A new class of cascade digital orthogonal filters of the Malmquist type based on bilinear transformation for mapping poles to zeroes and vice versa is presented in this paper. In a way, it is a generalization of the majority of the classical orthogonal filters and some newly designed filters as well. These filters are orthogonal with respect to the generalized inner product which is actually a generalization of the classical inner product. Outputs of these filters are obtained by using polynomials orthogonal with respect to the new inner product. The main quality of these filters is that they are parametric adaptive. The filter with six sections is practically realized in the Laboratory for Modeling, Simulation and Control Systems. Performances of the designed filter are proved on modeling and identification of the system for differential pulse code modulation. Real response and response from the proposed filter are compared with regard to the chosen criteria function. Also, a comparative analysis of the proposed filter with some existing filters is performed.

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.

This paper presents generalized orthogonal cascade filters based on bilinear transformation for mapping poles to zeroes and zeroes to poles in transfer functions. The filters are orthogonal with respect to a new generalized inner product. Actually, they represent a generalization of several classes of existing traditional filters: the ones obtained by using linear transformation of poles to zeroes, and the ones obtained by reciprocal transformation of poles to zeroes. Generalized filters provide obtaining more precise models of dynamic systems. This is verified by comparison between models based on new filters and models based on classical filters. Practical realization of these filters with adjusting parameters of bilinear transformation and transfer function is performed. An application in modeling continuous-time systems as a complex industrial process is given, and it is shown that in that way we obtain more quality models than by using the classical filters.

The computational burden could be an issue of traditional model predictive control (MPC) in real-time applications. There are different procedures to cope with this problem such as using explicit MPC or approximation of the control inputs using orthogonal-basis functions. This paper presents the design procedure and experimental validation of a generalized discrete-time Malmquist orthogonal functions-based model predictive control (MbMPC) whose usage can decrease calculation concerns. To the authors’ knowledge, this is the first time the Malmquist functions are introduced into the MPC design. The discrete-time orthogonal Malmquist functions properties are used within this approach for approximating the future control input increments with a smaller number of parameters than in traditional MPC approaches. It is shown that the satisfactory controller and closed-loop system performances can be achieved using smaller number of tuning parameters. The performance of the proposed MbMPC is shown and compared with discrete-time Laguerre orthogonal functions based MPC (LbMPC) applied to a DC motor servo system. The simulation and experimental results demonstrate better IAE, ITAE, ISE and ITSE controller performance indices as well as faster average calculation time in comparison with the LbMPC approach. Additionally, the advantage of using the proposed method is emphasized by showing how the length of the prediction horizon affects the computational burden in comparison to the traditional MPC approaches.

In this paper, we are using the Kepware tools as a data collection tool to collecting data for identifying the process and making the mathematical models is described in this paper. The connection to the process was made using a programmable logic controller like a real time DAQ (Data Acquisition Board and System) device, database and a client application developed for these purposes. Special attention is paid to the possibility of collecting a large amount of process data as the same moment time of data sampling.

This paper presents one method for probability estimation of some property of imperfect systems (stability, reliability, oscillations appearance, controllability, sensitivity, etc.). The region of certain system property is approximated in parameter space and relations for probability of defined properties are obtained. Application systems with one nonlinearity: of this approximate method in the real technical system is given for the case of determining the probability of oscillations appearance.