Abdullah Ates

A numerical investigation for robust stability of fractional-order uncertain systems

This study presents numerical methods for robust stability analysis of closed loop control systems with parameter uncertainty. Methods are based on scan sampling of interval characteristic polynomials from the hypercube of parameter space. Exposed-edge polynomial sampling is used to reduce the computational complexity of robust stability analysis. Computer experiments are used for demonstration of the proposed robust stability test procedures.

A stochastic multi-parameters divergence method for online auto-tuning of fractional order PID controllers

Abstract This paper presents a stochastic multi-parameters divergence method for online parameter optimization of fractional-order proportional–integral–derivative (PID) controllers. The method is used for auto-tuning without the need for exact mathematical plant model and it is applicable to diverse plant transfer functions. The proposed controller tuning algorithm is capable of adaptively responding to parameter fluctuations and model uncertainties in real systems. Adaptation skill enhances controller performance for real-time applications. Simulations and experimental observations are carried on a prototype helicopter model to confirm the performance improvements obtained by the online auto-tuning of fractional-order PID structure in laboratory conditions.

Optimal fractional order PID design via Tabu Search based algorithm

This paper presents an optimization method based on the Tabu Search Algorithm (TSA) to design a Fractional-Order Proportional-Integral-Derivative (FOPID) controller. All parameter computations of the FOPID employ random initial conditions, using the proposed optimization method. Illustrative examples demonstrate the performance of the proposed FOPID controller design method.

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.

Tuning of fractional order PID with master-slave stochastic multi-parameter divergence optimization method

This paper presents master-slave stochastic multi-parameters divergence optimization (SMDO) method for tuning of fractional order proportional-integral-derivative (FOPID) controllers. Bodes ideal control loop (BICL) is used as a reference model that guides the optimization process. Master-slave SMDO performs optimization of FOPID and BICL parameters together. In the first stage called as locking, step responses of FOPID and BICL approximate each other. In the second stage called as drifting, BICL guides tuning of the FOPID towards a desired step response. One of the advantages of presented optimization approach is that both optimization of the reference model (BICL) and controller (FOPID) cooperates and the tuning of FOPID is governed by BICL in the drifting stage. Operation and performance of the proposed algorithm are demonstrated by simulation examples.

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.

Sigmoid based PID controller implementation for rotor control

This paper presents a sigmoid based variable coefficient PID (SBVC-PID) controller design for Twin Rotor MIMO System (TRMS). The proposed SBVC-PID controller dynamically changes controller coefficients according to a modified sigmoid function of the error signal. The modified sigmoid function is used to limit variability of PID controller coefficients in a predefined range. In the proposed method, each parameters of PID, namely pk, kt and kd, alter between predefined upper and lower bounds. A modified sigmoid function adjusted by a transition coefficient is used to alter each of the PID parameters between these bound limits. The variable coefficients of SBVC-PID maintain a hypercube in kp, kt and kd parameter space satisfying robust stability of the system. Well-known Kharitonov polynomials are used to ensure that the SBVC-PID coefficient alteration takes place in the robust stability intervals. Due to dynamically change of PID coefficients depending on magnitude of error signal, the control performance can be improved compared to conventional PID control. Performance of SBVC-PID controller is demonstrated via theoretical examples and TRMS rotor control simulations.

An experimental investigation for error-cube PID control:

This experimental study investigates the practical benefits and drawbacks of error-cube control for closed-loop PID control structures. The error-cube control approach employs the cube power of the error signal for controllers and this causes variability in control characteristics due to the non-linearity of the cube power operation. The error-cube signal introduces attenuated and magnified error regions. These two characteristic error regions result in a tight control regime and a slack control regime, depending on magnitude of the error signal. The study presents a discussion on non-linear error signals in a practical aspect and demonstrates the effects of non-linear error signals on the step response of closed-loop PID control systems via simulation results and experimental measurements. An enhanced error-cube controller was proposed to improve the control performance of the error-cube control and results are discussed.

Probabilistic robust stabilization of fractional order systems with interval uncertainty

This study investigates effects of fractional order perturbation on the robust stability of linear time invariant systems with interval uncertainty. For this propose, a probabilistic stability analysis method based on characteristic root region accommodation in the first Riemann sheet is developed for interval systems. Stability probability distribution is calculated with respect to value of fractional order. Thus, we can figure out the fractional order interval, which makes the system robust stable. Moreover, the dependence of robust stability on the fractional order perturbation is analyzed by calculating the order sensitivity of characteristic polynomials. This probabilistic approach is also used to develop a robust stabilization algorithm based on parametric perturbation strategy. We present numerical examples demonstrating utilization of stability probability distribution in robust stabilization problems of interval uncertain systems.

Tabu search algorithm for fractional order PID via nonlinear multi objective functions

This paper proposes to use multi objective nonlinear functions with Tabu Search Algorithm (TSA) to design a fractional order proportional integral derivative (FOPID) controller. Classical TSA modified to satisfy the maximum number of multi nonlinear functions that define important criteria for FOPID design. Simulation result exhibits the performance of the algorithm.