LQ optimal and reaching law based design of sliding mode supply policy for inventory management systems

• Autorzy: Ignaciuk P. , Bartoszewicz A.
• Języki publikacji: EN

Abstrakty

EN

In this paper, the theory of discrete sliding-mode control is used to design new supply strategies for periodic-review inventory systems. The proposed strategies guarantee that demand is always entirely satisfied from the on-hand stock (yielding the maximum service level), and the warehouse capacity is not exceeded (what eliminates the cost associated with emergency storage). In contrast to the classical, stochastic approaches, in this paper, we focus on optimizing the inventory system dynamics. The parameters of the first control strategy are selected by minimizing a quadratic cost functional. Next, it is shown how the system dynamical performance can be improved by applying the concept of reaching law combined with dead-beat control. The stable, non-oscillatory behavior of the closed-loop system is demonstrated, and the properties of the designed controllers are discussed and strictly proved.

Słowa kluczowe

EN

sliding-mode control; inventory control; discrete-time systems

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2009
• Tom: Vol. 19, no. 3
• Strony: 261--277
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Ignaciuk P.

autor

Bartoszewicz A.

• Technical University of Lodz, Lodz, Poland,

Bibliografia

• [1] E. AGGELOGIANNAKI and H. SARIMVEIS: Design of a novel adaptive inventory control system based on the online identification of lead time. Int. J. Production Economics, 114(2), (2008), 781-792.
• [2] B. BANDYOPADHYAY and S. JANARDHANAN: Discrete-time sliding mode control. A multirate output feedback approach. Series: Lecture Notes in Control and Information Sciences, 323, Springer-Verlag Berlin Heidelberg, 2006.
• [3] A. BARTOSZEWICZ: Discrete time quasi-sliding mode control strategies. IEEE Trans, lndustrial Electronics, 45(4), (1998), 633-637.
• [4] A. BARTOSZEWICZ and A. NOWACKA: SMC without the reaching phase - the switching piane design for the third order system. IET Control Theory and Applications, 1(5), (2007), 1461-1470.
• [5] J.-L. CHANG: Robust discrete-time model reference sliding-mode controller design with state and disturbance estimation. IEEE Trans. lndustrial Electronics, 55(11), (2008), 4065-4074.
• [6] D. CHU, W.-W. LIN and C.E.R. TAN: A numerical method for a generalized algebraic Riccati equation. SI AM J. Control and Optimization, 45(4), (2006), 1222-1250.
• [7] W. GAO, Y. WANG and A. HOMAIFA: Discrete-time variable structure control systems. IEEE Trans. lndustrial Electronics, 42(2), (1995), 117-122.
• [8] G. GOLO and C. MILOSAVLJEVIĆ: Robust discrete-time chattering free sliding mode control. Systems & Control Lettters, 41(1), (2000), 19-28.
• [9] P. IGNACIUK and A. BARTOSZEWICZ: Linear quadratic optimal discrete time sliding mode controller for connection oriented communication networks. IEEE Trans. lndustrial Electronics, 55(11), (2008), 4013-4021.
• [10] S. JANARDHANAN and V. KARIWALA: Mułtirate output feedback based LQ op-timal discrete-time sliding modę control. IEEE Trans. Automatic Control, 53(1), (2008), 367-373.
• [11] C. MILOSAVLJEVIĆ: General conditions for the existence of a quasisliding modę on the switching hyperplane in discrete variable structure systems. Automation and Remote Control, 46(3), (1985), 307-314.
• [12] M. ORTEGA and L. LIN: Control theory applications to the production-hwentory problem: a review. Int. J. Production Research, 42(11), (2004), 2303-2322.
• [13] J. P. RICHARD, F. GOUAISBAUT and W. PERRUQUETTI: Sliding modę control in the presence of delay. Kybernetika, 37(3), (2001), 277-294.
• [14] L. RODRIGUES and E.-K. BOUKAS: Piecewise-linear Hx controller synthesis with applications to inventory control of switched production systems. Automatica, 42(8), (2006), 1245-1254.
• [15] B. SAMANTA and S.A. AL-ARAIMI: An inventory control model using fuzzy logie. Int. J. Production Economics, 73(3), (2001), 217-226.
• [16] E. A. SILVER, D.F. PYKE and R. PETERSON: Inventory management and production planning and scheduling. John Wiley & Sons, New York, 1998.
• [17] B. VESELIĆ, B. PERUNICIC-DRAZENOVIC and C. MILOSAVLJEVIC: High-performance position control of induction motor using discrete-time sliding-mode control. IEEE Trans. Industrial Electronics, 55(11), (2008), 3809-3817.
• [18] A. S. WHITE: Management of inventory using control theory. Int. J. Technology Management, 17(7), (1999), 847-860.
• [19] M. YAN and Y. Sm: Robust discrete-time sliding modę control for uncertain systems with time-varying state delay. IET Control Theory and Applications, 2(8), (2008), 662-674.
• [20] J. ZABCZYK: Remarks on the control of discrete-time distributed parameter systems. SIAMJ. Control, 12(4), (1974), 721-735.
• [21] P. H. ZIPKIN: Foundations of inventory management. McGraw-Hill, New York, 2000.