Archive | 2019
Use Of Matlab / Simulink Environment For Identification Of Real System: Case Study
Abstract
The static and dynamic behaviour of technical systems (e.g. electrical and mechanical systems, systems from the area of chemical and process engineering) and nontechnical systems from the areas as biology, medicine and economics can be described by mathematical models. There exist two general approaches to modelling – the theoretical and experimental approach, which both have advantages and disadvantages. This contribution is focused on an identification and modelling of a laboratory equipment by various approaches. Individual approaches were verified and compared with each other. INTRODUCTION System identification deals with design of mathematical models of real objects both by analytical or experimental approaches by means of measured data. In the area of automatic control, the methods of system identification are utilized for obtaining of models, which are suitable for controller synthesis; design of prediction algorithms or for simulation. In the area of signal processing (e.g. communications, geophysical engineering and mechanics), models obtained by identification are utilized for spectral analysis, fault detection, filtering etc. System identification is also utilized in non-technical disciplines like biology, econometrics or ecology. The term identification can be defined as follows: Identification is the experimental determination of the temporal of a process or system. One uses measured signals and determines the temporal behaviour within a class of mathematical model shall as small as possible. This definition stems from (Zadeh 1962); see also (Eykhoff 1974). The measured signals are typically only the input to the system and the output from the system. However, if it is also possible to measure states of the process, then one can also detect information about the internal structure of the process (Isermann and Münchhof 2011). Both theory and applications of system identification are content of a number of books, e.g. (Isermann and Münchhof 2011, Keesman 2011, Åström and Wittemark 2008, Ljung 1999, Mikleš and Fikar 2007, Nelles 2001, Södeström and Stoica 1989) etc. Many journal papers concerning system identification were also published. This paper is focused on utilization of the MATLAB/SIMULINK program system and the System Identification Toolbox for experimental identification and modelling of a laboratory model. In the following, a linear SISO (single input-single output) processes as a black-box model are used. In the following part, basic terms connected with the application of the identification methods are explained: • Non-parametric model – represents a dynamic relation between the input and output signals. It can be expressed either in a graphical or tabular forms. It is necessary to parametrize the model. It means to determine parameters for a given structure. • Parametric model – it is necessary to know a structure of the system for purpose of parameters estimation computation. An advantage of non-parametric models is that they do not require any information about the structure of the model. It is necessary to parametrize them. The parametric models require knowledge of the structure of the model. To achieve credible results during experimental system identification, it is important to choose suitable conditions for the experiment. The paper is organized in the following way. The fundamental principle of the system identification is illustrated in Section 1. Conditions of the experimental identification are described in Section 2. The identification of the laboratory model DR300 (Speed Control with Variable Load) with the results are presented in Section 3. Section 4 concludes this paper. Communications of the ECMS, Volume 33, Issue 1, Proceedings, ©ECMS Mauro Iacono, Francesco Palmieri, Marco Gribaudo, Massimo Ficco (Editors) ISBN: 978-3-937436-65-4/978-3-937436-66-1(CD) ISSN 2522-2414 CONDITIONS FOR EXPERIMENTAL IDENTICATION Exciting Input Signals During the choice of the testing signals, it is necessary to take into account also the aspect of the practical feasibility. A lot of testing signals has only theoretical character. They are practically realizable only approximately. Typical representatives of these signals are the unit (Dirac) impulse, step function, white noise etc. Deterministic input testing signals are characterized namely by their spectral properties, which are continuous-time spectrum in case of continuous-time signals and discrete spectrum in case of discrete signals. Random and pseudorandom signals are characterized by autocorrelation functions and power spectral densities. During the choice of the testing signals it necessary to keep the following rules: • a signal must be physically realizable, • spectral properties of the signal must correspond to the spectral properties of the identified system, • the signal must correspond to the type of the identified object with respect to its deterministic or stochastic character, • the signal must not be correlated with other signals affecting the object and with the noise, • the signal must not affect a normal operation of the identified equipment, • only deterministic and pseudorandom signals enables reproducibility of the measurement. From the spectral point of view, the area of automation and control is in the band of low and ultra-low frequencies. Thus, the situation may be handled by using a white noise generator with limited frequency band on the side of high frequencies. The program environment MATLAB/SIMULINK contains a range of routines for generating of input signals for examination of dynamical properties of systems. The Control Toolbox enables plot of impulse and step responses of transfer functions as well as frequency characteristics both in the Gauss complex plain (Nyquist) and logarithmic coordinates (Bode). The System Identification Toolbox contains the following command (Ljung 2017) = idinput( , , , ) u N type band levels (1) The SIMULINK also contains several random signal generators, which can be used for experimental identification. These types of signals with corresponding parameters were used in this contribution. Process Models For purposes of experimental identification of parametric input-output models both in the continuoustime and discrete forms were used in this paper. The continuous-time models are in the forms of differential equation and transfer functions ( ) 0 1 1 1 m m n n b b s b s G s a s a s + + + = + + + ... ... (2) where s is the Laplace variable. The discrete models are in the form of stochastic difference equations and ARX (AutoRegresive with eXogenous input) models. The ARX model can be expressed by the following equation ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 s B z y k u k e k A z A z −