Nonlinear FOPDT model identification for the superheat dynamic in a refrigeration system

Abstract

An on-line nonlinear FOPDT system identification method is proposed and applied to model the superheat dynamic in a supermarket refrigeration system. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its parameters are time dependent. After the considered system is discretized, the nonlinear FOPDT identification problem is formulated as a Mixed Integer Non-Linear Programming problem, and then an identification algorithm is proposed by combining the Branch-and-Bound method and Least Square technique, in order to on-line identify these timedependent parameters. The proposed method is firstly tested through a number of numerical examples, and then applied to model the superheat dynamic in a supermarket refrigeration system based on experimental data. As shown in these studies, the proposed method is quite promising in terms of reasonable accuracy, large flexibility and low computation load. The study on the superheat also clearly showed time varying properties of superheat dynamic, which indicate some necessity of adaptive mechanism of efficient superheat control.

Time-Varying FOPDT Modeling and On-line Parameter Identification

“…We also observed that the estimation of varying time-delay can result in a nonconvex optimization problem (Yang and Sun (2011)). The simplest and straightforward way to estimate the inputoutput delay of a LTI system is to use the cross-correlation analysis (Richard (2003)), or by some experimental approaches (Åström and Hägglund (1995)).…”

“…and τ k are called as the kth-step sampled system gains and time constant, respectively (Yang and Sun (2011) (2) and (3), correspondingly. The former ones are piecewise-constant (i.e., constant during every sampling period) time functions, while the latter ones are continuously-varying time functions.…”

“…x(t) is the "noise-free" output, and X(s), {U i (s)} i=1,2 are the corresponding Laplacetransforms of the system output and inputs, respectively. The two transfer functions in (1) are type of TV-FOPDT models (Yang and Sun (2011)), i.e.,…”

“…The TV-FOPDT model is an extension of the standard FOPDT by allowing the system parameters, i.e., the system gain, the time constant and the time-delay, to be time dependent. Of course, this time dependency could also be due to the situation that some system parameters are correlated with some system variables, such as the input dependent time-delay which is studied in (Sun and Yang (2011)). …”

“…For instance, Gralda and MacArthur (1992); Li et al (2008); Rasmussen and Larsen (2009) have discovered that system parameters, such as the system gain, time-constant and time-delay, in a standard FOPDT formulation of the transient superheat dynamic can be time-varying. In order to keep the FOPDT model's merit, but, meanwhile be able to correctly reflect system's key transient dynamics, Sun and Yang (2011); Yang and Sun (2011) proposed a type of nonlinear FOPDT model, named Time-Varying FOPDT (TV-FOPDT), to model the transient superheat dynamic in a refrigeration system. The TV-FOPDT model is an extension of the standard FOPDT by allowing the system parameters, i.e., the system gain, the time constant and the time-delay, to be time dependent.…”