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Öğe An Evolutionary Field Theorem: Evolutionary Field Optimization in Training of Power-Weighted Multiplicative Neurons for Nitrogen Oxides-Sensitive Electronic Nose Applications(Mdpi, 2022) Alagoz, Baris Baykant; Simsek, Ozlem Imik; Ari, Davut; Tepljakov, Aleksei; Petlenkov, Eduard; Alimohammadi, HosseinNeuroevolutionary machine learning is an emerging topic in the evolutionary computation field and enables practical modeling solutions for data-driven engineering applications. Contributions of this study to the neuroevolutionary machine learning area are twofold: firstly, this study presents an evolutionary field theorem of search agents and suggests an algorithm for Evolutionary Field Optimization with Geometric Strategies (EFO-GS) on the basis of the evolutionary field theorem. The proposed EFO-GS algorithm benefits from a field-adapted differential crossover mechanism, a field-aware metamutation process to improve the evolutionary search quality. Secondly, the multiplicative neuron model is modified to develop Power-Weighted Multiplicative (PWM) neural models. The modified PWM neuron model involves the power-weighted multiplicative units similar to dendritic branches of biological neurons, and this neuron model can better represent polynomial nonlinearity and they can operate in the real-valued neuron mode, complex-valued neuron mode, and the mixed-mode. In this study, the EFO-GS algorithm is used for the training of the PWM neuron models to perform an efficient neuroevolutionary computation. Authors implement the proposed PWM neural processing with the EFO-GS in an electronic nose application to accurately estimate Nitrogen Oxides (NOx) pollutant concentrations from low-cost multi-sensor array measurements and demonstrate improvements in estimation performance.Öğe FOPID Controllers and Their Industrial Applications: A Survey of Recent Results(Elsevier, 2018) Tepljakov, Aleksei; Alagoz, Baris Baykant; Yeroglu, Celaleddin; Gonzalez, Emmanuel; HosseinNia, S. Hassan; Petlenkov, EduardThe interest towards using Fractional-order (FO) PID controllers in the industry is mainly fueled by the fact that these controllers have two additional tuning knobs that can be used to adjust the control law in a way that would benefit the control loop. However, there are certain points that are rarely addressed in literature, namely: (1) What are the particular advantages (in concrete numbers) of FOPID controllers versus conventional, integer-order (IO) PID controllers in the light of complexities arising in the implementation of the former? (2) For real-time implementation of FOPID controllers, approximations are used that are equivalent to high order linear controllers. What, then, is the benefit of using FOPID controllers? In the present paper, we attempt to address these issues by reviewing recent literature in the field and by providing relevant analysis and recommendations. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Öğe Fractional Order Model Identification of Receptor-Ligand Complexes Formation by Equivalent Electrical Circuit Modeling(Ieee, 2019) Ates, Abdullah; Alagoz, Bans Baykant; Tepljakov, Aleksei; Petlenkov, Eduard; Yeroglu, Celaledddin; Kuznetsov, Aleksei; Sobolev, InnokentiIn this study, relevant time resolved kinetic system is modeled according to linear fractional order model structure under the electrical circuit model assumption. The data, which were obtained from receptor ligand, are very noisy. Particularly, the unstable flowing of liquids around surfaces leads to irregular mass-transfer between the layers of reagent near the surface. Current flow of equivalent electric circuit modeling resembles overall mass flow and accumulation on surface corresponds to charge collection in capacitance. Thus, the charging and discharging process of fractional order capacitor can be used to represent accumulation and relaxation mechanisms of the receptor ligand complexes formation by using Stochastic Multi-parameter Divergence Optimization (SMDO) method. Meanwhile, error function that is comparison between model output with real output is used as an objective function for optimization of the fractional order model parameters.Öğe A graphical method to determine robust stabilizing region of FOPID controllers for stable/unstable fractional-order plants with interval uncertainties of a fractional order and model coefficients(Taylor & Francis Ltd, 2024) Ghorbani, Majid; Alagoz, Baris Baykant; Tepljakov, Aleksei; Petlenkov, EduardThis paper focuses on robustly stabilizing stable and unstable fractional-order plants with one uncertain fractional-order term and interval uncertainties using fractional order $ PI<^>{\mu }D<^>{\lambda } $ PI mu D lambda controllers. Two necessary and sufficient conditions are provided to check the robust stability of the closed-loop control system. Moreover, the D-decomposition technique is utilized to determine the robust stability region of the system. Subsequently, evolutionary algorithms, such as the Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE), can be utilized to discover a fractional-order controller within the region of robust stability. This work introduces three primary contributions, outlined as follows: (1) Utilizing a graphical approach, a set of stabilizing controller is obtained. (2) Rather than employing just a single stabilizing fractional-order controller, a collection of controllers is provided for the control system. (3) Employing evolutionary algorithms to find an optimal fractional-order controller. Finally, four numerical examples are presented to validate the results.Öğe Model Reference Adaptive Control Scheme for Retuning Method-Based Fractional-Order PID Control with Disturbance Rejection Applied to Closed-Loop Control of a Magnetic Levitation System(World Scientific Publ Co Pte Ltd, 2018) Tepljakov, Aleksei; Alagoz, Baris Baykant; Gonzalez, Emmanuel; Petlenkov, Eduard; Yeroglu, CelaleddinThis study demonstrates the utilization of model reference adaptive control (MRAC) for closedl-oop fractional-order PID (FOPID) control of a magnetic levitation (ML) system. Design specifications of ML transportation systems require robust performance in the presence of environmental disturbances. Numerical and experimental results demonstrate that incorporation of MRAC and FOPID control can improve the disturbance rejection control performance of ML systems. The proposed multiloop MRAC-FOPID control structure is composed of two hierarchical loops which are working in conjunction to improve robust control performance of the system in case of disturbances and faults. In this multiloop approach, an inner loop performs a regular closed-loop FOPID control, and the outer loop performs MRAC based on Massachusetts Institute of Technology (MIT) rule. These loops are integrated by means of the input-shaping technique and therefore no modification of any parameter of the existing closed-loop control system is necessary. This property provides a straightforward design solution that allows for independent design of each loop. To implement FOPID control of the ML system, a retuning technique is used which allows transforming an existing PID control loop into an FOPID control loop. This paper presents the simulation and experimental results and discusses possible contributions of multiloop MRAC-FOPID structure to disturbance rejection control of the ML system.Öğe Multi-loop Model Reference Adaptive Control of Fractional-order PID Control Systems(Ieee, 2017) Alagoz, Baris Baykant; Tepljakov, Aleksei; Petlenkov, Eduard; Yeroglu, CelaleddinThis paper presents an application of Model Reference Adaptive Control (MRAC) method based on MIT rule for closed loop fractional-order control systems. The main advantage of the method is that it may gain adaptation capability for existing fractional-order systems. It essentially contains two loops, which are the inner loop for fractional-order PID ( FOPID) control of plant, and the outer loop for implementation of MIT rule for model reference adaptive control. This approach do not modify any parameter of existing closed loop control system, instead it performs input shaping for the closed loop control system so that response of closed loop control system approximates to a desired control response, which is described by the reference model. The method can be useful in fault diagnosis and fault-tolerant control of systems because it may allow maintaining control performance for tolerable system perturbation. The paper presents a simulation study for FOPID and plant models that were obtained by Fractional-order Modeling and Control (FOMCON) toolbox. Results showing the response of proposed system for amplifications type faults are also discussed.Öğe Multi-Loop Model Reference Proportional Integral Derivative Controls: Design and Performance Evaluations(Mdpi, 2020) Alagoz, Baris Baykant; Tepljakov, Aleksei; Petlenkov, Eduard; Yeroglu, CelaleddinDue to unpredictable and fluctuating conditions in real-world control system applications, disturbance rejection is a substantial factor in robust control performance. The inherent disturbance rejection capacity of classical closed loop control systems is limited, and an increase in disturbance rejection performance of single-loop control systems affects the set-point control performance. Multi-loop control structures, which involve model reference control loops, can enhance the inherent disturbance rejection capacity of classical control loops without degrading set-point control performance; while the classical closed Proportional Integral Derivative (PID) control loop deals with stability and set-point control, the additional model reference control loop performs disturbance rejection control. This adaptive disturbance rejection, which does not influence set-point control performance, is achieved by selecting reference models as transfer functions of real control systems. This study investigates six types of multi-loop model reference (ML-MR) control structures for PID control loops and presents straightforward design schemes to enhance the disturbance rejection control performance of existing PID control loops. For this purpose, linear and non-linear ML-MR control structures are introduced, and their control performance improvements and certain inherent drawbacks of these structures are discussed. Design examples demonstrate the benefits of the ML-MR control structures for disturbance rejection performance improvement of PID control loops without severely deteriorating their set-point performance.Öğe A NARX Model Reference Adaptive Control Scheme: Improved Disturbance Rejection Fractional-Order PID Control of an Experimental Magnetic Levitation System(Mdpi, 2020) Alimohammadi, Hossein; Alagoz, Baris Baykant; Tepljakov, Aleksei; Vassiljeva, Kristina; Petlenkov, EduardReal control systems require robust control performance to deal with unpredictable and altering operating conditions of real-world systems. Improvement of disturbance rejection control performance should be considered as one of the essential control objectives in practical control system design tasks. This study presents a multi-loop Model Reference Adaptive Control (MRAC) scheme that leverages a nonlinear autoregressive neural network with external inputs (NARX) model in as the reference model. Authors observed that the performance of multi-loop MRAC-fractional-order proportional integral derivative (FOPID) control with MIT rule largely depends on the capability of the reference model to represent leading closed-loop dynamics of the experimental ML system. As such, the NARX model is used to represent disturbance-free dynamical behavior of PID control loop. It is remarkable that the obtained reference model is independent of the tuning of other control loops in the control system. The multi-loop MRAC-FOPID control structure detects impacts of disturbance incidents on control performance of the closed-loop FOPID control system and adapts the response of the FOPID control system to reduce the negative effects of the additive input disturbance. This multi-loop control structure deploys two specialized control loops: an inner loop, which is the closed-loop FOPID control system for stability and set-point control, and an outer loop, which involves a NARX reference model and an MIT rule to increase the adaptation ability of the system. Thus, the two-loop MRAC structure allows improvement of disturbance rejection performance without deteriorating precise set-point control and stability characteristics of the FOPID control loop. This is an important benefit of this control structure. To demonstrate disturbance rejection performance improvements of the proposed multi-loop MRAC-FOPID control with NARX model, an experimental study is conducted for disturbance rejection control of magnetic levitation test setup in the laboratory. Simulation and experimental results indicate an improvement of disturbance rejection performance.Öğe A Numerical Study for Plant-Independent Evaluation of Fractional-order PID Controller Performance(Elsevier, 2018) Alagoz, Baris Baykant; Tepljakov, Aleksei; Yeroglu, Celaleddin; Gonzalez, Emmanuel; HosseinNia, S. Hassan; Petlenkov, EduardA stunning outcome of fractional calculus for control practice are fractional-order PID (FOPID) controllers. Based on their experimental and numerical results, several studies have reported improvements in control performance of closed loop control systems by FOPID controllers compared to classical PID controllers. However, the industry at large is still cautious about adopting FOPID controllers because of the lack of concrete data about the related cost benefit trade-off. Main concerns arise at the point that there have not been a quantitative evaluation scheme that clearly demonstrates for which concrete cases FOPID controllers can provide considerable improvements in control. Therefore, there is a need for more thorough theoretical and quantitative demonstrations. To that end, this study presents a plant function independent evaluation methodology to reveal inherent advantages of FOPID control. Impacts of two additional controller coefficients, namely fractional orders of differentiator and integrator, are analyzed in the frequency domain and their contributions to open loop gain maximization, phase margin and Reference to Disturbance Rate (RDR) performance are investigated. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.Öğe A Theoretical Investigation on Consideration of Initial Conditions in Fractional-order Transfer Function Modeling(Ieee, 2017) Alagoz, Baris Baykant; Tepljakov, Aleksei; Petlenkov, Eduard; Yeroglu, CelaleddinThis paper presents an investigation on contributions of initial condition consideration to fractional-order transfer functions in modeling linear time invariant systems. In this theoretical study, firstly, initial conditions are considered for fractional-order transfer function modeling in s-domain, and then impacts of initial conditions on model dynamics are discussed. An illustrative example is also presented to evaluate theoretical findings.Öğe Time-domain identification of One Noninteger Order Plus Time Delay models from step response measurements(World Scientific Publ Co Pte Ltd, 2019) Alagoz, Baris Baykant; Tepljakov, Aleksei; Ates, Abdullah; Petlenkov, Eduard; Yeroglu, CelaleddinPractical performances of controller design methods strongly depend on relevancy of identified models. Fractional order system models promise advantage of more accurate modeling of real systems. This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole (NOPTD-I) models. The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data. In the study, step responses of NOPTD-I models are numerically calculated according to two fundamental methods, which are Mittag-Leffler (ML) function and Grunwald-Letnikov (GL) definition. Particle swarm optimization (PSO) algorithm is used to perform data fitting. Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data. An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.Öğe Towards Industrialization of FOPID Controllers: A Survey on Milestones of Fractional-Order Control and Pathways for Future Developments(Ieee-Inst Electrical Electronics Engineers Inc, 2021) Tepljakov, Aleksei; Alagoz, Baris Baykant; Yeroglu, Celaleddin; Gonzalez, Emmanuel A.; Hosseinnia, S. Hassan; Petlenkov, Eduard; Ates, AbdullahThe interest in fractional-order (FO) control can be traced back to the late nineteenth century. The growing tendency towards using fractional-order proportional-integral-derivative (FOPID) control has been fueled mainly by the fact that these controllers have additional tuning knobs that allow coherent adjustment of the dynamics of control systems. For instance, in certain cases, the capacity for additional frequency response shaping gives rise to the generation of control laws that lead to superior performance of control loops. These fractional-order control laws may allow fulfilling intricate control performance requirements that are otherwise not in the span of conventional integer-order control systems. However, there are underpinning points that are rarely addressed in the literature: (1) What are the particular advantages (in concrete figures) of FOPID controllers versus conventional, integer-order (IO) PID controllers in light of the complexities arising in the implementation of the former? (2) For real-time implementation of FOPID controllers, approximations are used that are indeed equivalent to high-order linear controllers. What, then, is the benefit of using FOPID controllers? Finally, (3) What advantages are to be had from having a near-ideal fractional-order behavior in control practice? In the present paper, we attempt to address these issues by reviewing a large portion of relevant publications in the fast-growing FO control literature, outline the milestones and drawbacks, and present future perspectives for industrialization of fractional-order control. Furthermore, we comment on FOPID controller tuning methods from the perspective of seeking globally optimal tuning parameter sets and how this approach can benefit designers of industrial FOPID control. We also review some CACSD (computer-aided control system design) software toolboxes used for the design and implementation of FOPID controllers. Finally, we draw conclusions and formulate suggestions for future research.
