翻译部分英文原文： Nonlinear Identification of Hydraulic Servo-Drive Systems1. IntroductionHydraulic servo-drives are used in many industrial plants, because they can produce large forces and torques with high speed .However,the rather complex structures of such drive systems make it difficult to develop suitable, preferably low-or-der models of the dynamic of the plant. The models are needed for the design of state observers, filters and controllers . The design is most simplified if the model of the plant has a nonlinear canonical form. In actual hardivare , however, systems rarely have these suitable forms.Nonlinear transformations into canonical forms therefore must first be determined under rigor-ous conditions and with considerable mathematico effort(inte-gration of partial differential equations and inversion of nonlinear algebraic equations). To avoid this, the practical application of system identification techniques provides satisfactory models of individual units in some desired form.The aim of the research presented in this article is to obtain models of a hydraulic servo-drive directly, in the nonlinear observer canonical form, via parameter identification. In recent years, much effort has been devoted to modeling of hydraulic systems using bilinear models. Several of these models have been evaluated by tests on real plants, and are well established. However, the identification methods used, the maximum likelihood method and prediction error method, require suitably specified(a good enough)initial values of the unknown parameters and states of the system. An unsuitable choice causes con-vergence and singularity problems that, in real applications, are very difficult to solve.In this article, the parameter estimation is based on a modified Recursive Instrumental Variables algorithm that enables us to cvercome the difficulties mentioned above. We consider state quadratic nonlinearities for better modeling of the real dynamics of hydraulic drives. For handing time derivatives of measure-ments, the so-called Linear Integral. Filter proposed by sagara and Zhao is used. The identification procedure is applied to an experimental setup. A good correspondence is obtained between the date and the models which are identified directly in nonlinear especially quadratic observer canonical form.2. Description of the Hydraulic Drive The physical process used as testing bench consists of a servo value and a hydraulic cylinder coupled with a moving mass. Iuustrates the test stand used in this study. In order to avoid the representation of many equations which may be found, for instance, in Dietz and Prochnio and Koeckemann, a schematic diagram of the system is shown in and a detailed block diagram is given in. The input signal of the system is the voltage and the output signal is the position x of the moving mass.The state variables are listed in Table.The most significant nonlinearities of the plant are the multi-pliers, the square root functions, the oil elasticity and the friction.In practice,it is difficult to determine the physical parameters associated with these nonlinearities. Thus system identification techniques are needed to obtain approximate models of the system such that the error between measured data and model is minimized.3. Identification The continuous parameter estimation from sampled data of input-output measurements. For this, Sagara and Zhao proposed an operation of numerical integration, the so-called Linear Integral Filter(LE) for linear differential equations. This method will be extended with the goal to identify some lineat-in parameters nonlinear systems like those in observer canonical form.4Linear Integral FilterCommonly, only the linear terms in (10) are considered. The higher-order terms are thus ignored following the assumption that they are negligible when the systems state close to the reference point chosen for the linearization. In this article we go two steps further by taking into account also the bilinear and the quadratic approximation while adding a lot to the computational burden, they will be left aside in the application on the hydraulic drive presented here. Nevertheless, the identification method will be derived for any.Furthermore, the filter parameter 1 affects considerably the accuracy of the parameter estimation. It is pointed out by Sagara and Zhao 6 that should be chosen so that the frequency bandwidth of the LIF matches as closely as possible the frequency band of the system.In paractical use, however, a-prioriinformation about the frequency band of the system are often not available. Therefore, many identification experiment trials must be taken.One very effective method is to use the recursive instrumental variable(IV) method, which is asymptotically linbiased for a suitable choice of the IV and does not require a pricri knowledge of the noise statistics. The following algorithm is given by Ljung and soederstro