Abstract
Case studies are reported which show that ideas from stochastic control theory can be exploited to design useful practical controllers. The ideas indicate that the way to design a feedback controller is to implement two separate functions of estimation and control, each matched to some simple mathematical model capturing essential features of the controlled object. Good design does not usually require that either the estimator or the control law be exactly optimal, not even for the simplified model. Where the controlled object is essentially nonlinear, as in many real applications, this suboptimal stochastic design may give better performance than is achievable with classical, black-box linear controllers or their adaptive derivatives.
Two current collaborative case studies are summarised.
1. Control of pressure and position in an air knife which regulates the thickness of zinc deposit on sheet steel galvanized by hot dip. Feedback in the form of a time-delayed measurement of deposited thickness drives a Kalman filter which estimates an uncertain multiplicative coefficient in a simplified model of the deposition. The updated model is then used to determine control action.
2. Fishery management as a problem in feedback control. In collaboration with the Fisheries Laboratory of the UK Ministry of Agriculture Food and Fisheries, management of one particular harvested population (mackerel) has been considered from the point of view of control engineering. A suboptimal, certainty-equivalent control law is derived to regulate fluctuations about a specified equilibrium state. This control law includes as special cases strategies of constant effort and constant catch which are well known to fishery managers.
The overall conclusion is that the structural, stochastic, suboptimal approach can be recommended as a general procedure for designing feedback controllers to achieve desired performance of controlled objects which are subject to uncertainty.
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6 References
Åström K.J. and B. Wittenmark (1988). Adaptive Control. Prentice Hall.
Ballance. D.J. (1988). Control Methodology Applied to National Fishing Strategies., D. Phil Thesis, U. of Oxford.
Ballance, D.J., O.L.R. Jacobs, and J.W. Horwood (1988a). Application of CADCS Methods to a problem in Fishery Management. 4th IFAC Symp. on CADCS, Beijing.
Ballance, D.J., O.L.R. Jacobs, and J.W. Horwood (1988b). State Estimation in Regulating a Harvested Population. 8th IFAC/IFORS Symp. Ident. and Par. Est., Beijing.
Beddington, J.R., and R.M. May (1977). Harvesting Natural Populations in a Randomly Fluctuating Environment. Science, 197,463–465.
Bertin M.C., Brown L., Whitehead R.L. and E. Yrisarri (1978). Computer Control of Coating Weight on Galvanizing and Tinning Lines. 7th IFAC World Congress, Helsinki. pp 199–206.
Beverton, R.J.H. and S.J. Holt (1957). On the dynamics of exploited fish populations. Fishery Invest., Lond., Ser. 2, 19.
Biermann G.J. (1977). Factorisation Methods for Discrete Sequential Estimation. Academic Press.
Butler J.J., Beam D.J. and J.C.Hawkins (1970). The Development of Air Coating Control for Continuous Strip Galvanizing. Iron and Steel Engineer, Feb, pp 77–86.
Clark, C.W. (1976). Mathematical Bioeconomics: The Optimal management of Renewable Resources. Wiley, New York.
Clark, C.W. (1985). Bioeconomic Modelling and Fisheries Management. Wiley, New York.
Clark, C.W. and G.P. Kirkwood (1974). On uncertain renewable resource stocks: optimal harvest policies and the value of stock surveys. Tech. Rep. Inst. Appl. Math. Stats., 84-4, University of British Columbia, Canada.
Edwards W.J., Carlton A.J., Harvey G.F., Evans R.F. and P.J. McKerrow (1975). Continuous Mass Control System Design for a Continuous Galvanizing Line. 6th IFAC World Congress, Boston, 46.3.
Ellen C.H. and C.V. Tu (1983). An Analysis of Jet Stripping of Molten Metallic Coatings. Fluid Mechs Conf, Univ of Newcastle, N.S.W.
Fel'dbaum A.A. (1965). Optimal Control Systems. Academic Press.
Friedland B. (1986). Control System Design. Prentice-Hall.
Garrod, D.J. (1983). On the Variability of Year-class Strength. J. Cons. Int. Explor. Mer, 41, 63–66.
Goh, B.S. (1980). Management and Analysis of Biological Populations, Chap 4, Elsevier, Amsterdam.
Hansard (1988). HMSO Vol 143, 12 Dec, 664–676.
Harvey G.F. and A.J. Carlton (1974). Mathematical Modelling of Air Jet Coating Mass. John Lysaght (Australia) Ltd Res. and Tech. Report, 533.
Horwood, J.W. (1982). The variance of population and yield from an age-structured stock, with application to the North Sea herring. J. Cons. Int. Explor. Mer, 40, 237–244.
Horwood, J.W., and J.G. Shepherd (1981). The Sensitivity of Age-Structured Populations to Environmental Variability. Math. Biosci., 57, 59–82.
Jacobs O.L.R. (1974). Introduction to Control Theory. OUP.
Jacobs O.L.R. (1982). Integral control action and separated stochstic control. IFAC Symp. Theory and Applications of Digital Control. Delhi.
Jacobs, O.L.R. (1987). Management procedure and stochastic control theory. IWC Comprehensive assessment workshop on management, Section 6.3, Reykjavik.
Jacobs O.L.R. (1989). Adaptive cautious control of an air knife. OUEL internal report.
Jacobs O.L.R., Badran W.A., Proudfoot C.G. and C. While (1987). On Controlling pH. Proc IEE D, 134D, 3, pp196–200.
Jacobs O.L.R., Ballance D.J. and J.W. Horwood (1990). Fishery Management as a Problem in Feedback Control. In press, Automatica.
Jacobs O.L.R., Bullingham R.E.S., Lammer P., McQuay H.J., O'Sullivan G. and M.P. Reasbeck (1985). Modelling Estimation and Control in the relief of Post-Operative Pain. Automatica, 21, 4, pp 349–360.
Jacobs O.L.R. and J.W. Patchell (1972). Caution and Probing in Stochastic Control. Int J. Cont., 16, 1, pp189–199.
Lockwood, S.J., J.H. Nichols, and W.A. Dawson (1981). The Estimation of a Mackerel (Scomber scombrus L.) Spawning Stock Size by Plankton Survey. J. Plankton Research, 3(2), 217–233.
Lockwood, S.J., and J.G. Shepherd (1984). An assessment of the Western stock of Mackerel. J. Cons. Int. Explor. Mer, 41, 167–180.
Mangel, M. (1985). Decision and Control in Uncertain Resource Systems, Chap 6. Academic Press, New York.
May, R.M., J.R. Beddington, J.W. Horwood, and J.G. Shepherd (1978). Exploiting Natural Populations in an Uncertain World. Math. Biosci., 42, 219–252.
Muratori, S., S. Rinaldi, and B. Trincher (1989). Performance evaluation of positive regulators for population control. Modelling, Identification and Control, 10, 125–134.
Noe T.G. and T.R. Schuerger (1975). Computer Control of Zinc-Coating Weight on the Fairfield No 4 Galvanizing Line. 6th IFAC World Congress, Boston, 46.2.
Pope, J.G. (1982a). Background to Scientific Advice on Fisheries Management. Lab. Leafl., M.A.F.F. Direct. Fish. Res., Lowestoft, (54).
Pope, J.G. (1982b). Analogies to the Status Quo T.A.C.'s: Their Nature and Variance. Can. Spec. Publ. Fish. Aquat. Sci., 66, 99–113.
Pope, J.G., and J.G. Shepherd (1982). A Simple Method for the Consistent Interpretation of Catch-at-Age Data. J. Cons. Int. Explor. Mer, 40, 176–184.
Reid P., (1972). The Theory of Jet Stripping, Part 1. John Lysaght (Australia) Ltd Res. and Tech. Report, 465.
Schaefer, M.B. (1954). Some aspects of the dynamics of populations important to the management of commercial marine fisheries. Bull. Inter-Amer. Trop. Tuna Comm., 1, 25–56.
Sendzimir T., (1938). Process for Coating Metallic Objects with Layers of Other Metals. US Patent, 2110893.
Shepherd, J.G. (1982). A Versatile New Stock-recruitment Relationship for Fisheries, and the Construction of Sustainable Yield Curves. J. Cons. Int. Explor. Mer, 40(1), 67–75.
Tanaka, S. (1980). A Theoretical Consideration on the Management of a Stock-Fishery system by Catch Quota and its dynamical properties. Bull. Japan. Soc. Sci. Fish, 46, 1477–1482.
Thornton J.A. and H.F. Graff (1976). An Analytical Description of the Jet Finishing Process for Hot-Dip Metallic Coatings on Strip. Metallurgical Trans. B, 7b, pp 607–618.
Walters, C. (1986). Adaptive Management of Renewable Resources. MacMillan.
Wilhelm R.G. Jnr, (1972). Control Eng., Nov, pp 44–47.
Wynne D.C., Vickers A.L. and F.Graham Williams (1987). Galvanizing Developments in the U.K. Iron and Steel Eng., July, pp 40–47.
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Jacobs, O.L.R. (1991). Case studies in application of stochastic control theory. In: Warwick, K., Kárný, M., Halousková, A. (eds) Advanced Methods in Adaptive Control for Industrial Applications. Lecture Notes in Control and Information Sciences, vol 158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0003823
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DOI: https://doi.org/10.1007/BFb0003823
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