OPEN ACCESS
This work deals with production and control design management, for basic logistics systems facing some uncertainties on customer demands and time lags estimations. The contribution is characterized by the inclusion of both the delay that governs the dynamics of these systems and the inherent constraints involved in their structures, such as positivity and saturations. The delay can be known exactly, or estimated within an uncertainty margin. Based on a control theory framework, and the use of invariance approaches, a robust saturated feedback predictor controller is used to handle stability issues of the system and the constraints meeting. The applicability of this approach is illustrated by simulation.
inventory control, saturated command, feedback predictor, robustenss control.
Artstein Z. (1982). Linear systems with delayed controls: A reduction. IEEE Transactions on Automatic Control. Vol. 27, n° 4, p. 869-879.
Blanchini F. (1999). Set invariance in control. Survey paper. Automatica, vol. 35, n°11, p. 1747-1767.
Edghill J.S., Towill D.R., (1989). The use of systems dynamics in manufacturing systems. Transaction of the Institute of Measurement and Control, vol. 11, n° 4, p. 208-216.
Forrester J. W. (1961). Industrial Dynamics. Cambridge MA: MIT press. Hu T. L. Z. (2001). Control Systems with Actuator Saturation: Analysis and Design. Birkhäuser, Boston.
John S., Naim M.M., Towill D.R. (1994). Dynamic analysis of a WIP compensated decision support system. International Journal of Management Systems and Design, vol. 1, n° 4, p. 283-297.
Manitius A., Olbrot A. (1979). Finite spectrum assignment problems for systems with delays. IEEE Trans. Automatic Control. 24, p. 541-553.
Milani B.E.A. (1994). Robust linear regulator design for continuous-time systems under state and control constraints. 33rd IEEE Conference on Decision and Control. Vol. 3, p. 2067- 2068.
Mirkin L., Raskin N. (2003). Every stabilizing dead-time controller has an observer predictor- based structure. Automatica. Vol. 39, n°10, p. 1747-1754.
Moussaoui C., Abbou R., Loiseau JJ. (2014). Controller Design for a Class of Delayed and Constrained Systems: Application to Supply Chains. In Low Complexity Controllers for Time-Delay Systems. Advances in Delays and Dynamics, vol. 2, p. 61-75.
Nagumo M. (1942). Über die Lage der Integralkurven gewhönlicher Differentialgleichungen. Proceedings of the Physico-Mathematical Society of Japan. p. 551-559.
Riddalls C.E., Bennett S. and Tipi N.S. (2000). Modeling the dynamics of supply chains. International Journal of System Science, 31, p. 969- 976.
Simon H. A. (1952). On the application of servomechanism theory in the study of production control. Econometrica, vol. 20, p. 247-268.
Sipahi R., Delice I.I. (2010). Stability of Inventory Dynamics in Supply Chains with Three Delays. International Journal of Production Economics, vol. 123, n°1, p. 107-117.
Sterman J. D. (1989). Modelling managerial behaviour misinterpretations of feedback in a dynamic decision-making experiment. Management science, vol.35, n°3, p. 321-339.
Towill D.R. (1982). Dynamic analysis of an inventory and order based production control system. International Journal of Production Research, vol. 20, n° 6, p. 671-687.
Wang X., Disney S.M. and Wang J. (2012). Stability analysis of constrained inventory systems with transportation delay. European Journal of Operational Research., vol. 223, n° 1, p. 86-95.
Wang X., Disney S.M. and Wang J. (2014). Exploring the oscillatory dynamics of a forbidden returns inventory system. International Journal of Production Economics, p. 3-12.
Warburton R. D. H. (2004). An exact analytical solution to the production inventory control problem. International Journal of Production Economics, 92, p. 81-96.
Manitius A., and Olbrot A. (1979). Finite spectrum assignment problems for systems with delays. IEEE Trans. Automatic Control, 24, p. 541-553.
Mirkin L., and Raskin N. (2003). Every stabilizing dead time controller has an observer predictor-based structure. Automatica, vol. 39, n° 10, p. 1747-1754.
Tarbouriech S., Garcia G., Da Silva J., and Queinnec I. (2011). Stability and Stabilization of Linear Systems with Saturating Actuators. Springer.
Warburton R. D. H., Disney S. M., Towill D. R. and Hodgson J. P. E. (2004). Technical Note: Further insights into ‘the stability of supply chains’, International Journal of Production Research, vol. 42, n° 3, p. 639-648.