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Behavioural modelling of delayed imbalance dynamics in nature: a parametric modelling for simulation of delayed instability dynamics
(Taylor & Francis Ltd, 2022) Alagoz, Baris Baykant; Deniz, Furkan Nur; Koseoglu, Murat
Imbalance dynamics can develop very slowly, and real systems and structures may seem to be stable or balanced for long periods of time before signs of instability behaviour become apparent. This study presents two dynamic system modelling approaches for simulation of delayed instability: Firstly, frequency domain properties of the system instability are investigated, and a parametric model to represent delayed instability behaviour is formulated according to the system pole placement technique. Secondly, a new type of instability modelling approach, which is based on time-domain characteristics of fractional order derivative operators, is introduced by utilizing the finite convergence regions of the Binomial series. This special instability modelling technique essentially uses the region of convergence in the series expansion of impulse responses. Several illustrative modelling and simulation examples are illustrated for engineering problems such as slowly developing cracks in metals, the voltage collapse in power systems and the delayed instability in control systems.
Bilgisayarlı tomografi ile elde edilen volumetrik verinin işlenerek üç boyutlu görüntüye dönüştürülmesi
(İnönü Üniversitesi, 2011) Deniz, Furkan Nur
Medikal görüntüleme teknikleri tıp biliminin tanı ve tedavi süreçlerinde, oldukça yaygın bir şekilde kullanılmaktadır. Bu nedenle bu tekniklerin araştırılıp geliştirilmesi tıp ve mühendislik bilimleri alanında çok önemlidir. Bu çalışmada medikal görüntüleme tekniklerinden biri olan bilgisayarlı tomografi ile görüntü elde etme yöntemleri üzerine bazı araştırmalar ve uygulamalar yapılmıştır. İlk aşamada Radon Dönüşümü kullanılarak tomografik görüntülerden sinogram verisi (tomografik veri) Matlab ortamında elde edilmiştir. Çalışmanın esas amacını teşkil eden ikinci aşamada, bu sinogram verilerinden yeniden görüntü elde etmek amacıyla Matlab ortamında dört farklı rekonstrüksiyon yöntemi modellenmiş ve bu modeller kullanılarak görüntüler yeniden oluşturulmuştur. Çalışmada kullanılan yöntemler şu şekildedir: i) filtrelenmiş geri izdüşüm algoritması (FBP), ii) yelpaze hüzme algortiması (FBBP), iii) cebirsel rekonstrüksiyon algoritması (ART), iv) eşzamanlı cebirsel rekonstrüksiyon algoritması (SART). Matlab ortamında modellenen rekonstrüksiyon algoritmaları kullanılarak elde edilen görüntüler, görüntü kalitesi ve rekonstrüksiyon süreleri bakımından karşılaştırılmış ve değerlendirilmiştir. Görüntü kalitesi bakımından iteratif yöntemlerin direkt yöntemlere kıyasla daha kaliteli sonuçlar verdiği, fakat rekonstrüksiyon süresi ve büyük boyutlara sahip matrislerin kullanımı bakımdan bazı problemler oluştuğu görülmüştür. Daha sonra, rekonstrüksiyon algoritmaları modifiye edilmiş ve 34 tomografi kesitine uygulanmıştır. Matlab ortamında bulunan ?Volume Visualization? algoritması kullanılarak üç boyutlu görüntüler elde edilmiş ve elde edilen görüntüler görüntü kalitesi bakımından karşılaştırılmıştır. SART ve FBP algoritması sonucu elde edilen üç boyutlu görüntülerin diğer görüntülere göre daha kaliteli olduğu gözlemlenmiştir.
Coefficient Diagram Method Based Decentralized Controller for Fractional Order TITO Systems
(2022) Bulut, Miray Günay; Deniz, Furkan Nur
Fractional calculus has gained increasing attention from researchers because of providing accurate modelling and flexible controller design in control applications. More research to design controllers for Fractional Order Two-Input Two-Output (FOTITO) systems, which inherently have certain difficulties, is needed when the studies on such control applications are reviewed. In this study, Coefficient Diagram Method (CDM) based decentralized controllers are designed for FOTITO systems. To this end, integer order approximate models of FOTITO systems are obtained and decoupled into two subsystems by using simplified and inverted decoupling configurations. The resulting higher-order approximate subsystem transfer functions are reduced by a model reduction method to facilitate CDM-based decentralized controllers design. Then, CDM-based decentralized controllers are designed by using each subsystem, which enable to control the FOTITO system. Simulation results for two different FOTITO systems, one of which is time delayed, show that the proposed approach exhibits successful performance.
Computation of Stabilizing Decentralized PI Controllers for Fractional Order TITO (FOTITO) Systems
(Ieee, 2021) Bulut, Miray Gunay; Deniz, Furkan Nur
This paper deals with computation of stabilizing decentralized PI controllers for fractional order two-input-two-output (FOTITO) systems. Inverted and simplified decoupling methods are adapted to FOTITO systems and the systems are decoupled into simpler subsystems. Stability regions of the subsystems are obtained and the parameters of the decentralized PI controllers that allows to be stable are calculated. It is demonstrated that both outputs of the FOTITO system are stable when the controller parameters are selected from the common of stable regions of subsystems.
Computation of Stabilizing Decentralized PI Controllers for TITO Systems with Simplified and Inverted Decoupling
(Ieee, 2020) Bulut, Miray Gunay; Deniz, Furkan Nur
In this paper, all stabilizing decentralized PI controllers for Two Input-Two Output (TITO) systems using simplified and inverted decoupling methods are calculated in parameter plane. Two Single Input-Single Output (SISO) systems (independent subsystems) are determined from simplified and inverted decoupling configurations and stability regions of both subsystems are calculated in an illustrative example. Test points selected from different regions to examine stability of both subsystems are used to design decentralized PI controllers. Using selected points from intersection of both stability regions provide a limited region to search the controller parameters guaranteeing the stability for both output of TITO systems. In addition to this advantage, a pair of controller parameters with the same values may be sufficient for both decentralized PI controllers.
Design of Fractional-Order PI Controllers for Disturbance Rejection Using RDR Measure
(Ieee, 2014) Deniz, Furkan Nur; Alagoz, Baris Baykant; Keles, Cemal; Tan, Nusret
Parameter uncertainties and unpredictable environmental disturbances reduce control performance of real control systems. For a robust control performance, stability and disturbance rejection are two main concerns that should be addressed in practical controller design problems. This paper presents an analysis to deal with system stability and disturbance rejection control for fractional-order PI (FOPI) controllers. Stability Boundary Locus (SBL) is calculated for an example with FOPI control system and Reference to Disturbance Rate (RDR) performance is investigated for the chosen stable FOPI designs from the stability region obtained using SBL. MATLAB/Simulink simulation examples are used to demonstrate stable and Disturbance Rejection Control (DRC) of FOPI control systems and presents comparisons for various designs of FOPI controllers.
Disturbance rejection performance analyses of closed loop control systems by reference to disturbance ratio
(Elsevier Science Inc, 2015) Alagoz, Bans Baykant; Deniz, Furkan Nur; Keles, Cemal; Tan, Nusret
This study investigates disturbance rejection capacity of closed loop control systems by means of reference to disturbance ratio (RDR). The RDR analysis calculates the ratio of reference signal energy to disturbance signal energy at the system output and provides a quantitative evaluation of disturbance rejection performance of control systems on the bases of communication channel limitations. Essentially, RDR provides a straightforward analytical method for the comparison and improvement of implicit disturbance rejection capacity of closed loop control systems. Theoretical analyses demonstrate us that RDR of the negative feedback closed loop control systems are determined by energy spectral density of controller transfer function. In this manner, authors derived design criteria for specifications of disturbance rejection performances of PID and fractional order PID (FOPID) controller structures. RDR spectra are calculated for investigation of frequency dependence of disturbance rejection capacity and spectral RDR analyses are carried out for PID and FOPID controllers. For the validation of theoretical results, simulation examples are presented. (C) 2014 ISA. Published by Elsevier Ltd. All rights reserved.
An effective analog circuit design of approximate fractional-order derivative models of M-SBL fitting method
(Elsevier - Division Reed Elsevier India Pvt Ltd, 2022) Koseoglu, Murat; Deniz, Furkan Nur; Alagoz, Baris Baykant; Alisoy, Hafiz
There is a growing interest in fractional calculus and Fractional Order (FO) system modeling in many fields of science and engineering. Utilization of FO models in real-world applications requires practical realization of FO elements. This study performs an analog circuit realization of approximate FO derivative models based on Modified Stability Boundary Locus (M-SBL) fitting method. This study demonstrates a low-cost and accurate analog circuit implementation of M-SBL fitting based approximate model of FO derivative elements for industrial electronics. For this purpose, a 4th order approximate derivative transfer function model of the M-SBL method is decomposed into the sum of first order low-pass filters form by using Partial Fraction Expansion (PFE) method, and the analog circuit design of the approximate FO derivative model is performed. Firstly, by using the final value theorem, authors theoretically show that the time response of the sum of first order low-pass filter form can converge to the time response of fractional order derivative operators. Then, the approximation performance of proposed FO derivative circuit design is validated for various input waveforms such as sinusoidal, square and sawtooth waveforms via Multisim simulations. Results indicate an accurate realization of the FO derivative in time response (an RMSE of 0.0241). The derivative circuit realization of the M-SBL fitting model in the form of the sum of first order low pass filters can yield a better time response approximation performance compared to the Continued Fraction Expansion (CFE) based ladder network realization of the approximate derivative circuit.
An effective Smith predictor based fractional-order PID controller design methodology for preservation of design optimality and robust control performance in practice
(Taylor & Francis Ltd, 2022) Deniz, Furkan Nur
In this study, an optimal and robust fractional order PID (FOPID) controller design approach is suggested for Smith predictor based FOPID (SP-FOPID) control system design. This new design approach considers continued fraction expansion (CFE) based approximate models in the optimal design task of FOPID controllers, and this approach preserves the design optimality in control applications. For this purpose, an inverse controller loop shaping design methodology is performed in order to approximate the frequency response of a Bode's ideal loop reference model, and robust performance CFE based FOPID controller models are obtained by solving a multi-objective optimisation problem via a genetic algorithm. Thus, the suggested algorithm can deal with several controller realisation concerns in the design task of FOPID controllers and overcome real-world controller performance issues related with model approximation errors and signal saturation boundaries of electronic hardware. Illustrative design examples demonstrate that the suggested design scheme can preserve design optimality and improve practical control performance in practice.
An efficient PID-based optimizer loop and its application in De Jong's functions minimization and quadratic regression problems
(Elsevier, 2022) Alagoz, Baris Baykant; Deniz, Furkan Nur; Koseoglu, Murat
The Proportional-Integral-Derivative (PID) control law has been commonly used for process control in control engineering applications. However, it has potential to work as a solver in optimization problems. This study introduces a PID-based optimizer loop that is designed to solve nonlinear, unconstrained, multi-parameter optimization problems. To achieve the minimization of multi-parameter positive real objective functions by using a closed loop PID control loop, a slope sentient objective function model is suggested to allow zero-crossing of the error signal. Thus, this objective function model enhances the convergence efficiency of the PID-based optimizer loop by indicating slope direction of the objective function and operating in both positive and negative error regions. The boundedness and convergence theorems for the proposed PID optimizer loop are presented, and a theoretical background for the PID-based minimization is established. To demonstrate practical minimization performance, numerical applications of the proposed PID optimizer loops are illustrated in the solution of two fundamental optimization problems. These are the minimization of 30 parameters De Jong's functions and the solution of quadratic regression problems. Also, an experimental study is presented for the quadratic regression modeling of measurement data from a hole-drilling experiment. Optimization results reveal that the proposed PID-based optimizer system can improve convergence speed and accuracy compared to performances of fundamental nonlinear optimization techniques. (c) 2021 Elsevier B.V. All rights reserved.
Estimating the Time Response of Control Systems with Fractional Order PI from Frequency Response
(Ieee, 2015) Tan, Nusret; Yuce, Ali; Atherton, Derek P.; Deniz, Furkan Nur
This paper deals with the time response computation of closed loop control systems with fractional order PI controllers using the frequency response data of the closed loop system. The time response of fractional order transfer functions from frequency response data was first obtained by the authors using Fourier Series Method(FSM) and Inverse Fourier Transform Method(IFTM). In this paper, these methods are further extended for estimating unit step and unit impulse responses of control systems with fractional order PI controllers from the frequency response information of the closed loop system.
An experimental analog circuit realization of Matsuda's approximate fractional-order integral operators for industrial electronics
(Iop Publishing Ltd, 2021) Koseoglu, Murat; Deniz, Furkan Nur; Alagoz, Baris Baykant; Yuce, Ali; Tan, Nusret
Analog circuit realization of fractional order (FO) elements is a significant step for the industrialization of FO control systems because of enabling a low-cost, electric circuit realization by means of standard industrial electronics components. This study demonstrates an effective operational amplifier-based analog circuit realization of approximate FO integral elements for industrial electronics. To this end, approximate transfer function models of FO integral elements, which are calculated by using Matsuda's approximation method, are decomposed into the sum of low-pass filter forms according to the partial fraction expansion. Each partial fraction term is implemented by using low-pass filters and amplifier circuits, and these circuits are combined with a summing amplifier to compose the approximate FO integral circuits. Widely used low-cost industrial electronics components, which are LF347N opamps, resistor and capacitor components, are used to achieve a discrete, easy-to-build analog realization of the approximate FO integral elements. The performance of designed circuit is compared with performance of Krishna's FO circuit design and performance improvements are shown. The study presents design, performance validation and experimental verification of this straightforward approximate FO integral realization method.
HYBRID APPROXIMATION METHOD FOR TIME RESPONSE IMPROVEMENT OF CFE BASED APPROXIMATE FRACTIONAL ORDER DERIVATIVE MODELS BY USING GRADIENT DESCENT ALGORITHM
(2023) Köseoğlu, Murat; Deniz, Furkan Nur; Alagöz, Barış Baykant
Due to its high computational complexity, fractional order (FO) derivative operators have been widely implemented by using rational transfer function approximation methods. Since these methods commonly utilize frequency domain approximation techniques, their time responses may not be prominent for time-domain solutions. Therefore, time response improvements for the approximate FO derivative models can contribute to real-world performance of FO applications. Recent works address the hybrid use of popular frequency-domain approximation methods and time-domain approximation methods to deal with time response performance problems. In this context, this study presents a hybrid approach that implements Continued Fraction Expansion (CFE) method as frequency domain approximation and applies the gradient descent optimization (GDO) for step response improvement of the CFE-based approximate model of FO derivative operators. It was observed that GDO can fine-tune coefficients of CFE-based rational transfer function models, and this hybrid use can significantly improve step and impulse responses of CFE-based approximate models of derivative operators. Besides, we demonstrate analog circuit realization of this optimized transfer function model of the FO derivative element according to the sum of low pass active filters in Multisim and Matlab simulation environments. Performance improvements of hybrid CFE-GDO approximation method were demonstrated in comparison with the stand-alone CFE method.
Implicit disturbance rejection performance analysis of closed loop control systems according to communication channel limitations
(Inst Engineering Technology-Iet, 2015) Alagoz, Baris Baykant; Tan, Nusret; Deniz, Furkan Nur; Keles, Cemal
This study investigates limits of implicit disturbance rejection capacity of negative feedback control systems on the basis of communication channel limitations. Disturbance rejection performance of closed loop control structure is evaluated by using reference to disturbance ratio (RDR). Boundaries of RDR performance for stable control system are investigated by using stability boundary locus analyses. For computer-aided system design problems, a graphical design method for disturbance rejection PID control system is presented and illustrative examples are shown. Numerical examples show that disturbance rejection control with improved step response performance is obtainable by two-degree-of-freedom design combining high gain PID control and input prefiltering.
An integer order approximation method based on stability boundary locus for fractional order derivative/integrator operators
(Elsevier Science Inc, 2016) Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret; Atherton, Derek P.
This paper introduces an integer order approximation method for numerical implementation of fractional order derivative/integrator operators in control systems. The proposed method is based on fitting the stability boundary locus (SBL) of fractional order derivative/integrator operators and SBL of integer order transfer functions. SBL defines a boundary in the parametric design plane of controller, which separates stable and unstable regions of a feedback control system and SBL analysis is mainly employed to graphically indicate the choice of controller parameters which result in stable operation of the feedback systems. This study reveals that the SBL curves of fractional order operators can be matched with integer order models in a limited frequency range. SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges. Thus, the proposed method can effectively deal with stability preservation problems of approximate models. Illustrative examples are given to show performance of the proposed method and results are compared with the well-known approximation methods developed for fractional order systems. The integer-order approximate modeling of fractional order PID controllers is also illustrated for control applications. (C) 2016 ISA. Published by Elsevier Ltd. All rights reserved.
An interactive design strategy for fractional order PI controllers in LabVIEW
(Inderscience Enterprises Ltd, 2018) Yuce, Ali; Deniz, Furkan Nur; Tan, Nusret; Atherton, Derek P.
This paper presents an interactive design for fractional order PI (FOPI) controller based on inverse Fourier transform method (IFTM) in accordance with stability region of a closed-loop control system in LabVIEW, which is a powerful graphical program. Stability boundary locus (SBL) method is used to obtain the stability region including all stabilising FOPI controller parameters in (K-p, K-i) plane. The time response of the closed-loop control system with FOPI controller is then obtained by IFTM using the stabilising controller parameters selected from stability region. Changing the selected fractional order controller parameters in stability region, users can observe the step response of the system interactively.
Obtaining the Time Response of Control Systems with Fractional Order PID from Frequency Responses
(Ieee, 2015) Yuce, Ali; Deniz, Furkan Nur; Tan, Nusret; Atherton, Derek P.
The paper deals with obtaining the time response of closed loop control system with fractional order PID controller using frequency response data. For this aim, a feedback control system with an integer order plant and a fractional order PID controller are studied. The real and imaginary parts of the closed loop transfer function are obtained which depend on the parameters K-p, K-i, K-d, lambda and mu of fractional order PID controller and real and imaginary parts of the plant. Then the time domain responses of the closed loop control system with fractional order PID controller are plotted by using Inverse Fourier Transform Method (IFTM) or Fourier Series Method (FSM). The presented idea is supported by some numerical examples.
PID Controller Design Based on Second Order Model Approximation by Using Stability Boundary Locus Fitting
(Ieee, 2015) Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret
This study presents a model reduction method based on stability boundary locus (SBL) fitting for PID controller design problems. SBL analysis was commonly applied for controller stabilization problems. However, we use SBL analysis for the reduction of high order linear time invariant system models to second-order approximate models to facilitate analytical design of closed loop PID control systems. The PID design is implemented by a multiple pole placement strategy which enforces the control system had real poles with a desired time constant specification. Illustrative design examples are presented for the analytical PID design of high-order plant models by means of second-order SBL model approximations.
Revisiting four approximation methods for fractional order transfer function implementations: Stability preservation, time and frequency response matching analyses
(Pergamon-Elsevier Science Ltd, 2020) Deniz, Furkan Nur; Alagoz, Baris Baykant; Tan, Nusret; Koseoglu, Murat
Due to high computational load of ideal realization of fractional order elements, fractional order transfer functions are commonly implemented via integer-order, limited-band approximate models. An important side effect of such a non-ideal fractional order controller function realization for control applications is that the approximate fractional order models may deteriorate practical performance of optimal control tuning methods. Two major concerns come out for approximate realization in fractional-order control. These are stability preservation and model response matching properties. This study revisits four fundamental fractional order approximation methods, which are Oustaloup's method, CFE method, Matsuda's method and SBL fitting method, and considers stability preservation, time and frequency response matching performances. The study firstly presents a detailed review of Oustaloup's method, CFE method, Matsuda's method. Then, a modified version of SBL fitting method is presented. The stability preservation properties of approximation methods are investigated according to critical root placements of corresponding approximation method. Stability issue is highly significant for control applications. For this reason, a detailed analysis and comparision of stability preservation properties of these four approximation methods are investigated. Moreover, approximate implementations of an optimally tuned FOPID controller function are performed according to these four methods and compared for closed loop control of a large time delay system. Findings of this study indicate a fact that approximate models can considerably influence practical performance of optimally tuned FOPID control systems and ignorance of limitations of approximation methods in optimal tuning solutions can significantly affect real world performances. (C) 2020 Elsevier Ltd. All rights reserved.
Stability region analysis in Smith predictor configurations using a PI controller
(Sage Publications Ltd, 2015) Deniz, Furkan Nur; Tan, Nusret; Hamamci, Serdar Ethem; Kaya, Ibrahim
This paper deals with the stabilization problem of Smith predictor structures using a PI controller. Stability regions that include all stabilizing parameters of a PI controller for the case of perfect matching between the plant and model and for mismatched case are obtained. The models of the plant are assumed to be FOPDT (first-order plus dead time) and SOPDT (second-order plus dead time) transfer functions. Thus, the aim of this study is to determine all stabilizing PI controllers for the Smith predictor scheme and to compare the stability regions obtained for perfectly matched and mismatched models. It is observed that the stability regions obtained for both cases are quite different and the stability regions for FOPDT and SOPDT models are broader than the stability region of the actual model. Furthermore, an approach is presented to find different models of an actual system using the stability region and it is shown that the stability region of these models can fit the stability region of actual system. A simulation example is provided to illustrate the results.

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