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A new adaptive inventory control strategy is developed by applying online adaptation in the framework of passivity-based control. By using the system model and definition of the inventory, a feedback-feedforward control structure is derived from the passivity theorem. The stability analysis and the extension of the controller to a non-passive system are also given in this paper. This control strategy is demonstrated in a transfer function example and an application to a pressure tank unit in a chemical plant.

The concept of passivity has played a key role of nonlinear control theory since it was formalized in 1970s [1]. Being related to Lyapunov and View the MathML sourceL2 stability, the passivity theory provides a useful tool for nonlinear system analysis [2]. An important conclusion from passivity is that a strictly passive system with a negative feedback of another passive system is stable [4]. Further more, the degree of passivity can be quantified by the passivity indices for both passive and non-passive systems. The shortage of passivity of a system can be compensated by the excess of passivity of a feedback controller, which motivated the passivity-based controller design [4]. Passivity theory has not been applied in process control until recent years. The notion of process system is first defined by connecting thermodynamics and passivity [5] and [6]. By using macroscopic balance of inventories (such as total mass and energy) to construct passive input-output pairs, an inventory control strategy is further proposed based on the idea that the manipulated variables are chosen so that the selected inventories follow their set points [7], [8] and [9]. This control strategy has been applied to several control problem examples such as drum boiler, ternary flash and reactor flow sheet [7]. In industry, it was successfully applied to the temperature control problem of the float glass process for PPG company [9]. If there are unknown parameters in the process model, online adaptation can be used in the passivity-based inventory control frame [8]. In this article, the passivity-based adaptive inventory control is studied in both theory and applications, and the paper is organized as follows. In the following section, the notion of a passive system and the passivity theorem is summarized. The loop-shifting technique to render a non-passive system passive is also described. Then the adaptive feedforward and feedback controller is derived from passivity theorem and the inventory control theory. The Lyapunov stability analysis and extension to a non-passive system by loop-shifting are also given in this section. Finally, the control strategy is applied to a general transfer function example and a pressure tank unit of a chemical plant and simulation results are discussed.

The adaptive control is applied in the passivity-based inventory control scheme. Mass-energy balance dynamic models are used and certain model parameters are adapted on line, so that the dynamic changes and the effects of disturbances can be compensated by the adaptive feedforward controller. The controller is tested on transfer function models and simulation result shows that the online adaptation makes it outperform the classic feedforward controller. The control strategy is also applied on a chemical pressure tank system, and the plant data shows that much better performance can be obtained by adding the passivity-based adaptive controller as the feedforward component to the existing feedback control system.