INTRODUCTION Mathematical models of dynamic systems are required in most areas of scientific inquiry and take various forms, such as differential equations, state-space equations and transfer functions. The most widely used approach to mathematical modelling involves the construction of math- ematical equations based on physical laws that are known to govern the behavior of the system. Amongst the draw- backs to this approach are that the resulting models are often complex and not easily estimated directly from the available data because of identifiability problems caused by over-parameterization. This complexity also makes them difficult to use in applications and control system design. If operational data are available, an alternative to physically- based mathematical modelling is data-based system iden- tification, which can be applied to virtually any system and typically yields relatively simple models that can well describe the systems behavior within a defined operational regime.67744

One of the fundamental modeling techniques is the black- box modeling in which the model is identified only using the data set acquired from the process during a dynamical test and no other source of knowledge is used [1]. It is often desirable to find workable models with good static and dynamical responses [2]-[10]. The estimation of nonlinear models with such features is quite hard mainly because static and dynamic information are not equally weighed in a single set of data. Although flexible black-box structures are able to accurately fit a single piece of data, there are two main drawbacks with most of such structures [3]. First, the static information is not readily available analytically once such models are estimated. Second, not all such model structures and algorithms have been adapted to permit the effective use of static information during parameter estimation.

In this paper, we aim to identify models of a 15 kW hydraulic pumping system. There has been a clear increase of variable frequency drives as the final control element for such systems. This has enabled the implementation of fast and automatic control systems. Models of such systems are highly desirable for characterization and control. Such models should, ideally, represent the system accurately both in transient and steady-state regimes over a wide range of operating conditions. Different identification ap- proaches were implemented to guarantee a good balance between such features. A group of identification methods are closely examined and evaluated with respect to the pa- rameters estimation of polynomial models of a 15 kW hy- draulic pumping system. The aim is to determine models with good performance in both transient and steady-state regimes. The linear methods based on parametric model structures cover autoregressive (AR), autoregressive with exogenous variables (ARX), autoregressive with moving average and exogenous variables (ARMAX), Box-Jenkins (BJ) and state-space schemes. The nonlinear method is a nonlinear autoregressive with moving average and exoge- nous variables (NARMAX) which uses free-run simulation. Through extensive simulations, it is concluded that NAR- MAX yields the best fit amongst the selected identification schemes.论文网

This paper is organized as follows. In Section II, the hydraulic pumping system is briefly presented together with the dynamical data. Section III deals with para- metric model structures including AR, ARX, ARMAX, Box-Jenkins and state-space methods for the hydraulic pumping system. In Section IV, the simulation results of various identification techniques have  been discussed  and a comparative study of various linear control has been presented.

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2. HYDRAULIC  PUMPING SYSTEM

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In a full-scale hydroelectric power plant (over 80% of Brazilian electrical energy is produced in such plants) the water head can be considered constant over reasonably long periods of time. At testing plants, however, the turbines are fed by powerful hydraulic systems and not by a water head. Because of the characteristics of the centrifugal pumps used in such plants, the pressure on the turbine decreases as the water flow increases. Therefore, in realistic testing plants, pressure must be controlled over a wide range of operating conditions. Mathematical models are desired to simulate and to design the closed- loop control of the real pumping system, where the models output is the system pressure and the models input is the pumps reference speed.