PIalphaDbeta feedback type control of expansion turbine e in the liquid air cryogenic production process

Abstract

The paper presents a new algorithm of control for the cryogenic production process of technical gases. Cryogenics is the science and technology dealing with temperatures less than 120 K, although this summary does not adhere to a strict 120 K definition. New way to the technical production of liquid air was introduced by C. Linde at the end of the nineteenth century [1]. The successful simple and economical production of liquid air may be achieved using the reversing heat exchangers, where damping from the higher down to the lower pressure occurs. Production of liquid air at low pressure was first introduced in 1938 by the Russian academician P. L. Kapica and includes production of liquid air at pressure p2 = 6 ¸-7 bar and then its expansion in the gas turbine. Moreover, the expansion turbine in the process of liquid air production was used for expansion of the air from the thermodynamic state P (Pp,Tp) to the state K( (Pk,Tk=lowering when the air temperature decrease from Tp to Tk and the pressure decrease from Pp to Pk . When the cold air expands in the turbine then the heat losses arise due to the heat exchange with the environment. The amount of air that expands in the gas turbine does not exceed 25% of the overall usable air [1, 2]. For application in the synthesis of control, input temperature, and the flow of air expansion turbine, it is necessary to determine the appropriate linear parts of differential equations of the building guidance as well as the procedural object in these differential equations. These equations describe the work guidance part of the building which consists of positionbody, pneumatic amplifier (booster volume), the pneumatic motor and work process, i.e. the appropriate equation of state and output are given. In recent years, fractional calculus has been applied in the modeling and control of various kinds of physical systems, as it is well known and documented in many control theories or in the literature data [3]. The fractional integro-differential operators-(fractional calculus) are a generalization of integration and derivation to non-integer order (fractional) operators. Recently, published results [4, 5] indicate that the use of a fractional-order PID controller can improve both the stability and performance robustness of feedback control systems. In this paper, a fractional order PID controller ( PIalpha Dbeta ) is used to control the production process of technical gases. The objective of this work is to find out optimum settings for a fractional PIalpha Dbeta controller in order to fulfill different design specifications for the closed-loop system, taking advantage of the fractional orders, alpha and beta . Also, problem of discretization of proposed PIalpha Dbeta will be treated as a key step in digital implementation. This difficulty arises from the mathematical nature of fractional operators, which demand hard requirements of processors memory and velocity capacities.