Staniša Lj. Perić

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.

Modeling of Dynamic Systems Using Orthogonal Endocrine Adaptive Neuro-Fuzzy Inference Systems

This paper presents a new method for designing adaptive neuro-fuzzy inference systems (ANFIS). Improvements are made by introducing specially developed orthogonal functions into the very structure of ANFIS, specifically, into the layer that imitates Sugeno stile defuzzification. These functions are specially tailored for analysis and synthesis of dynamic systems and they also contain an adaptive measure of the variability of the systems operating in a real environment, which can be implemented inside the ANFIS as hormonal effect.

Fuzzy sliding mode control for anti-lock braking systems

A combination of two control methods, sliding mode and fuzzy, for the wheel slip control in anti-lock braking system, is presented in this paper. The fuzzy block is used to determine the values of key parameters important for establishing switching function dynamics. It is demonstrated, via performed experiments, that proposed control algorithm gives good system performances.

Adaptive PID control based on orthogonal endocrine neural networks

A new intelligent hybrid structure used for online tuning of a PID controller is proposed in this paper. The structure is based on two adaptive neural networks, both with built-in Chebyshev orthogonal polynomials. First substructure network is a regular orthogonal neural network with implemented artificial endocrine factor (OENN), in the form of environmental stimuli, to its weights. It is used for approximation of control signals and for processing system deviation/disturbance signals which are introduced in the form of environmental stimuli. The output values of OENN are used to calculate artificial environmental stimuli (AES), which represent required adaptation measure of a second network-orthogonal endocrine adaptive neuro-fuzzy inference system (OEANFIS). OEANFIS is used to process control, output and error signals of a system and to generate adjustable values of proportional, derivative, and integral parameters, used for online tuning of a PID controller. The developed structure is experimentally tested on a laboratory model of the 3D crane system in terms of analysing tracking performances and deviation signals (error signals) of a payload. OENN-OEANFIS performances are compared with traditional PID and 6 intelligent PID type controllers. Tracking performance comparisons (in transient and steady-state period) showed that the proposed adaptive controller possesses performances within the range of other tested controllers. The main contribution of OENN-OEANFIS structure is significant minimization of deviation signals (17%-79%) compared to other controllers. It is recommended to exploit it when dealing with a highly nonlinear system which operates in the presence of undesirable disturbances.

Application of neural networks with orthogonal activation functions in control of dynamical systems

In this article, we present a new method for the synthesis of almost and quasi-orthogonal polynomials of arbitrary order. Filters designed on the bases of these functions are generators of generalised quasi-orthogonal signals for which we derived and presented necessary mathematical background. Based on theoretical results, we designed and practically implemented generalised first-order (k = 1) quasi-orthogonal filter and proved its quasi-orthogonality via performed experiments. Designed filters can be applied in many scientific areas. In this article, generated functions were successfully implemented in Nonlinear Auto Regressive eXogenous (NARX) neural network as activation functions. One practical application of the designed orthogonal neural network is demonstrated through the example of control of the complex technical non-linear system – laboratory magnetic levitation system. Obtained results were compared with neural networks with standard activation functions and orthogonal functions of trigonometric shape. The proposed network demonstrated superiority over existing solutions in the sense of system performances.

Sliding Mode Based Anti-Lock Braking System Control

In this paper we consider different continuous- and discrete-time sliding mode control (SMC) techniques in the control of antilock braking system (ABS). Having in mind that ABS is characterized by nonlinear and uncertain dynamics, SMC is a right choice for its control because of its robust characteristics. The survey of continuous-time SMC algorithms based on nonlinear models of ABS is given first. Then, the discrete-time nonlinear model of ABS is derived, and the overview of existing discrete-time SMC techniques is presented. The experimental results are given to show the effectiveness of analyzed SMC methods.

The Probability of Stability Estimation of an Arbitrary Order DPCM Prediction Filter: Comparison Between the Classical Approach and the Monte Carlo Method

This paper presents the stability analysis of the linear recursive (prediction) filters with higher order predictors in a DPCM (differential pulse-code modulation) system, where traditional methods become too difficult and complex. Stability conditions for the third- and fourth-order predictor are given by using the Schur–Cohn stability criterion. The probability of stability estimation is performed by using the Monte Carlo method. Verification of the proposed method is performed for lower order predictors (the first- and second-order). We calculated numerical values of the probability of stability for higher order predictors and previously experimentally obtained parameters. With large enough number of trials (samples) in Monte Carlo simulation, we reach the desired accuracy. DOI: http://dx.doi.org/10.5755/j01.itc.46.2.14038