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Öğe Analysis of Fractional Order Polynomials Using Hermite-Biehler Theorem(Ieee, 2014) Senol, Bilal; Yeroglu, Celaleddin; Tan, NusretThis paper presents some results for stability analysis of fractional order polynomials using the Hermite-Biehler theorem. The possibilities of the extension of the Hermite-Biehler theorem to fractional order polynomials is investigated and it is observed that the Hermite-Biehler theorem can be an effective tool for the stability analysis of fractional order polynomials. Variable changing has been applied to the fractional order polynomial to transform it into an integer order one. Roots of this polynomial are found and verified with the roots obtained using the Hermite-Biehler theorem. Stability analysis has been done investigating the interlacing property of the polynomial. Results are verified with the Radwan procedure. The method is clarified via illustrative examples.Öğe Application of Value Set Concept to Ellipsoidal Polynomial Families with Multilinear Uncertainty Structure(Springer International Publishing Ag, 2019) Matusu, Radek; Senol, BilalThe contribution intends to present the application of the value set concept to the ellipsoidal polynomial families with multilinear uncertainty structure. It is a follow-up to the previously published work, where the ellipsoidal polynomial families with affine linear uncertainty structure were studied. In the first parts of this paper, the basic terms related to the robustness under parametric uncertainty (e.g., uncertainty structure, uncertainty bounding set, family, and value set) are briefly recalled, with the accent on the ellipsoidal polynomial families. Subsequently, the non-convex value sets of the illustrative ellipsoidal polynomial family with multilinear uncertainty structure are plotted and analyzed. It is shown that the boundaries of the value set need not to mapped only from the boundaries in the parameter space but possibly also from the internal points.Öğe Calculation of robustly relatively stabilizing PID controllers for linear time-invariant systems with unstructured uncertainty(Elsevier Science Inc, 2022) Matusu, Radek; Senol, Bilal; Pekar, LiborThis article deals with the calculation of all robustly relatively stabilizing (or robustly stabilizing as a special case) Proportional-Integral-Derivative (PID) controllers for Linear Time-Invariant (LTI) systems with unstructured uncertainty. The presented method is based on plotting the envelope that corresponds to the trios of P-I-D parameters marginally complying with given robust stability or robust relative stability condition formulated by means of the H infinity norm. Thus, this approach enables obtaining the region of robustly stabilizing or robustly relatively stabilizing controllers in a P-I-D space. The applicability of the technique is demonstrated in the illustrative examples, in which the regions of robustly stabilizing and robustly relatively stabilizing PID controllers are obtained for a controlled plant model with unstructured multiplicative uncertainty and unstructured additive uncertainty. Moreover, the method is also verified on the real laboratory model of a hot-air tunnel, for which two representative controllers from the robust relative stability region are selected and implemented.Öğe Description and Analysis of Systems with Unstructured Additive Uncertainty(Springer International Publishing Ag, 2018) Matusu, Radek; Senol, BilalThis contribution is focused on systems with unstructured additive uncertainty, their description and robust stability analysis. The work presents particularly the example of the additive uncertainty model creation on the basis of a third order integrating plant with parametric uncertainty by means of the selection of a nominal system and a suitable weight function. Moreover, it compares the results of robust stability border investigation for parametric, multiplicative and additive uncertainty model cases.Öğe Design of Robust PI Controllers for Interval Plants With Worst-Case Gain and Phase Margin Specifications in Presence of Multiple Crossover Frequencies(Ieee-Inst Electrical Electronics Engineers Inc, 2022) Matusu, Radek; Senol, Bilal; Alagoz, Baris Baykant; Pekar, LiborThis article deals with the computation of robustly performing Proportional-Integral (PI) controllers for interval plants, where the performance measures are represented by the worst-case Gain Margin (GM) and Phase Margin (PM) specifications, in the event of multiple Phase Crossover Frequencies (PCFs) and/or Gain Crossover Frequencies (GCFs). The multiplicity of PCFs and GCFs poses a considerable complication in frequency-domain control design methods. The paper is a continuation of the authors' previous work that applied the robust PI controller design approach to a Continuous Stirred Tank Reactor (CSTR). This preceding application represented the system with a single PCF and a single GCF, but the current article focuses on a case of multiple PCFs and GCFs. The determination of a robust performance region in the P-I plane is based on the stability/performance boundary locus method and the sixteen plant theorem. In the illustrative example, a robust performance region is obtained for an experimental oblique wing aircraft that is mathematically modeled as the unstable interval plant. The direct application of the method results in the (pseudo-)GM and (pseudo-)PM regions that illogically protrude from the stability region. Consequently, a deeper analysis of the selected points in the P-I plane shows that the calculated GM and PM boundary loci are related to the numerically correct values, but that the results may be misleading, especially for the loci outside the stability region, due to the multiplicity of the PCFs and GCFs. Nevertheless, the example eventually shows that the important parts of the GM and PM regions, i.e., the parts that have an impact on the final robust performance region, are valid. Thus, the method is applicable even to unstable interval plants and to the control loops with multiple PCFs and GCFs.Öğe Disturbance rejection FOPID controller design in v-domain(Elsevier, 2020) Tufenkci, Sevilay; Senol, Bilal; Alagoz, Baris Baykant; Matusu, RadekDue to the adverse effects of unpredictable environmental disturbances on real control systems, robustness of control performance becomes a substantial asset for control system design. This study introduces a v-domain optimal design scheme for Fractional Order Proportional-Integral-Derivative (FOPID) controllers with adoption of Genetic Algorithm (GA) optimization. The proposed design scheme performs placement of system pole with minimum angle to the first Riemann sheet in order to obtain improved disturbance rejection control performance. In this manner, optimal placement of the minimum angle system pole is conducted by fulfilling a predefined reference to disturbance rate (RDR) design specification. For a computer-aided solution of this optimal design problem, a multi-objective controller design strategy is presented by adopting GA. Illustrative design examples are demonstrated to evaluate performance of designed FOPID controllers. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.Öğe Disturbance Rejection Fractional Order PID Controller Design in v-domain by Particle Swarm Optimization(Ieee, 2019) Tufenkci, Sevilay; Senol, Bilal; Alagoz, Baris BaykantDesign and stabilization problems of fractional order PID (FOPID) controllers have been generally solved in frequency, time and s-domains. This study presents a design scheme in v-domain for optimal disturbance reject FOPID controller tuning problem. The proposed method is based on optimally placement of minimum angle system poles inside stability region of the first Riemann sheet to improve disturbance rejection control performance. For a given stabilizing target angle of minimum angle system pole, the purposed design approach maximizes reference to disturbance rate (RDR) index. For this purpose, optimization problem is defined as maximization of RDR index subject to minimum angle pole placement constraint. This constraint ensures stability of resulting FOPID control system by placing the minimum angle system pole into stability region of v-domain. Particle swarm optimization (PSO) is implemented to solve this optimization problem. An illustrative design example is presented to show effectiveness of the proposed design method.Öğe An experimental investigation for error-cube PID control(Sage Publications Ltd, 2015) Alagoz, Baris Baykant; Ates, Abdullah; Yeroglu, Celaleddin; Senol, BilalThis 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.Öğe FGATool for Time and Frequency Analysis of Systems with Uncertainties(Ieee, 2017) Senol, BilalFGATool is a MATLAB tool for graphical analysis of systems represented with transfer functions having orders of integer and fractional numbers. It offers easy-to-use tools for students and researchers working in the field of system analysis. This paper presents the motivation of its development, an overview of the uncertainty module of the toolbox and the relation with existing tools concerned to system analysis. One of the two main modules of the toolbox is introduced which deals with systems including parametric uncertainties. Analysis tools such as step response, Bode and Nyquist diagrams, interlacing property, root analysis on the first Riemann sheet and value set analysis have been studied overall the toolbox. Main motivation of FGATool lays on its ease of use without much knowledge on mathematical background and its user friendly graphical interface. It also brings more easiness and attraction on fractional order system analysis.Öğe Filter Approximation and Model Reduction Comparison for Fractional Order Systems(Ieee, 2014) Senol, Bilal; Yeroglu, CelaleddinThis paper presents a comparison study for filter approximations and model reduction techniques for control systems of fractional orders. Oustaloup's recursive filter and a refined Oustaloup's filter are represented to obtain higher integer order approximations of fractional order systems. Then these higher integer order systems are exposed to model reduction with some existing techniques preserving some of the dominant eigenvalues. Original system and reduced order systems are compared on a Bode diagram and average errors of the reduced systems are computed. Then, a Matlab toolbox is developed which one can easily enter the fractional order system and apply filter approximations and model reductions. Average errors of each technique for desired fractional order system can be computed using the toolbox. Thus, this study is thought to be useful for the related area of research.Öğe Fractional order proportional derivative control for first order plus time delay plants: achieving phase and gain specifications simultaneously(Sage Publications Ltd, 2019) Senol, Bilal; Demiroglu, UgurThe aim of the method in this paper is to achieve desired gain and phase specifications for robustness and performance of first order plus time delay plants. The previously proposed method frequency frame, implemented for tuning fractional order proportional integral controllers, is applied on such plants controlled with a fractional order proportional derivative controller. Four specifications of gain and phase are considered in the Bode plot inspired from an ideal system. The frame is drawn enclosing the magnitude and phase curves limited by gain and phase crossover frequencies. Then, the size of the frame is tuned to provide loop-shaping of the curves to meet desired properties. The iso-damping property is achieved by shaping the phase curve. Similarly, numerous studies in the literature work on robustness achievement by loop shaping the phase curve of the Bode plot. However, the frequency frame approach is a new perspective in controller tuning. Two examples are illustratively given to prove the proposed method. Plants in the examples are also considered to be due to load disturbances. Simulation results and effects of the method are clearly explained.Öğe Fractional order proportional derivative control for time delay plant of the second order: The frequency frame(Pergamon-Elsevier Science Ltd, 2020) Senol, Bilal; Demiroglu, Ugur; Matusu, RadekThis paper intends to tune fractional order proportional derivative controller for the performance, stability and robustness of second order plus time delay plant. The tuning method is based on the previously proposed frequency frame which is a rectangular frame enclosing gain and phase margins limited with gain and phase crossover frequencies in the Bode plot. Edges of the frame are tuned to achieve desired crossover frequencies and margins. By shaping the curves of the Bode plot, improvements are observed in the performance and robustness of the second order plus time delay system controlled by a fractional order proportional derivative controller. Generalized equations to obtain the parameters of the fractional order proportional derivative controller for second order plus time delay plant are given. In contrast to existing studies, this method reduces mathematical complexity when providing desired properties. Three examples are considered and effectiveness of the frequency frame is shown. (c) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.Öğe Fractional Order Stability of Systems(Ieee, 2017) Senol, Bilal; Matusu, Radek; Gul, EmineThis paper investigates and offers some stability analysis methods for systems of non-integer orders. Well known analysis methods such as Hurwitz, interlacing property, monotonic phase increment property are reconsidered in a fractional order way of thinking. A method to find the roots of the so-called fractional order polynomials is proposed and Hurwitz-like stability of the pseudo-polynomials is investigated. Effectiveness of the interlacing property and outcomes of the monotonic phase increment property for fractional order case is shown. Results are comparatively proved and illustrated clearly.Öğe Frequency boundary of fractional order systems with nonlinear uncertainties(Pergamon-Elsevier Science Ltd, 2013) Senol, Bilal; Yeroglu, CelaleddinThis paper proposes a method to compute frequency boundaries of fractional order control systems with nonlinear uncertainty structures that include and guarantee the Bode and Nyquist envelopes. Then, a lag-lead compensator is designed based on the frequency boundary to provide desired gain and phase specifications. Two types of nonlinear uncertainty structures, namely polynomial and general uncertainties, have been concerned in illustrative examples to explain computing process clearly. (C) 2013 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.Öğe Frequency frame approach on loop shaping of first order plus time delay systems using fractional order PI controller(Elsevier Science Inc, 2019) Senol, Bilal; Demiroglu, UgurThis study proposes an analytical design method of fractional order proportional integral (FOP!) controllers for first order plus time delay (FOPTD) systems. Suggested technique obtains the general computation equations of controllers for such systems. These equations are used to tune controller parameters to meet specified frequency and phase properties to satisfy the stability of whole system. It is found that the designed controllers not only make the system stable, but also have positive effect on the performance and robustness of the system. Main contribution of the paper lays on this thought. There proposed a concept, frequency frame which encloses the curves between phase and gain crossover frequencies in Bode plot. Robustness of the control system can be improved by expanding or constricting the edges of this frame and flattening the curves inside the frame. Thus, any case that leads the system to instability can be avoided. Analytically derived equations are tested with proper examples and the results are shown illustratively. Advantages and disadvantages of the method are comparatively given. (C) 2018 ISA. Published by Elsevier Ltd. All rights reserved.Öğe Frequency frame approach on tuning FOPI controller for TOPTD thermal processes(Elsevier Science Inc, 2021) Demiroglu, Ugur; Senol, BilalThe frequency frame is used to tune fractional order proportional-integral controllers for stability, performance and robustness of third order plus time delay plants. Such plants are frequently used in describing thermal processes such as an air heater or a fired boiler. The aim is to tune the controller to meet some frequency domain properties. As robustness is an indispensable issue for thermal processes, main inspiration of the paper comes from flattening the phase curve in the Bode plot to provide improved robustness for the system. In spite of some existing studies, flattening is not realized by equalizing the phase derivative to zero at a given frequency value. Firstly, gain and phase crossover frequency points are enclosed with a rectangular frame. Then, lengths of the edges of this frame are changed to tune phase and gain margins. Curves inside the frame can be flattened by proper tuning of the edges. This will enhance the robustness and also ensure the iso-damping property. Equations to obtain the controller are given with two theorems. Demonstrations are made on two different thermal plants which are a novel electrical air heater and a bagasse fired boiler and the results are given on detailed illustrations. The results proved that preferred gain and phase properties are successfully obtained and improved performance and robustness are provided for related systems. (c) 2020 ISA. Published by Elsevier Ltd. All rights reserved.Öğe Having a Sensitivity with a Genetic Algorithm Optimal FOPID Controller Design(Ieee, 2019) Tufenkci, Sevilay; Senol, Bilal; Alagoz, Baris BaykantResearchers have demonstrated that Fractionalorder Proportional Integral Derivative (FOPID) controllers can provide superior control performance compared to classical PID controllers. This study presents an optimal FOPID controller design method in v-domain to achieve lower sensitivity to disturbance. For this purpose, an optimal FOPID controller design method is proposed, where a multi-objective optimization problem, which reduces sensitivity of system to external disturbances and stabilizes the system, is defined and solved by Genetic Algorithm (GA). This design is performed in the stability region of the first Riemann Sheet in v-plane. To increase system robustness against disturbances, sensitivity function of the system is minimized. Hence, a multi-objective optimization problem, which is solved by GA algorithm, is stated for placement of minimum angle system pole to a target angle within the stability region and minimization of system sensitivity function. Thus, for fractional order systems, FOPID controller design can be performed in v-domain. An illustrative design example and comparison of the resulting design with other design methods are presented.Öğe Investigation of robust stability of fractional order multilinear affine systems: 2q-convex parpolygon approach(Elsevier Science Bv, 2013) Yeroglu, Celaleddin; Senol, BilalThis paper discusses the robust stability problem of fractional order systems with the multi-linear affine uncertainty structure. The 2q-convex parpolygon approach has been extended to compute the value set of the fractional order uncertain system and to investigate the robust stability via zero exclusion principle. An illustrative example is included for fractional order multi-linear affine system to present the advantages of the 2q-convex parpolygon approach over classical value set computation methods in the stability investigation. (C) 2013 Elsevier B.V. All rights reserved.Öğe Linear systems with unstructured multiplicative uncertainty: Modeling and robust stability analysis(Public Library Science, 2017) Matusu, Radek; Senol, Bilal; Yeroglu, CelaleddinThis article deals with continuous-time Linear Time-Invariant (LTI) Single-Input Single-Output (SISO) systems affected by unstructured multiplicative uncertainty. More specifically, its aim is to present an approach to the construction of uncertain models based on the appropriate selection of a nominal system and a weight function and to apply the fundamentals of robust stability investigation for considered sort of systems. The initial theoretical parts are followed by three extensive illustrative examples in which the first order time-delay, second order and third order plants with parametric uncertainty are modeled as systems with unstructured multiplicative uncertainty and subsequently, the robust stability of selected feedback loops containing constructed models and chosen controllers is analyzed and obtained results are discussed.Öğe A numerical investigation for robust stability of fractional-order uncertain systems(Elsevier Science Inc, 2014) Senol, Bilal; Ates, Abdullah; Alagoz, B. Baykant; Yeroglu, CelaleddinThis 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. (C) 2013 ISA. Published by Elsevier Ltd. All rights reserved.
