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Spherical tanks have been predominantly used in process industries due to their large storage capability. The fundamental challenges in process industries require a very efficient controller to control the various process parameters owing to their nonlinear behavior. The current research work in this paper aims to propose the Approximate Generalized Time Moments (AGTM) optimization technique for designing Fractional-Order PI (FOPI) and Fractional-Order PID (FOPID) controllers for the nonlinear Single Spherical Tank Liquid Level System (SSTLLS). This system features a large dead time, and its real-time modeling generally represents a Single Input Single Output (SISO) model. However, in practice, the derived SISO model is often a First Order Plus Dead Time (FOPDT) model, necessitating an effective controller to maintain the tank's steady-state level. In this research, the proposed AGTM method, based on the conventional Proportional Integral (PI) and Proportional Integral Derivative (PID) controllers, is compared with the FOPI and FOPID controllers for the nonlinear SSTLLS. The performance of these controllers is contrasted using metrics such as Integral Squared Error (ISE) and Integral Absolute Error (IAE), as well as time-domain characteristics containing Rise time, Peak time, Settling time, Peak overshoot, and Steady-state error. The implementation of the aforementioned controllers is done in simulation and real-time employing the MATLAB software environment and the Data Acquisition (DAQ) device National Instrument NI-DAQmx 6211. The simulation and experimental results demonstrate the exceptional performance of the designed Fractional-Order controllers based on the proposed method which offers an increased degree of freedom despite the more complex design process. [ABSTRACT FROM AUTHOR]

This work explores efficiency improvements in the copper flotation stage, a complex nonlinear, multivariable process subject to numerous perturbations. The primary objective is to design a fractional-order PID (FOPID) control strategy and a fractional-order model reference adaptive control (FOMRAC) system. The parameters for these controllers are optimized using the particle swarm optimization (PSO) algorithm with an objective function tailored to the control goals. This study employs models of both a bank series of five flotation cells and a flotation column. Their performance results are compared against traditional controllers, such as an integer-order PID and MRAC. The findings reveal that fractional-order controllers offer notable advantages over their integer-order counterparts, showing improved performance metrics with minimal changes to the existing control framework. This research highlights the effectiveness of fractional control in enhancing flotation processes and introduces a novel application of fractional control techniques in this area. [ABSTRACT FROM AUTHOR]

The escalating demand for energy and the mounting environmental impacts of fossil fuel usage necessitate a paradigm shift toward the integration of renewable energy sources (RES) as the core of the electrical energy sector. Solar photovoltaic (SPV) and wind-based generation have emerged as the most promising and viable solutions, leading to a significant increase in the RES-based microgrid penetration into the power grid. However, the grid-connected microgrid operation presents challenges to the stability of the main grid. Due to small aggregated physical inertia of these microgrid, there is a significant deviation in system inertia that contributes to low frequency oscillations (LFO). These oscillations have a significant risk to power system stability. In the proposed work, a grid-connected microgrid that incorporates a synchronous generator along with SPV and wind integration is investigated. A synchronized governor combined with a power system stabilizer features a cascade structure, encompassing tilt integral derivative and fractional-order proportional integral derivative with a filter to effectively mitigate the oscillations. Furthermore, this cascaded controller is optimized using the improved reptile search algorithm. The controller efficacy is validated in the MATLAB platform by subjecting it to random variations in reference torque. Comparative analysis against conventional controllers, including Proportional Integral, Lead-Lag and Fractional Lead-Lag, demonstrates superior damping efficiency of the proposed controller since it damps LFO within the time period of 15 s. [ABSTRACT FROM AUTHOR]

The robust stability assessment of the second order plus interval time delay (SOPITD) plant controlled by Fractional-Order Proportional Integral Derivative (FOPID) controllers is the focus of this research. A simple graphical procedure for analyzing the robust stability of the interval system is presented based on the zero exclusion condition and the value set concept. The incorporation of an auxiliary function, derived through a judicious application of fundamental geometric principles intrinsic to convex polygons, serves to significantly alleviate the complexity and facilitate the application of the robust stability analysis approach, thereby affording a more streamlined and efficient means of designing robust control systems. Moreover, the computational burden for the robust stability analysis is also reduced by novel bounds. Moreover, a novel robust performance checking function is provided to improve the performance system. Three illustrative examples are then given to support the findings and show their applicability. [ABSTRACT FROM AUTHOR]

Power quality (PQ) is a major issue in today's electrical system that affects both utilities and customers. The proliferation of power electronics devices, smart grid technology, and renewable energy sources (RES) have all contributed to the emergence of PQ concerns in today's power system. The Unified Power Quality Conditioner (UPQC) is a versatile tool that can be used to fix distribution grid issues caused by irregular voltage, current, or frequency. Several tuning parameters, however, restrict the effectiveness of the Fractional-Order Proportional Integral Derivative (FOPID) control technique, which is proposed to improve UPQC performance. To move beyond these restrictions and find the optimal solution for the FOPID controller problem, a hybrid optimization strategy called the Hybrid Jellyfish Search Optimizer and Particle Swarm Optimizer (HJSPSO) is employed. To meet the load requirement during PQ issue periods, the suggested model incorporates a renewable energy source into the grid system. Whether the load is linear or non-linear, the design maintains PQ problems to a minimum. Furthermore, the FOPID control technique is compared with other controllers. Results show that grid-connected RES systems using the proposed FOPID control approach for UPQC have fewer PQ problems. The presented UPQC with HJSPSO strategy significantly outperformed, with the shortest computing time of 127.474 s and an objective function value of 1.423. [ABSTRACT FROM AUTHOR]

In this study, a nonlinear Archimedes wave swing (AWS) energy conversion system was employed to enable the use of irregular sea waves to provide useful electricity. Instead of the conventional PI controllers used in prior research, this study employed fractional-order PID (FOPID) controllers to control the back-to-back configuration of AWS. The aim was to maximize the energy yield from waves and maintain the grid voltage and the capacitor DC link voltage at predetermined values. In this study, six FOPID controllers were used to accomplish the control goals, leading to an array of thirty parameters required to be fine-tuned. In this regard, a hybrid jellyfish search optimizer and particle swarm optimization (HJSPSO) algorithm was adopted to select the optimal control gains. Verification of the performance of the proposed FOPID control system was achieved by comparing the system results to two conventional PID controllers and one FOPID controller. The conventional PID controllers were tuned using a recently presented metaheuristic algorithm called the Coot optimization algorithm (COOT) and the classical particle swarm optimization algorithm (PSO). Moreover, the FOPID was also tuned using the well-known genetic algorithm (GA). The system investigated in this study was subjected to various unsymmetrical and symmetrical fault disturbances. When compared with the standard COOT-PID, PSO-PID, and GA-FOPID controllers, the HJSPSO-FOPID results show a significant improvement in terms of performance and preserving control goals during system instability [ABSTRACT FROM AUTHOR]

The research focused on two-mass electromechanical systems widely utilized in industry. The challenge addressed in this work was to improve the synthesis of controllers for such systems to simplify it and enhance the quality of transition processes. Traditionally, the synthesis of control system loops for these systems was carried out using integer controllers and standard forms. However, this approach led to the synthesis of complex integer controllers that are difficult to implement. To overcome this issue, an original approach to the synthesis of control system loops based on the fractional characteristic polynomial is proposed. The fractional characteristic polynomial ensures the desired quality of the transition process given the implementation of a specified structure of the fractional controller. A new method of structural-parametric synthesis of fractional-order controllers is developed for the case of their cascade connection in multi-loop twomass electromechanical systems. Additionally, an algorithm for synthesizing fractional-order controllers for the corresponding control loops is presented. This enabled the structural-parametric synthesis of fractional-order controllers for a two-mass electromechanical system with the cascade connection of controllers. Such an approach provides better quality of transition processes compared to classical integer controllers, simplifies the synthesis, and thereby enhances the quality of the synthesized systems. The impact of the synthesized fractional-order controllers using the proposed approach on the dynamic properties of the two-mass «thyristor converter – motor» system was investigated. The research results demonstrated the practical applicability of fractional controllers designed using the proposed method for the synthesis of automatic control systems of two-mass electromechanical systems in the industry [ABSTRACT FROM AUTHOR]

The most recent advancements in renewable energy resources, as well as their broad acceptance in power sectors, have created substantial operational, security, and management concerns. As a result of the continual decrease in power system inertia, it is critical to maintain the normal operating frequency and reduce tie-line power changes. The preceding issues sparked this research, which proposes the Fuzzy Tilted Fractional Order Integral Derivative with Fractional Filter (FTFOIDFF), a unique load frequency controller. The FTFOIDFF controller described here combines the benefits of tilt, fuzzy logic, FOPID, and fractional filter controllers. Furthermore, the prairie dog optimizer (PDO), a newly developed metaheuristic optimization approach, is shown to efficiently tune the suggested controller settings as well as the forms of the fuzzy logic membership functions in the two-area hybrid power grid investigated in this paper. When the PDO results are compared to those of the Seagull Optimization Algorithm, the Runge Kutta optimizer, and the Chaos Game Optimizer for the same hybrid power system, PDO prevails. The system model incorporates physical constraints such as communication time delays and generation rate constraints. In addition, a unified power flow controller (UPFC) is put in the tie-line, and SMES units have been planned in both regions. Furthermore, the contribution of electric vehicles (EVs) is considered in both sections. The proposed PDO-based FTFOIDFF controller outperformed many PDO-based traditional (such as proportional integral derivative (PID), proportional integral derivative acceleration (PIDA), and TFOIDFF) and intelligent (such as Fuzzy PID and Fuzzy PIDA) controllers from the literature. The suggested PDO-based FTFOIDFF controller has excellent performance due to the usage of various load patterns such as step load perturbation, multi-step load perturbation, random load perturbation, random sinusoidal load perturbation, and pulse load perturbation. Furthermore, a variety of scenarios have been implemented to demonstrate the advantageous effects that SMES, UPFC, and EV units have on the overall performance of the system. The sensitivity of a system is ascertained by modifying its parameters from their standard configurations. According to the simulation results, the suggested PDO-based FTFOIDFF controller can improve system stability despite the multiple difficult conditions indicated previously. According to the MATLAB/Simulink data, the proposed method decreased the total fitness function to 0.0875, representing a 97.35% improvement over PID, 95.84% improvement over PIDA, 92.45% improvement over TFOIDFF, 83.43% improvement over Fuzzy PID, and 37.9% improvement over Fuzzy PIDA. [ABSTRACT FROM AUTHOR]

In the literature, different approaches that are employed in designing automatic voltage regulators (AVRs) usually model the AVR as a single-input-single-output system, where the input is the generator reference voltage, and the output is the generator voltage. Alternately, it could be thought of as a double-input, single-output system, with the excitation voltage change serving as the additional input. In this paper, unlike in the existing literature, we designed the AVR system as a sextuple-input single-output (6ISO) system. The inputs in the model include the generator reference voltage, regulator signal change, exciter signal change, amplifier signal change, generator output signal change, and the sensor signal change. We also compared the generator voltage responses for various structural configurations and regulator parameter choices reported in the literature. The effectiveness of numerous controllers is investigated; the proportional, integral and differential (PID) controller, the PID with second-order derivative (PIDD2) controller, and the fractional order PID (FOPID) controller are the most prevalent types of controllers. The findings reveal that the regulator signal change and the generator output signal change significantly impact the generator voltage. Based on these findings, we propose a new approach to design the regulator parameter to enhance the response to generator reference voltage changes. This approach takes into consideration changes in the generator reference voltage as well as the regulator signal. We calculate the regulator settings using a cutting-edge hybrid technique called the Particle Swarm Optimization African Vultures Optimization algorithm (PSO–AVOA). The effectiveness of the regulator design technique and the proposed optimization algorithm are demonstrated. [ABSTRACT FROM AUTHOR]

Complex systems, as interwoven miscellaneous interacting entities that emerge and evolve through self-organization in a myriad of spiraling contexts, exhibit subtleties on global scale besides steering the way to understand complexity which has been under evolutionary processes with unfolding cumulative nature wherein order is viewed as the unifying framework. Indicating the striking feature of non-separability in components, a complex system cannot be understood in terms of the individual isolated constituents' properties per se, it can rather be comprehended as a way to multilevel approach systems behavior with systems whose emergent behavior and pattern transcend the characteristics of ubiquitous units composing the system itself. This observation specifies a change of scientific paradigm, presenting that a reductionist perspective does not by any means imply a constructionist view; and in that vein, complex systems science, associated with multiscale problems, is regarded as ascendancy of emergence over reductionism and level of mechanistic insight evolving into complex system. While evolvability being related to the species and humans owing their existence to their ancestors' capability with regards to adapting, emerging and evolving besides the relation between complexity of models, designs, visualization and optimality, a horizon that can take into account the subtleties making their own means of solutions applicable is to be entailed by complexity. Such views attach their germane importance to the future science of complexity which may probably be best regarded as a minimal history congruent with observable variations, namely the most parallelizable or symmetric process which can turn random inputs into regular outputs. Interestingly enough, chaos and nonlinear systems come into this picture as cousins of complexity which with tons of its components are involved in a hectic interaction with one another in a nonlinear fashion amongst the other related systems and fields. Relation, in mathematics, is a way of connecting two or more things, which is to say numbers, sets or other mathematical objects, and it is a relation that describes the way the things are interrelated to facilitate making sense of complex mathematical systems. Accordingly, mathematical modeling and scientific computing are proven principal tools toward the solution of problems arising in complex systems' exploration with sound, stimulating and innovative aspects attributed to data science as a tailored-made discipline to enable making sense out of voluminous (-big) data. Regarding the computation of the complexity of any mathematical model, conducting the analyses over the run time is related to the sort of data determined and employed along with the methods. This enables the possibility of examining the data applied in the study, which is dependent on the capacity of the computer at work. Besides these, varying capacities of the computers have impact on the results; nevertheless, the application of the method on the code step by step must be taken into consideration. In this sense, the definition of complexity evaluated over different data lends a broader applicability range with more realism and convenience since the process is dependent on concrete mathematical foundations. All of these indicate that the methods need to be investigated based on their mathematical foundation together with the methods. In that way, it can become foreseeable what level of complexity will emerge for any data desired to be employed. With relation to fractals, fractal theory and analysis are geared toward assessing the fractal characteristics of data, several methods being at stake to assign fractal dimensions to the datasets, and within that perspective, fractal analysis provides expansion of knowledge regarding the functions and structures of complex systems while acting as a potential means to evaluate the novel areas of research and to capture the roughness of objects, their nonlinearity, randomness, and so on. The idea of fractional-order integration and differentiation as well as the inverse relationship between them lends fractional calculus applications in various fields spanning across science, medicine and engineering, amongst the others. The approach of fractional calculus, within mathematics-informed frameworks employed to enable reliable comprehension into complex processes which encompass an array of temporal and spatial scales notably provides the novel applicable models through fractional-order calculus to optimization methods. Computational science and modeling, notwithstanding, are oriented toward the simulation and investigation of complex systems through the use of computers by making use of domains ranging from mathematics to physics as well as computer science. A computational model consisting of numerous variables that characterize the system under consideration allows the performing of many simulated experiments via computerized means. Furthermore, Artificial Intelligence (AI) techniques whether combined or not with fractal, fractional analysis as well as mathematical models have enabled various applications including the prediction of mechanisms ranging extensively from living organisms to other interactions across incredible spectra besides providing solutions to real-world complex problems both on local and global scale. While enabling model accuracy maximization, AI can also ensure the minimization of functions such as computational burden. Relatedly, level of complexity, often employed in computer science for decision-making and problem-solving processes, aims to evaluate the difficulty of algorithms, and by so doing, it helps to determine the number of required resources and time for task completion. Computational (-algorithmic) complexity, referring to the measure of the amount of computing resources (memory and storage) which a specific algorithm consumes when it is run, essentially signifies the complexity of an algorithm, yielding an approximate sense of the volume of computing resources and seeking to prove the input data with different values and sizes. Computational complexity, with search algorithms and solution landscapes, eventually points toward reductions vis à vis universality to explore varying degrees of problems with different ranges of predictability. Taken together, this line of sophisticated and computer-assisted proof approach can fulfill the requirements of accuracy, interpretability, predictability and reliance on mathematical sciences with the assistance of AI and machine learning being at the plinth of and at the intersection with different domains among many other related points in line with the concurrent technical analyses, computing processes, computational foundations and mathematical modeling. Consequently, as distinctive from the other ones, our special issue series provides a novel direction for stimulating, refreshing and innovative interdisciplinary, multidisciplinary and transdisciplinary understanding and research in model-based, data-driven modes to be able to obtain feasible accurate solutions, designed simulations, optimization processes, among many more. Hence, we address the theoretical reflections on how all these processes are modeled, merging all together the advanced methods, mathematical analyses, computational technologies, quantum means elaborating and exhibiting the implications of applicable approaches in real-world systems and other related domains. [ABSTRACT FROM AUTHOR]

In this comment, it is shown that there are some non‐negligible big mistakes in the analyses and stability proof of the proposed controller in the quoted paper, which makes the main results of this paper to be incorrect. The main unavoidable mistakes in the stability analysis of the main theorem (Theorem 1) are stated and some remarks are also mentioned to fix some of them. [ABSTRACT FROM AUTHOR]

A generalized structure for implementing fractional-order controllers is introduced in this paper. This is achieved thanks to the consideration of the controller transfer function as a ratio of integer and non-integer impedances. The non-integer order impedance is implemented using RC networks, such as the Foster and Cauer networks. The main offered benefit, with regards to the corresponding convectional implementations, is the reduced active and, also, passive component count. To demonstrate the versatility of the proposed concept, a controller suitable for implementing a cardiac pacemaker control system is designed. The evaluation of the performance of the system is performed through circuit simulation results, using a second-generation voltage conveyor as the active element. [ABSTRACT FROM AUTHOR]

This paper concentrates on computing the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval delayed fractional‐order plants. An interval delayed fractional‐order plant is defined as a fractional‐order transfer function with a time delay whose denominator and numerator coefficients are all uncertain and lie in specified intervals. In the present study, first, a theorem is proven to analyze the robust stability of the given closed‐loop. Then, a method is proposed to solve the problem of robustly stabilizing interval delayed fractional‐order plants by using FOPID controllers. Moreover, two auxiliary functions are presented to fulfill the additional specifications of design, ensuring better performance of the controlled system with respect to the disturbance and noise. Finally, two examples are provided to illustrate the design procedure. [ABSTRACT FROM AUTHOR]

This paper focuses on computing the stabilizing region of fractional-order proportional integral derivative (FOPID) controllers for interval fractional-order plants. In this study, first, a theorem is presented to investigate the robust stability of the given closed-loop system. Then, an algorithm is proposed to solve the problem of robustly stabilizing the interval fractional-order plant using FOPID controllers. Also, two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction. Finally, four numerical examples are presented to confirm the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the conceptualization of a control hardware architecture aimed to the implementation of integer- and fractional-order identification and control algorithms is presented. The proposed hardware architecture combines the capability of implementing PC-based control applications with embedded applications on microprocessor- and FPGA-based real-time targets. In this work, the potential advantages of this hardware architecture over other available alternatives are discussed from different perspectives. The experimental prototype that has been designed and built to evaluate the control hardware architecture proposed in this work is also described in detail. The thermal-based process taking place in the prototype is characterized for being reconfigurable and exhibiting fractional behaviour, which results in a suitable equipment for the purpose of fractional-order identification and control. In order to demonstrate the applicability and effectiveness of the proposed control hardware architecture, integer- and fractional-order identification and control algorithms implemented in various control technologies have been applied to the temperature-based experimental prototype described before. Detailed discussion about results and identification and control issues are provided. The main contribution of this work is to provide an efficient and practical hardware architecture for implementing fractional-order identification and control algorithms in different control technologies, helping to bridge the gap between real-time hardware solutions and software-based simulations of fractional-order systems and controllers. Finally, some conclusions and concluding remarks are offered in the industrial context. [ABSTRACT FROM AUTHOR]

This paper studies the problem of robust stabilization of interval fractional-order plants with complex uncertain parameters by using fractional-order controllers. An interval fractional-order plant with complex uncertain parameters means that the coefficients of the numerator and denominator of the plant are all uncertain and may be complex numbers and lie in specified intervals. At first, by using a graphical approach, necessary and sufficient conditions are presented for the stabilization of the fractional-order plant containing complex coefficients. Then, by using some interesting geometric features of convex polygons, a robust stability checking function is presented for the stabilization. Also, an upper frequency bound is introduced to reduce the computational burden. Finally, six examples are provided to illustrate the results. • Robust stability analysis of interval fractional order systems having complex uncertain coefficients. • Presenting new necessary and sufficient robust conditions for fractional-orders systems. • Presenting a novel graphical method to analyze the robust stability of the closed-loop system. • Introducing a robust stability testing function to investigate the robust stabilization. • Presenting a frequency range to reduce the computational cost for robust stability analysis. [ABSTRACT FROM AUTHOR]

Nowadays, advances in different fields of technology have increased demands for reliable controllers. Uncertainty and disturbances, which are inevitable in most real‐world systems, as well as increasing complexity in the dynamics of many systems, are requiring the design and application of intelligent controllers. Fuzzy controllers, and specifically type‐2 fuzzy control techniques, could play a beneficial role in a variety of control purposes, since they are robust against uncertainties. Therefore, an immense body of research is devoted to these fuzzy control techniques. This paper introduces a comprehensive review about the most recent advances in the design and implementation of type‐2 fuzzy control schemes both for integer‐ and fractional‐order systems. Thus, in addition to the past and present achievements in this context, future trends are also delineated. Moreover, most important works dealing with type‐2 fuzzy controller are discussed, and their advantages and drawbacks are outlined. Consequently, we firmly believe the present paper will pave the way for future research in this area. [ABSTRACT FROM AUTHOR]

The current study presented a novel single-input control technique, called the single-input interval type-2 fractional-order fuzzy (SIT2FOF) controller. This controller is suitable for the control problems in which the plant deals with hard external disturbance and model uncertainties. Fractional calculus and interval type-2 fuzzy sets are considered as two seminal parts of the SIT2FOF controller which provide robust control performance. In addition, single-input interval type-2 fuzzy (SIT2F) sets in the structure of the proposed controller reduce computational efforts and the number of tuning parameters. Accordingly, the controller can be implemented and tuned easily. Thus, the control problem of an automatic voltage regulator in a power system and a Kubota M110X tractor active suspension system were considered as case studies to validate the suggested method. To this end, simulations were performed in three scenarios, followed by comparing the proposed technique in each scenario with single-input type-1 fuzzy (ST1F), single-input type-1 fractional-order fuzzy (ST1FOF), and single-input interval type-2 fuzzy (SIT2F) controllers. The results revealed that the SIT2FOF control technique can significantly handle external disturbances and model uncertainties more efficiently compared to the other controllers. [ABSTRACT FROM AUTHOR]

This article deals with analyzing the phase–frequency response of commande robuste d'ordre non-entier approximations of fractional-order differentiators. More precisely, an algebraic tight upper bound is derived for the phase of the approximations obtained from the commande robuste d'ordre non-entier method. Then, some applications for this achievement are discussed in the viewpoint of control systems analysis. These applications include usefulness of the obtained upper bound in stability preservation analysis during the commande robuste d'ordre non-entier–based approximation process and applicability of such a bound in finding necessary or sufficient conditions for test of positive realness/negative imaginariness of a fractional-order transfer function. [ABSTRACT FROM AUTHOR]

This paper studies the active damping of the oscillations of lightly damped linear systems whose parameters are indeterminate or may change through time. Systems with an arbitrary number of vibration modes are considered. Systems described by partial differential equations, that yield an infinite number of vibration modes, can also be included. In the case of collocated feedback, i.e. the sensor is placed at the same location of the actuator, a simple fractional order differentiation or integration of the measured signal is proposed that provides an effective control: (1) it guarantees a minimum phase margin or damping of the closed-loop system at all vibration modes, (2) this feature is robustly achieved, i.e., it is attained for very large variations or uncertainties of the oscillation frequencies of the system and (3) it is robust to spillover effects, i.e., to the unstabilizing effects of the vibration modes neglected in the controller design (especially important in infinite dimensional systems). Moreover, the sensitivity of the gain crossover frequency to such variations is assessed. Finally, these results are applied to the position control of a single link flexible robot. Simulated results are provided.

In this work, a comparative study is analysed between the fractional‐order controllers such as fractional‐order proportional–integral–derivative (FOPID), two‐degree‐of‐freedom proportional–integral–derivative (DOF FOPID) and 3DOF FOPID, and conventional controllers such as proportional–integral–derivative (PID), 2DOF PID and 3DOF PID employed in automatic generation control (AGC) in power system. The proposed 3DOF FOPID controller is validated as superior one among all other controllers. The gains of all the controllers are optimally plucked by novel salp swarm algorithm (SSA). Further, hybrid salp swarm algorithm–simulated annealing (hSSA‐SA) algorithm is introduced to enhance the proficiency of 3DOF FOPID controller by sensibly plucking the gain parameters. The proposed approaches are implemented in a two‐area thermal‐hydro‐diesel system. Small hydro plants (SHPs) of similar characteristics are enforced in both areas with their dynamic responses by conceding frequency deviations of each area. Further, sensitivity and robustness analysis of the system with and without SHP are observed by varying some important parameters of the system. Finally, the supremacy of three novel approaches (fractional based controllers, hSSA‐SA and SHP) is substantiated gracefully.

A generalized structure for implementing fractional-order controllers is introduced in this paper. This is achieved thanks to the consideration of the controller transfer function as a ratio of integer and non-integer impedances. The non-integer order impedance is implemented using RC networks, such as the Foster and Cauer networks. The main offered benefit, with regards to the corresponding convectional implementations, is the reduced active and, also, passive component count. To demonstrate the versatility of the proposed concept, a controller suitable for implementing a cardiac pacemaker control system is designed. The evaluation of the performance of the system is performed through circuit simulation results, using a second-generation voltage conveyor as the active element.

An alternative procedure for the implementation of fractional-order compensators is presented in this work. The employment of a curve-fitting-based approximation technique for the approximation of the compensator transfer function offers improved accuracy compared to the Oustaloup and Padé methods. As a design example, a lead compensator intended for usage in car suspension systems is realized. The open-loop and closed-loop behavior of the system is evaluated by post-layout simulation results obtained using the Cadence IC design suite and the Metal Oxide Semiconductor (MOS) transistor models provided by the Austria Mikro Systeme 0.35 µm Complementary Metal Oxide Semiconductor (CMOS) process. The derived results verify the efficient performance of the introduced implementation. [ABSTRACT FROM AUTHOR]

This paper investigates the robust stability of fractional-order plants suffering from interval uncertainties by using fractional-order controllers. Based on the zero-exclusion principle, at first, new necessary and sufficient criteria are proposed to analyze the robust stability of the corresponding characteristic polynomial. Then, an auxiliary function is presented to investigate the robust stability criteria. The results of this paper also help to reduce additional calculations noticeably since the vertices used in the auxiliary function are fixed for all positive frequencies. Finally, three numerical examples are given to indicate the effectiveness of the paper results. [ABSTRACT FROM AUTHOR]

This work presents an optimal projective synchronization of non-identical fractional-order chaotic systems (FOCS) in the presence of uncertainties and external disturbances using a fractional sliding mode controller (FSMC). For the first time, and based on Lyapunov stability theory, fractional-order sliding surfaces are proposed to design signal controllers for forcing errors behavior to zero and to make the states of the FOCS asymptotically stable. Then, to obtain optimal control parameters, GA and PSO algorithms will be introduced. An example of non-identical FOCS are proposed to demonstrate the effectiveness of the proposed optimal FSMC approach compared with the integer one. The simulation results show the applicability and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper studies the active damping of the oscillations of lightly damped linear systems whose parameters are indeterminate or may change through time. Systems with an arbitrary number of vibration modes are considered. Systems described by partial differential equations, that yield an infinite number of vibration modes, can also be included. In the case of collocated feedback, i.e. the sensor is placed at the same location of the actuator, a simple fractional order differentiation or integration of the measured signal is proposed that provides an effective control: (1) it guarantees a minimum phase margin or damping of the closed-loop system at all vibration modes, (2) this feature is robustly achieved, i.e., it is attained for very large variations or uncertainties of the oscillation frequencies of the system and (3) it is robust to spillover effects, i.e., to the unstabilizing effects of the vibration modes neglected in the controller design (especially important in infinite dimensional systems). Moreover, the sensitivity of the gain crossover frequency to such variations is assessed. Finally, these results are applied to the position control of a single link flexible robot. Simulated results are provided. [ABSTRACT FROM AUTHOR]

This paper presents a new optimization-based tuning method for fractional- and integer-order controllers. The method is based on minimizing an arbitrary cost function which is taken here as the integrated absolute tracking error, and it can be used for tuning purposes as well as the assessment of controller performance. The presented results are obtained from experiments with a servo drive system with a 2- and 3-parameter fractional-order controller. They depict performance improvement and ability of the proposed method to find the global minimum of a selected performance index in experimental conditions. The method does not need any model of the plant, and it has great potential for applications in general controllers or for an extension to different parameter tuning problems. The method offers a new way of changing dynamic properties of closed-loop systems, by rapid tuning of controllers. This makes possible new applications of this method, as opposed to other tuning methods, which basically require knowledge of the plant. • Novel method to optimally tune fractional-order controllers. • Can be used in an on-line fashion to optimal gains from a scratch, or to fine-tune the current ones. • Applicable to standard-order controllers. • Method with a very low computational complexity, suited for rapid tuning, with a deterministic running time. • Method requires no knowledge of the model of the plant. [ABSTRACT FROM AUTHOR]

In this work, a comparative study is analysed between the fractional‐order controllers such as fractional‐order proportional–integral–derivative (FOPID), two‐degree‐of‐freedom proportional–integral–derivative (DOF FOPID) and 3DOF FOPID, and conventional controllers such as proportional–integral–derivative (PID), 2DOF PID and 3DOF PID employed in automatic generation control (AGC) in power system. The proposed 3DOF FOPID controller is validated as superior one among all other controllers. The gains of all the controllers are optimally plucked by novel salp swarm algorithm (SSA). Further, hybrid salp swarm algorithm–simulated annealing (hSSA‐SA) algorithm is introduced to enhance the proficiency of 3DOF FOPID controller by sensibly plucking the gain parameters. The proposed approaches are implemented in a two‐area thermal‐hydro‐diesel system. Small hydro plants (SHPs) of similar characteristics are enforced in both areas with their dynamic responses by conceding frequency deviations of each area. Further, sensitivity and robustness analysis of the system with and without SHP are observed by varying some important parameters of the system. Finally, the supremacy of three novel approaches (fractional based controllers, hSSA‐SA and SHP) is substantiated gracefully. [ABSTRACT FROM AUTHOR]

The scientific community has recently seen a fast-growing number of publications tackling the topic of fractional-order controllers in general, with a focus on the fractional order PID. Several versions of this controller have been proposed, including different tuning methods and implementation possibilities. Quite a few recent papers discuss the practical use of such controllers. However, the industrial acceptance of these controllers is still far from being reached. Autotuning methods for such fractional order PIDs could possibly make them more appealing to industrial applications, as well. In this paper, the current autotuning methods for fractional order PIDs are reviewed. The focus is on the most recent findings. A comparison between several autotuning approaches is considered for various types of processes. Numerical examples are given to highlight the practicality of the methods that could be extended to simple industrial processes.

Fractional-order controllers have gained significant research interest in various practical applications due to the additional degrees of freedom offered in their tuning process. The main contribution of this work is the analog implementation, for the first time in the literature, of a fractional-order controller with a transfer function that is not directly constructed from terms of the fractional-order Laplacian operator. This is achieved using Padé approximation, and the resulting integer-order transfer function is implemented using operational transconductance amplifiers as active elements. Post-layout simulation results verify the validity of the introduced procedure.

Abstract A novel topology for implementing fractional-order differentiator and integrator transfer functions is presented in this paper. This topology is based on the employment of a second generation Current Conveyor with EXtra inputs (EX-CCII), passive resistors, and fractional-order capacitors. The main benefit offered by this implementation is that both fractional-order differentiator and integrator transfer functions are simultaneously available at different output terminals, and that their frequency characteristics can be orthogonally adjusted without disturbing each other. With only one EX-CCII device needed, the proposed design is attractive from the active component count point of view. As an application example, a fractional-order controller is designed in order to control the velocity of a small scale submersible equipped with one propeller. Evaluation of the performance of the presented topology is performed using Cadence and the Design Kit provided by the Austria Mikro Systeme (AMS) 0.35 μ m CMOS process, as well as through experimental results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing controllers that are robust to large changes in the undamped natural frequencies of a plant. Plants must be represented by means of minimum phase rational transfer functions of an arbitrary order whose oscillatory dynamics must fulfill the pole-zero interlacing property on the imaginary axis. The design specifications are as follows: (i) a phase margin for the nominal plant; (ii) a gain crossover frequency for the nominal plant; and (iii) a constant phase margin for large variations in the undamped natural frequencies of the plant, the zeros associated with the oscillatory part of the plant and the gain of the plant. Theorems are proposed that define the structure of the controllers that fulfill these specifications. We show that these robust controllers must necessarily include a fractional-order integro-differential term. Analytical simple expressions with which to obtain the simplest controllers that verify the aforementioned specifications are also obtained. Some relevant features of these fractional-order controllers are later highlighted. Finally, as an example, these controllers are applied to a Buck electronic converter. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main focus of this paper is on a graphical tuning method of non-linear fractional-order PID (FOPID)-type controllers, i.e. a class of FOPID-type controllers that non-linearly depend on the control parameters, e.g. FO[PI], FO[PD] etc. Firstly, a method is proposed to determine the stabilizing region of non-linear FOPID-type controllers, namely the complete sets of FOPID-type controllers providing stability of the control system. Secondly, two different approaches are proposed to determine the H∞ region of these FOPID-type controllers, namely the complete sets achieving H∞ robust performance specifications. The first approach maps the H∞ constraints into the parameter space by solving a series of non-linear equations. The second approach transforms the original H∞ region problem into simultaneous stabilization of a family of characteristic polynomials. It turns out that these two approaches are both very flexible, and the second approach is more efficient than the former. The main advantage of our proposed graphical tuning method is that the exact mathematical model of the controlled plant is not needed. The stabilizing and H∞ regions can be computed only from the frequency response data of the plant. Finally, numerical and experimental results are presented to demonstrate the proposed graphical tuning method. [ABSTRACT FROM AUTHOR]

The equivalence of fractional-order inverse filters with fractional-order controllers is demonstrated in this work. This is achieved by appropriately rewriting the filters transfer functions in order to clarify the correspondence between the gain and time-constant of the filters and the scaling factor and differentiation/integration constant of the controllers. Possible implementations of fractional-order inverse filters using second generation voltage conveyors are presented and an application example, related to the control of a motion system, is demonstrated for evaluating the behavior of the introduced structures. [ABSTRACT FROM AUTHOR]

This paper analyzes the fragility issue of fractional-order proportional-integral-derivative controllers applied to integer first-order plus-dead-time processes. In particular, the effects of the variations of the controller parameters on the achieved control system robustness and performance are investigated. Results show that this kind of controllers is more fragile with respect to the standard proportional-integral-derivative controllers and therefore a significant attention should be paid by the user in their tuning. [ABSTRACT FROM AUTHOR]

Highlights: [•] A new model of the SEIG is developed to simulate both the rotor and stator faults. [•] This model takes iron loss, main flux and cross flux saturation into account. [•] A new control strategy based on Fractional-Order Controller (FOC) is proposed. [•] The control strategy is developed for the control of the wind turbine speed. [•] An on-line diagnostic procedure based on the stator currents analysis is presented. [Copyright &y& Elsevier]

In recent years, it has been remarkable to see the increasing number of studies related to the theory and application of fractional-order controllers, especially PIλDμ controllers, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods to ensure robustness in new or classical control problems. In this paper, we investigate switching systems. A frequency-domain design method is developed for switching systems for both integer- or fractional-order controllers, taking into account specifications regarding performance and robustness and ensuring the quadratic stability of the controlled system. Some examples are given to show the applicability and effectiveness of the proposed tuning method. [ABSTRACT FROM PUBLISHER]

In this article, stabilisation of unstable first-order-plus-dead-time (FOPDT) processes with a single zero by fractional-order (FO) controllers is investigated. A Nyquist stability criterion-based approach is adopted to derive the conditions for stability. Sufficient stabilisability conditions by FO [proportional integral] controllers and FO-lead–lag controllers are established. In addition, robust stability of the system with these FO controllers is investigated. To illustrate the results, some examples are provided. [ABSTRACT FROM PUBLISHER]

In recent years, several research works proposed fractional-order controllers as means to improve the performances of common proportional, integral and derivative controllers. However, the design and tuning methods for these new controllers are still at their infancy. As a contribute for filling this gap, this article proposes a two-step design approach. First, differential evolution determines the fractional integral and derivative actions satisfying the required time-domain performance specifications. Second, particle swarm optimization determines rational approximations of the irrational fractional operators as low-order, stable, minimum-phase transfer functions with poles interlacing zeros. Extensive time- and frequency-domain simulations validate the efficiency of the proposed approach. [ABSTRACT FROM PUBLISHER]

The stabilization of all-pole unstable systems with time delay by fractional-order controllers is investigated in this paper. Sufficient conditions for stabilizability by fractional-order [PD]/[PI] controllers are determined. To derive the conditions for stability, an analysis based on Nyquist stability criterion is adopted and the upper bound for the time delay is determined. Furthermore, this paper provides the stabilizing range of the controller parameters. Theoretical proofs in company with illustrative examples are also provided. [ABSTRACT FROM AUTHOR]

In this article, the sufficient stabilisability criteria for unstable time-delay processes by fractional-order controllers are investigated. The process is a high-order system with a single unstable pole, which also has a stable zero. The adopted approach to derive the sufficient conditions for stability is based on the well-known Nyquist stability criterion. Stabilisability is studied by applying fractional-order proportional integral and proportional derivative controllers and the results are given in terms of the maximum allowable value of time delay. Additionally, limitations on the parameters of the controllers which must be taken into account in the controller design are proposed. [ABSTRACT FROM AUTHOR]

In the present paper stabilization of a class of fractional-order unstable delay systems by fractional-order controllers is investigated. To derive the sufficient conditions for stability, an analysis based on the Nyquist stability criterion has been adopted. The analysis is carried out with fractional-order [proportional–integral] and [proportional–derivative] controllers to obtain the upper bound for the time delay. Furthermore, the paper proposes the conditions on the parameters of the controllers which must be fulfilled in order to have a stabilized process. Two illustrated examples using fractional-order controllers are presented for demonstrating the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This article focuses on performance design for fractional-order systems with time-delay, using fractional-order proportional-derivative controllers. First, the stabilizing parameters region in proportional-derivative plane of controller, for a fixed derivative-order, is determined in terms of a graphical stability criterion applicable to fractional-order time-delay systems. Then, in the stabilizing region, the pairs of proportional and derivative gains of controller are calculated for a range of frequencies, which satisfy the -norm constraint of complementary sensitivity function and define the boundary curve. Finally, by changing the derivative-order of controller, we observe the relationship between the curve and the derivative-order. Examples are followed to illustrate the design procedure. [Copyright &y& Elsevier]

Abstract: In this paper we present a set of tuning rules for standard (integer-order) PID and fractional-order PID controllers. Based on a first-order-plus-dead-time model of the process, the tuning rules have been devised in order to minimise the integrated absolute error with a constraint on the maximum sensitivity. The achieved performance indexes can also be used for the assessment of the controller performance. Both set-point following and load disturbance rejection tasks are considered. By comparing the results obtained for the two kinds of controllers, it is shown that the use of fractional-order integral action is not advantageous, while the use of a fractional-order derivative action provides a performance improvement. [ABSTRACT FROM AUTHOR]

Recently, fractional (non-integer) differential and integral equations have received intensive attention and research. Consequently, there is an increasing interest in fractional-order dynamic systems and controllers. This paper uses fractional-order proportional- integral (PI) and proportional-integral-derivative (PID) controllers to improve stability and transient response of feedback automatic voltage regulator (AVR) control system. The interaction between the AVR system and the automatic generation control (AGC) has been investigated in the paper. The paper will show that fractional-order PI and PID controllers perform better than traditional integer-order PI and PID controllers. [ABSTRACT FROM AUTHOR]

Abstract: Differential evolution (DE) has recently emerged as a simple yet very powerful technique for real parameter optimization. This article describes an application of DE to the design of fractional-order proportional–integral–derivative (FOPID) controllers involving fractional-order integrator and fractional-order differentiator. FOPID controllers’ parameters are composed of the proportionality constant, integral constant, derivative constant, derivative order and integral order, and its design is more complex than that of conventional integer-order proportional–integral–derivative (PID) controller. Here the controller synthesis is based on user-specified peak overshoot and rise time and has been formulated as a single objective optimization problem. In order to digitally realize the fractional-order closed-loop transfer function of the designed plant, Tustin operator-based continuous fraction expansion (CFE) scheme was used in this work. Several simulation examples as well as comparisons of DE with two other state-of-the-art optimization techniques (Particle Swarm Optimization and binary Genetic Algorithm) over the same problems demonstrate the superiority of the proposed approach especially for actuating fractional-order plants. The proposed technique may serve as an efficient alternative for the design of next-generation fractional-order controllers. [Copyright &y& Elsevier]