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Discrete-time sliding mode control of linear systems with input saturation

Veselić Boban, Milosavljević Čedomir, Peruničić-Draženović Branislava, Huseinbegović Senad, Petronijević Milutin

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 3

517--528

The paper proposes a discrete-time sliding mode controller for single input linear dynamical systems, under requirements of the fast response without overshoot and strong robustness to matched disturbances. The system input saturation is imposed during the design due to inevitable limitations of most actuators. The system disturbances are compensated by employing nonlinear estimation by integrating the signum of the sliding variable. Hence, the proposed control structure may be regarded as a super-twisting-like algorithm. The designed system stability is analyzed as well as the sliding manifold convergence conditions are derived using a discrete-time model of the system in the δ-domain. The results obtained theoretically have been verified by computer simulations.

Sliding mode control of periodic review perishable inventories with multiple suppliers and transportation losses

Bartoszewicz A., Maciejewski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 4

885--892

The purpose of this paper is to develop robust and computationally efficient supply chain management strategy ensuring fast reaction to the demand variations for periodic review perishable inventory systems. For that purpose, we apply a sliding mode approach and we propose a new discrete time warehouse management strategy. The strategy employs the sliding hyperplane appropriately designed to ensure a dead-beat performance of the closed loop system. Our strategy not only explicitly takes into account decay of goods stored in the warehouse (perishing inventories) but it also accounts for transportation losses which take place on the way from suppliers to the warehouse. The proposed strategy ensures full customers’ demand satisfaction, minimizes the on-hand inventory volume and prevents from exceeding the warehouse capacity. This reflects the need of simultaneous minimization of the lost sales costs and inventory holding costs. Furthermore, the strategy ensures that the ordered quantities of goods are always non-negative and upper bounded. These favourable properties of the proposed strategy are formally stated as a lemma and three theorems and proved in the paper.