. Engrs, Part I: J. Systems and Control Engng, 2000, 214 (16), 389–394.
KookosI.On the feasibility of constrained linear control problems with application on the alstom gasifierProc. IMechE, Part I: J. Systems and Control Engng, 2005, 219 (13), 207–214.
25.
OsborneE. E.On pre-conditioning of matricesJ. Assoc. Comput. Mach.1960, 7, 338–345.
26.
ChinC. S.MunroN.The analysis and control of the alsotm gasifier benchmark problem. In Proceedings of XV IFAC World Congress, Barcelona, Spain., 2002.
27.
EdmundsJ.Input and output scaling and reduction for diagonal dominance and block diagonal dominanceIEE Proceedings-Control Theory Appl, 1998, 145 (6).
28.
NobakhtiA.MunroN.Minimal structure control: A proposition. IFAC Conference on Control systems design (CSD'03), Slovak Republic, 2003.
29.
NobakhtiA.A solution to the reduced structure control problemAmerican control conference, 2005. Portland.
30.
NobakhtiA.WangH.Controller structure selection using the reduced structure control methodologyAmerican control conference, 2006.
