Gurkan Kavuran

Improvement of IIR filter discretization for fractional order filter by discrete stochastic optimization

Fractional calculus has many implications for the field of signal processing, particularly in filter design. Fractional order filter functions are generalization of all rational filter structures including integer-order filter functions and it provides more options in term of frequency selectivity property. This study presents application of stochastic optimization methods for the improvement of IIR filter discretization of fractional order continuous filter structures. We used results of well-known fractional order discretization methods as initial filter model and improved the amplitude response of discrete filter for a better fitting to the continuous fractional-order filters. Illustrative examples demonstrate that it is possible to further improve amplitude responses of IIR filter discretization obtained for the fractional order differentiators, the first and second order continuous fractional-order filter structures by using basic random search algorithms. Digital filter design is very essential for digital signal processing applications and findings of this paper may contribute to digital filter design field in practice.

Detection of RR interval alterations in ECG signals by using first order fractional filter

Sleep apnea syndrome deteriorates sleeping quality and daily performance of many individuals. This study presents utilization of fractional-order low pass filtering for the detection of RR interval alteration from electrocardiogram (ECG) signals. In the case of sleeping apnea, cardiac interbeat intervals prolong and it is viewed as an indication of obstructive sleep apnea state. The prolonged interbeat intervals manifest themselves as the decrease of R peak frequency (increase of RR intervals) in ECG signals. It results in shifting of spectral components composing R peaks towards lower frequencies in energy signal of ECG. In order to detect prolonging interbeat intervals, energy signal calculated from ECG is applied to low-pass fractional-order filter. Transition band of the low-pass filter is used as a ramp filter in order to detect frequency variations in the energy of R peaks. We compare results of the first order fractional-order and integer order low-pass filters and demonstrate that the fractional-order filter can improve the detection performance of low-pass filtering by modifying transition band slope of low-pass filters.

Investigation of periodic modes in nonlinear systems with fractional order integrator

This paper investigates the effect of fractional order integrator on the nonlinear feedback systems. The effect of fractional order integrator, which is proposed to place in front of relay with dead zone on the second order system, is analysed comparatively using Describing Function method and simulation results. Since the proposed approach provides the opportunity for the selection of a wide phase range, it can be considered as an effective method to select relevant sampling frequency and to investigate limit cycles in modulators and demodulators that are used for signal conversion applications.

Computation of limit cycles in nonlinear feedback loops with fractional order plants

The paper deals with an aspect of the analysis of nonlinear feedback control systems with a fractional order transfer function. A review of the classical describing function (DF) method is given and its application to a control system with a fractional order plant is demonstrated. Unlike the DF method the frequency domain approach of Tsypkin is known to give exact results for limit cycles in relay systems and it is shown that this approach extends to systems with fractional order transfer functions. The formulation is done in terms of A loci which are related to and more general than the Tsypkin loci. Programs have been developed in MATLAB to compute the limit cycle frequency and also to show the results graphically. Examples are provided to illustrate the approach for a relay with no dead zone.

Reference-shaping adaptive control by using gradient descent optimizers

This study presents a model reference adaptive control scheme based on reference-shaping approach. The proposed adaptive control structure includes two optimizer processes that perform gradient descent optimization. The first process is the control optimizer that generates appropriate control signal for tracking of the controlled system output to a reference model output. The second process is the adaptation optimizer that performs for estimation of a time-varying adaptation gain, and it contributes to improvement of control signal generation. Numerical update equations derived for adaptation gain and control signal perform gradient descent optimization in order to decrease the model mismatch errors. To reduce noise sensitivity of the system, a dead zone rule is applied to the adaptation process. Simulation examples show the performance of the proposed Reference-Shaping Adaptive Control (RSAC) method for several test scenarios. An experimental study demonstrates application of method for rotor control.

Path planning for nonholonomic mobile robot based on Bézier curve

This study presents simulation results of nonholonomic mobile robot control with path planning which is based on Bézier Curves. The purpose of this paper is set to develop a simulation model for differential drive wheeled (DDW) robot by using MATLAB/Simulink environment. Fractional order PID structure is used to increase the tracking performance of DDW robot. Simulation results are compared for the various path scenario. It was shown that the proposed control scheme exhibits agreeable performance for the desired path tracking.