Marko Milojković

A CLASS OF ALMOST ORTHOGONAL FILTERS

In this paper we define a new class of the almost orthogonal filters. These filters are a generalization of the classical orthogonal filters commonly used in the circuit theory, control system theory, signal processing and process identification. Almost orthogonal filters generate the series of almost orthogonal Legendre functions on the interval (0, ∞). They can be successfully used for the analysis, synthesis and designing of imperfect technical systems. They can also be used for approximation of arbitrary functions on (0, ∞). A new method for obtaining the models of imperfect systems is presented as well. Simulations were performed in order to validate the theoretical results and the comparison of new filters with classical filters is given.

Modelling of dynamical systems based on almost orthogonal polynomials

A new class of the almost orthogonal filters is described in this article. These filters are a generalization of the classical orthogonal filters commonly used in the circuit theory, control system theory, signal processing, and process identification. Almost orthogonal filters generate the series of almost orthogonal Legendre functions over the interval (0, ∞). It is well known that all real systems suffer from some imperfections, so the models of these systems should reflect this fact. A new method for obtaining an imperfect system model is proposed. This method uses an almost orthogonal filter, which is based on almost orthogonal functions. Experiments with modular servo drive were performed to validate theoretical results and demonstrate that the method described in the article is suitable for modelling of imperfect systems.

Digital Sliding Mode Control of Anti-Lock Braking System

The control of anti-lock braking system is a great challenge, because of the nonlinear and complex characteristics of braking dynamics, unknown parameters of vehicle environment and sy ...

Approximation based on orthogonal and almost orthogonal functions

Abstract In this paper, we define a class of almost orthogonal rational functions of Legendre type in a new manner. Relations of these functions with classical exponentional functions orthogonal over interval (0, ∞), as well as classical polynomials orthogonal over (0, 1) are explained. Defining relations of these functions can be used for designing almost orthogonal filters. These filters are generators of orthogonal signals and can be successfully applied in finding the best signal approximation in the sense of the mean square error. The filters orthogonal property enables building of physical (in this case electrical) models of dynamical systems (the sources of signals to be approximated) either with less components for the same model accuracy or higher accuracy for the same number of components than the other known models. New filters represent further improvement of previously designed filters, by the same authors, in the sense of simplicity, higher accuracy, lesser approximation time and even a possibility to approximate signals generated by systems with built-in imperfections. Series of experiments were performed to analyze the dependence of approximation accuracy and the number of filters sections.

Quasi-Sliding Mode Control With Orthogonal Endocrine Neural Network-Based Estimator Applied in Anti-Lock Braking System

This paper presents a new control method for nonlinear discrete-time systems, described by an input-output model which is based on a combination of quasi-sliding mode and neural networks. First, an input-output discrete-time quasi-sliding mode control with inserted digital integrator, which additionally reduces chattering, is described. Due to the presence of various nonlinearities and uncertainties, the model of the controlled object cannot be described adequately enough. These imperfections in modeling cause a modeling error, resulting in rather poor system performances. In order to increase the steady-state accuracy, an estimated value of the modeling error in the next sampling period is implemented into the control law. For this purpose, we propose two improved structures of the neural networks by implementing the generalized quasi-orthogonal functions of Legendre type. These functions have already been proven as an effective tool for the signal approximation, as well as for modeling, identification, analysis, synthesis, and simulation of dynamical systems. Finally, the proposed method is verified through digital simulations and real-time experiments on an anti-lock braking system as a representative of the considered class of mechatronic systems, in a laboratory environment. A detailed analysis of the obtained results confirms the effectiveness of the proposed approach in terms of better steady-state performances.

On a new class of quasi-orthogonal filters

In this article, a new class of quasi-orthogonal filters, based on the Legendre and Malmquist-type quasi-orthogonal polynomials, is presented. These filters are generators of quasi-orthogonal functions for which we derive and present all important properties and relations. Our article is based on the classical theory of orthogonality and orthogonal functions, and also on new results in this field of mathematics. Based on theoretical results, we design schemes for the realisation of these filters. Finally, a trail quasi-orthogonal filter is practically realised and its quasi-orthogonality is proven by performing experiments. Quasi-orthogonal filters can be successfully used for signal approximation as well as for modelling, identification, analysis, synthesis and simulation of dynamical systems.

Optimal fuzzy sliding mode control with a time-varying sliding surface

It is well known that sliding mode control can achieve good transient performance and system robustness. However, the sensitivity of the sliding mode control before reaching the sliding surface and the presence of chattering may introduce problems to the tracking control of the system. In this paper, a new sliding surface design approach is proposed that varies the sliding surface in a nonlinear and time-varying fashion. Slope constant of the sliding surface is varied by fuzzy controller based on the ratio between the derivate of error and error itself. Optimal parameters of the fuzzy controller are determined using genetic algorithms. Proposed optimal fuzzy sliding mode control has been applied to an electrical servo drive system and the performed experiments have verified efficiency and improvements of a new control method.

Design of generalised orthogonal filters: application to the modelling of dynamical systems

In this article, we define a new class of orthogonal filters with complex poles and zeroes inside their transfer function. This further improvement of classical orthogonal filters allows the possibility to model a wider range of real systems, that is, the systems whose mathematical models have complex zeroes besides real ones. These filters can be applied in the following areas: circuit theory, telecommunications, signal processing, bond graphs, theory approximations and control system theory. First, we describe the rational functions with complex poles and zeroes, and prove their orthogonality. Based on these functions, we designed the block diagram of orthogonal Legendre-type filter with complex poles and zeroes. After that an appropriate analogue scheme of this filter for practical realisation is derived. To validate theoretical results, we performed an experiment with a cascade-connected system designed and practically realised in our laboratories. The experiments proved the quality of the designed orthogonal model in terms of accuracy and simplicity.

Systems modeling based on Legendre polynomials

A new method for obtaining models of continuous systems, based on Legendre orthogonal filters, is proposed in this paper. Recent results in the field of orthogonal functions were used to improve accuracy of modeling. First, Legendre orthogonal filters were designed on the basis of orthogonal functions. Then, adjustable models were formed. Models parameters were optimized using genetic algorithm. As a case study, an experimental simple DC drive was considered and described in details. Simulations were performed out to approve theoretical results and demonstrate that the method described in the paper is very suitable for modeling continuous systems. It achieves excellent results in the sense of model accuracy and modeling algorithm speed.

Tracking System Design Based on Digital Minimum Variance Control with Fuzzy Sliding Mode

This paper deals with the design of digital fuzzy sliding mode control where only the plant output is used for the realization of control algorithm. The suggested concept is based on minimum variance control approach with disturbance estimator. The additional filtration of nonlinear, fuzzy, control component is performed by using the digital integrator. The higher accuracy in steady-state is also reached for a size range relative to the existing solutions.