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This 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 } $ PIμDλ 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. [ABSTRACT FROM AUTHOR]

In this work, an in-depth investigation into enhancing quadcopter autonomy and control capabilities is presented. The focus lies on the development and implementation of three conventional control strategies to regulate the behavior of quadcopter UAVs: a proportional–integral–derivative (PID) controller, a sliding mode controller, and a fractional-order PID (FOPID) controller. Utilizing careful adjustments and fine-tuning, each control strategy is customized to attain the desired dynamic response and stability during quadcopter flight. Additionally, an approach called Dyna-Q learning for obstacle avoidance is introduced and seamlessly integrated into the control system. Leveraging MATLAB as a powerful tool, the quadcopter is empowered to autonomously navigate complex environments, adeptly avoiding obstacles through real-time learning and decision-making processes. Extensive simulation experiments and evaluations, conducted in MATLAB 2018a, precisely compare the performance of the different control strategies, including the Dyna-Q learning-based obstacle avoidance technique. This comprehensive analysis allows us to understand the strengths and limitations of each approach, guiding the selection of the most effective control strategy for specific application scenarios. Overall, this research presents valuable insights and solutions for optimizing flight stability and enabling secure and efficient operations in diverse real-world scenarios.

The performance of the robotic manipulator is negatively impacted by outside disturbances and uncertain parameters. The system's variables are also highly coupled, complex, and nonlinear, indicating that it is a multi-input, multi- output system. Therefore, it is necessary to develop a controller that can control the variables in the system in order to handle these complications. This work proposes six control structures based on neural networks (NNs) with proportional integral derivative (PID) and fractional-order PID (FOPID) controllers to operate a 2-link rigid robot manipulator (2-LRRM) for trajectory tracking. These are named as set-point-weighted PID (W-PID), set-point weighted FOPID (W-FOPID), recurrent neural network (RNN)-like PID (RNNPID), RNN-like FOPID (RNN-FOPID), NN+PID, and NN+FOPID controllers. The zebra optimization algorithm (ZOA) was used to adjust the parameters of the proposed controllers while reducing the integral-time-square error (ITSE). A new objective function was proposed for tuning to generate controllers with minimal chattering in the control signal. After implementing the proposed controller designs, a comparative robustness study was conducted among these controllers by altering the initial conditions, disturbances, and model uncertainties. The simulation results demonstrate that the NN+FOPID controller has the best trajectory tracking performance with the minimum ITSE and best robustness against changes in the initial states, external disturbances, and parameter uncertainties compared to the other controllers. [ABSTRACT FROM AUTHOR]

In this work, an in-depth investigation into enhancing quadcopter autonomy and control capabilities is presented. The focus lies on the development and implementation of three conventional control strategies to regulate the behavior of quadcopter UAVs: a proportional–integral–derivative (PID) controller, a sliding mode controller, and a fractional-order PID (FOPID) controller. Utilizing careful adjustments and fine-tuning, each control strategy is customized to attain the desired dynamic response and stability during quadcopter flight. Additionally, an approach called Dyna-Q learning for obstacle avoidance is introduced and seamlessly integrated into the control system. Leveraging MATLAB as a powerful tool, the quadcopter is empowered to autonomously navigate complex environments, adeptly avoiding obstacles through real-time learning and decision-making processes. Extensive simulation experiments and evaluations, conducted in MATLAB 2018a, precisely compare the performance of the different control strategies, including the Dyna-Q learning-based obstacle avoidance technique. This comprehensive analysis allows us to understand the strengths and limitations of each approach, guiding the selection of the most effective control strategy for specific application scenarios. Overall, this research presents valuable insights and solutions for optimizing flight stability and enabling secure and efficient operations in diverse real-world scenarios. [ABSTRACT FROM AUTHOR]

This paper focuses on the fractional-order modeling and analysis of single-phase quasi-Z-source rectifier (qZSR), aims to extend the single-phase qZSR from integer-order domain to fractional-order domain. Additionally, it has been demonstrated explicitly the mechanism by which fractional-order inductors (FOIs) and fractional-order capacitors (FOCs) affect the operating features of fractional-order quasi-Z-source rectifier (FO-qZSR). The fractional-order circuit model is built based on oustaloup’s approximation method, the operational principle and control strategy of FO-qZSR, the expression of input current, inductor current, capacitor voltage and output voltage are also derived and analyzed in detail. Then, the above theoretical analysis is verified by simulation results by using the fotf toolbox in Matlab/Simulink, and the FO-qZSR presents more flexible and diverse operating features than integer-order qZSR. Finally, the hardware prototype is established with the help of the RT-LAB platform and the experimental results are consistent with the theoretical analysis and simulation results.

The use of cable-driven parallel robots (CDPRs) has been steadily increasing across various sectors due to their expansive workspaces, impressive payload-to-mass ratios, and cost-effective designs. Controlling these robots, particularly those with substantial actuation redundancy, can present challenges. This research paper proposes the implementation of a fractionalorder proportional-integral-derivative (FOPID) controller to effectively regulate the end-effector of a planar CDPR with four actuation cables. The parameters of the controller are fine-tuned using the particle swarm optimization (PSO) algorithm to ensure optimal performance. The proposed controller's performance is evaluated through two numerical experiments: target tracking and trajectory tracking using a point-to-point approach. Furthermore, a comparative study is conducted to highlight the controller's performance, comparing the proposed FOPID controller with both the classical PID controller and an optimized PID controller. The achieved results demonstrate that the proposed controller exhibits superior performance in terms of tracking accuracy and smoothness of control signals when compared to the other controllers under investigation. As a result, the proposed controller design represents a substantial advancement in control performance and can be regarded as a promising control strategy for CDPRs. [ABSTRACT FROM AUTHOR]

Gantry-type dual-axis platforms can be used to move heavy loads or perform precision CNC work. Such gantry systems drive a single axis with two linear motors, and under heavy loads, a high driving force is required. This can generate a pulling force between the drive shafts in the coupling mechanism. In these situations, when a synchronization error becomes too large, mechanisms can become deformed or damaged, leading to damaged equipment, or in industrial settings, an additional power consumption. Effectively and accurately acquiring the synchronized movement of the platform is important to reduce energy consumption and optimize the system. In this study, a fractional-order fuzzy PID controller (FOFPID) using Oustaloup's recursive filter is used to control a synchronous X–Y gantry-type platform. The optimized controller parameters are obtained by the measurement of control errors in a simulated environment. Four optimization methods are tested and compared: particle swarm optimization, invasive weed optimization, a gray wolf optimizer, and biogeography-based optimization. The systems were tested and compared in order to optimize the control parameters. Each of the four algorithms is simulated on four contour shapes: a circle, bow, heart, and star. The simulations and control scheme of the experiments are implemented using MATLAB, and the reference paths were planned using non-uniform rational B-splines (NURBS). After running the simulations to determine the optimal control parameters, each set of acquired control parameters is also tested and compared in the experiments and the results are recorded. Both the simulations and experiments show good results, and the tracking of the X–Y platform showed improved performance. Two performance indices are used to determine and validate the relative performance of the models and results. [ABSTRACT FROM AUTHOR]

Because the majority of wind turbines operate in maximum output power tracking mode, power system frequency cannot be supported. However, if the penetration rate of wind power increases, the system inertia related to frequency modulation may decrease. In addition, frequency stability will be severely affected in the event of significant disturbances to the system load. Due to the high penetration of wind power in isolated power systems, this study suggests a coordinated frequency management approach for emergency frequency regulation. In order to prevent the phenomenon of load frequency control in doubly fed induction generators (DFIGs), a unique efficient control scheme is developed. The Cascaded Fractional Model Predictive Controller coupled with Fractional-Order PID controller (CFMPC-FOPID) is developed to provide the DFIG system with an efficient reaction to changes in load and system parameters. The proposed controller must have a robust tendency to respond quickly in terms of minimum settling time, undershoot, and overshoot. Nonlinear feedback controllers are designed using frequency deviations and power imbalances to achieve the reserve power distribution between generators and DFIGs in a variety of wind speed conditions. It makes upgrading quick and easy. In Matlab/Simulink, a simulation model is built to test the viability of the suggested approach.

In most chemical industries, continuous stirred-tank reactors (CSTRs) are essential for the production of chemicals. The CSTR process is highly nonlinear and has both stable and unstable equilibrium points. Control system engineers face a difficult issue when designing a single controller for temperature control in both stable and unstable areas. Due to these problems, implementing the conventional proportional-integral-derivative (PID) controller may lead to instability in controlled variables. Therefore, in this paper, the entire operating region is divided into three regions. The fractional-order PID controller as a local controller is designed in each operating region to control the temperature, and its parameters are tuned with a genetic algorithm by minimizing the integral of absolute error and control input change with a weighting factor. Then, a fuzzy gain scheduling scheme based on the Tagaki-Sugno fuzzy model is used to properly interpolate the outputs of the local controllers. A set of simulations are carried out to demonstrate the effectiveness of the proposed controller, and its performance is compared with that of an adaptive nonlinear controller and fuzzy gain scheduling of the PID controller. [ABSTRACT FROM AUTHOR]

Local hyperthermia is one of the most prevalent thermal therapies for cancerous tumors, near the skin surface or natural body orifices. Due to the requisiteness of temperature control during local hyperthermia, first, the heat conduction process during the mentioned therapy is analytically modeled via a fractional-order transfer function with time delay. Since the influence of the heat source and the patient`s physiological reaction may vary the patient body temperature and affect all of the model parameters, robust control of temperature during the treatment is necessary. Hereupon, this study suggests a novel robustness criterion to achieve the phase margin invariance despite concurrent uncertainty on different parameters of the process model. Afterward, an analytical method is presented to tune a Fractional-Order Proportional-Integral-Derivative (FO-PID) controller for desirably adjusting the values of phase margin and gaining crossover frequency, such that the proposed robustness feature is also satisfied. Finally, a numerical simulation is presented to evaluate the efficiency of the paper`s achievements, using practical parameters.

Inclusion of intermittent natured renewable energy resources in microgrid to reduce global warming, especially in shipboard power system and due to highly fluctuating propulsion load, frequency control strategy of isolated shipboard hybrid microgrid (ISHMG) is major point of attraction. Hence, a power system of marine vessel with dish‐stirling solar thermal system (DSTS), wind‐driven generation (WDG), solid oxide fuel cell (SOFC), super‐conducting magnetic energy storage (SMES), two different AC‐loads, and propulsion loads are considered as an ISHMG. The main objective of this paper is reducing the mismatch between generation and demand with the help of fractional‐order proportional integral‐derivative (FOPID) controller. To improve the frequency control, the tuning of the controller coefficients plays a major role as the controller's performance fully dependent on the parameters. Accordingly, the recently developed butterfly optimization algorithm (BOA) has been used to optimize the FOPID controller's parameters. Comparative analysis of several techniques like FA, PSO, GOA, SSA, and BOA used for PID, PI, FOPID controllers' optimization, and sensitivity analysis under different parametric variation has been presented to prove the stability of the ISHMG model. Analyzing all the results, it is found that BOA‐based FOPID controller is performing the frequency control far better than other techniques. [ABSTRACT FROM AUTHOR]

One of the most popular controllers for the automatic voltage regulator (AVR) in maintaining the voltage level of a synchronous generator is the fractional-order proportional–integral-derivative (FOPID) controller. Unfortunately, tuning the FOPID controller is challenging since there are five gains compared to the three gains of a conventional proportional–integral–derivative (PID) controller. Therefore, this research work presents a variant of the marine predators algorithm (MPA) for tuning the FOPID controller of the AVR system. Here, two modifications are applied to the existing MPA: the hybridization between MPA and the safe experimentation dynamics algorithm (SEDA) in the updating mechanism to solve the local optima issue, and the introduction of a tunable step size adaptive coefficient (CF) to improve the searching capability. The effectiveness of the proposed method in tuning the FOPID controller of the AVR system was assessed in terms of the convergence curve of the objective function, the statistical analysis of the objective function, Wilcoxon's rank test, the step response analysis, stability analyses, and robustness analyses where the AVR system was subjected to noise, disturbance, and parameter uncertainties. We have shown that our proposed controller has improved the AVR system's transient response and also produced about two times better results for objective function compared with other recent metaheuristic optimization-tuned FOPID controllers. [ABSTRACT FROM AUTHOR]

A fractional-order fuzzy proportional integral derivative (PID) controller is a controller that combines the benefits of fractional calculus and fuzzy logic with the conventional PID controller. In this paper, a four-stage optimization algorithm is proposed for the design of a Type-2 Fuzzy fractional-order PID controller based on the Fourier Series Method (FSM). Three distinct control structures are introduced: Type-2 fuzzy fractional PD + fractional PI controller, Type-2 fuzzy fractional PID, and Type-2 fuzzy fractional PD + Type-2 fuzzy fractional PI controller. In addition to a modified multi-performance criterion cost function, four integral performance criteria are employed as cost functions for each stage. The suggested algorithm avoids the utilization of the approximation equivalent for the fractional-order system and instead employs FSM. Furthermore, the approach optimizes the nonlinearity within the upper membership function (UMF) and the uncertainty range through the lower membership function, as opposed to arbitrary selection. By considering variations in the membership functions, the outcomes exhibit a superior response compared to previous investigations. The results of the three control structures are compared with the traditional PID controller, and simulation results demonstrate the feasibility of this technique. The findings suggest that by optimizing different integral performance criteria using this design technique, controllers for both integer and fractional-order plants can yield favorable step responses. The proposed algorithm is validated by comparing its step response performance with that of previous research, followed by a discussion on sensitivity analysis and computational requirements.

Allowing for a "virtual" full actuation of a rotary inverted pendulum (RIP) system with only a single physical actuator has been a challenging problem. In this paper, a hybrid control scheme that involves a pole-placement feedback controller and an optimal proportional–integral–derivative (PID) or fractional-order PID (FOPID) controller is proposed to simultaneously enable the tracking control of the rotary arm and the stabilization of the pendulum arm in an input–output feedback linearized RIP system. The PID controller is optimized first with the particle swarm optimization (PSO) to obtain three optimal gains, and then the other two parameters of the FOPID controller are optimized with the PSO. Compared to the optimized PID controller, the optimized FOPID controller improves the tracking and stabilizing accuracy by 53% and 29%, respectively, and demonstrates better adaptability for tracking different reference signals. Moreover, the hybrid FOPID controller exhibits 74.8% and 53% higher tracking accuracy than previous optimized model reference adaptive control PID (MRAC-PID) and linear–quadratic regulator (LQR) controllers, respectively. The proposed hybrid controllers are also digitized with different rules and sampling times, showing a closer performance between the discrete-time and continuous-time hybrid controllers under smaller sampling times. [ABSTRACT FROM AUTHOR]

The search for a better approach to design a convenient controlling scheme is one of the main challenges of the research field related to power converters. This paper brings forward a significant contribution as part of this challenge. In this regard, novel approaches have been proposed for both controller scheme and tuning algorithm. In terms of controlling scheme, a fractional-order proportional–integral–derivative (FOPID) controller was used alongside the Bode's ideal transfer function to achieve optimum performance of a buck converter system. To achieve a greater performance of the FOPID controller, a novel metaheuristic algorithm, which consists of a balanced structure in terms of explorative and exploitative phases, has also been developed by hybridizing the hunger games search algorithm with simulated annealing technique. The proposed hybrid algorithm helped tuning the FOPID controller optimally. The proposed algorithm and controlling scheme have been proved to be a better approach for controlling a buck converter system in terms of time and frequency domains along with disturbance rejection. To further verify the effectiveness of the proposed hybrid algorithm–based controlling scheme, it was compared with other reported and capable approaches which have also confirmed the greater performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Due to factors such as uneven guide rails and airflow disturbance in the hoistway, high-speed elevators may experience significant vibrations during operation. This paper proposes an optimized fractional-order PID (FOPID) method to suppress vibrations of high-speed elevators. First, an accurate horizontal vibration model is established for the elevator car, in which the car frame and body are separate. Then, taking the control cost and the system performance as objective functions, we obtained an optimized FOPID controller based on multi-objective genetic algorithm optimization. Finally, the effectiveness of the controller in reducing elevator vibration was verified through numerical simulation. The results indicate that the horizontal acceleration controlled by the FOPID controller is reduced by about 68% compared to the case without a controller and about 25% compared to the conventional PID controller. [ABSTRACT FROM AUTHOR]

Diffusion processes, as fundamental mechanisms for particle movement in systems with different concentrations, are used to describe many real-world physical, chemical, biological, engineering, economic and social phenomena. A diffusion process can be modelled via a fractional-order transfer function with time-delay, where its parameters may be affected by circumstance. Hereupon, this study proposes a pioneer robustness indicator to achieve the phase margin invariance regardless of concurrent uncertainty on different parameters of a diffusion process. Afterwards, an analytical procedure is suggested to tune a Fractional-Order Proportional-Integral-Derivative (FO-PID) controller for a diffusion process, to favourably regulate the values of gain crossover frequency and phase margin, such that the proposed robustness criterion is met. Moreover, the solvability of the problem is analytically investigated. Finally, a numerical simulation on robust temperature control during magnetic local hyperthermia, i.e. a common method to treat cancerous tumours, is presented to validate the efficiency of the paper achievements. [ABSTRACT FROM AUTHOR]

Gantry-type dual-axis platforms can be used to move heavy loads or perform precision CNC work. Such gantry systems drive a single axis with two linear motors, and under heavy loads, a high driving force is required. This can generate a pulling force between the drive shafts in the coupling mechanism. In these situations, when a synchronization error becomes too large, mechanisms can become deformed or damaged, leading to damaged equipment, or in industrial settings, an additional power consumption. Effectively and accurately acquiring the synchronized movement of the platform is important to reduce energy consumption and optimize the system. In this study, a fractional-order fuzzy PID controller (FOFPID) using Oustaloup’s recursive filter is used to control a synchronous X–Y gantry-type platform. The optimized controller parameters are obtained by the measurement of control errors in a simulated environment. Four optimization methods are tested and compared: particle swarm optimization, invasive weed optimization, a gray wolf optimizer, and biogeography-based optimization. The systems were tested and compared in order to optimize the control parameters. Each of the four algorithms is simulated on four contour shapes: a circle, bow, heart, and star. The simulations and control scheme of the experiments are implemented using MATLAB, and the reference paths were planned using non-uniform rational B-splines (NURBS). After running the simulations to determine the optimal control parameters, each set of acquired control parameters is also tested and compared in the experiments and the results are recorded. Both the simulations and experiments show good results, and the tracking of the X–Y platform showed improved performance. Two performance indices are used to determine and validate the relative performance of the models and results.

A cascade technique with two control loops is designed for a DC\DC Buck‐Boost converter that is a right half‐plane zero (RHPZ) structure called a non‐minimum phase system. This concept presents several challenging constraints for designing well‐behaved control techniques. Cascade controllers can provide various benefits compared with single loop controllers such as higher safety, higher robustness, and higher stability. This strategy assumes the system as a black‐box structure without the need for a mathematical model of the system. This benefit can decrease the computational burden and provides faster dynamics along with ease of implementation. This technique consisted of an outer Fractional‐order PID voltage controller tuned with the Antlion Optimizer (ALO) algorithm, which provides a reference current for the inner control loop of the Neural Network‐based LQR (NN‐LQR) controller. The basic principle in cascade controllers is a more rapid performance of the inner loop that has been satisfied with the NN‐LQR strategy, which optimizes and tunes the gains of the LQR controller and shows faster dynamics and higher robustness. It should be mentioned that the number of neurons is limited to 2 and 4 in each layer to decrease the computational burden with lower complexity. Also, the ALO algorithm is a modern nature‐inspired algorithm used to tune the PID gains with better results under‐constrained problems with diverse search spaces. Considering the negative impacts of various disturbances on a power converter, a Fractional‐order‐based PID (FO‐PID) control technique is a proper alternative since it shows higher robustness in load uncertainties along with better dynamical responses based on its extra degree of freedom. Moreover, to evaluate the superiority of this controller, two other controllers are designed using the PSO algorithm for PID and FO‐PID controllers. Finally, the presented cascade controller has been tested in various working conditions through simulation and experiment results. [ABSTRACT FROM AUTHOR]

The application of the fractional-order PID (FOPID) controller is recently becoming a topic of research interest for vibration control of structures. Some researchers have successfully implemented the FOPID controller in a single-input single-output (SISO) control structural system subjected to earthquake excitations. However, there is a lack of research that focuses on its application in multi-input multi-output (MIMO) control systems to implement it in seismic-excited structures. In this case, the cross-coupling of the process channels in the MIMO control structural system may result in a complex design process of controllers so that each loop is independently designed. From an operational point of view, the time delay and saturation limit of the actuators are other challenges that significantly affect the performance and robustness of the controller so that ignoring them in the design process may lead to unrealistic results. According to the challenges, the present study proposed an optimal fractional-order PID control design approach for structural control systems subjected to earthquake excitation. Gases Brownian motion optimization (GBMO) algorithm is utilized for optimal tuning of the controller parameters. Considering six real earthquakes and seven performance indices, the performance of the proposed controller, implemented on a ten-story building equipped with an active tendon system (ATS), is compared with those provided by the classical PID controller. Simulation results indicate that the proposed FOPID controller is more efficient than the PID in both terms of seismic performance and robustness against time-delay effects. The proposed FOPID controller can maintain suitable seismic performance in small time delays, while a significant performance loss is observed for the PID controller. [ABSTRACT FROM AUTHOR]

In this paper, an online optimization approach of a fractional-order PID controller based on a fractional-order actor-critic algorithm (FOPID-FOAC) is proposed. The proposed FOPID-FOAC scheme exploits the advantages of the FOPID controller and FOAC approaches to improve the performance of nonlinear systems. The proposed FOAC is built by developing a FO-based learning approach for the actor-critic neural network with adaptive learning rates. Moreover, a FO rectified linear unit (RLU) is introduced to enable the AC neural network to define and optimize its own activation function. By the means of the Lyapunov theorem, the convergence and the stability analysis of the proposed algorithm are investigated. The FO operators for the FOAC learning algorithm are obtained using the gray wolf optimization (GWO) algorithm. The effectiveness of the proposed approach is proven by extensive simulations based on the tracking problem of the two degrees of freedom (2-DOF) helicopter system and the stabilization issue of the inverted pendulum (IP) system. Moreover, the performance of the proposed algorithm is compared against optimized FOPID control approaches in different system conditions, namely when the system is subjected to parameter uncertainties and external disturbances. The performance comparison is conducted in terms of two types of performance indices, the error performance indices, and the time response performance indices. The first one includes the integral absolute error (IAE), and the integral squared error (ISE), whereas the second type involves the rising time, the maximum overshoot (Max. OS), and the settling time. The simulation results explicitly indicate the high effectiveness of the proposed FOPID-FOAC controller in terms of the two types of performance measurements under different scenarios compared with the other control algorithms. [ABSTRACT FROM AUTHOR]

This article validates the operational effectiveness of a fuzzy-based multistage cascaded proportional integral derivative fractional filter (PIDFN) controller which enhances the frequency regulation of an interconnected islanded microgrid system. The effect of the ambiguous nature of renewable energy resources and test cases concerning different load variations are applied to verify the robustness of the proposed controller. The superiority of the proposed controller upon proportional-integral-derivative (PID), fractional-order PID (FOPID), and Fuzzy FOPID controller in minimizing frequency alteration has been verified through MATLAB/SIMULINK environment.

The steady-state operation with low error and the fast dynamic response in transient of the DC-DC converter circuits depend on the controller design. The performance of the controller used in DC-DC converters, which vary the level of DC voltage depends on the controller coefficients. Although classical methods are often used to determine these coefficients in controller design, various modern optimization methods have been recently used. In this study, the DC-DC buck converter control simulation is performed with FOPID, PID and TID controllers. Aquila Optimizer, African Vultures Optimization Algorithm and Hunger Games Search optimization algorithms are used to determine the coefficients of these controllers in the literature. However, Fitness-Distance Balance Based Runge Kutta is employed first time for PID controller in buck converter in this study. The performance indices integral absolute error, integral square error, integral time absolute error, and integral time squared error are employed to assess the outcomes. When the results obtained are examined, the FOPID controller gives the best results in the control of the buck converter. These results are obtained by using the coefficients determined by the Fitness-Distance Balance Based Runge Kutta (FDBRUN) optimization algorithm. It has better performance than the other algorithms.

One of the main challenges in power converters is to adopt a convenient controller that is designed with an appropriate approach. In terms of controllers, linear and nonlinear types are available. Nonlinear controllers may be good for achieving dynamic capabilities; however, designing them involves undesirable complexity. Thus, alternative linear counterparts are desirable to achieve optimum performance. Fractional-order proportional-integral derivative (FOPID) controller stands as a good choice for this purpose since it is a more capable version of one of widely adopted linear controller known as PID. Therefore, in this study, a FOPID controller was used to achieve optimum performance for a buck converter. To obtain the best performance, a novel hybridized metaheuristic algorithm, which combines both Lévy flight distribution and simulated annealing algorithms (LFDSA), was utilized. The developed algorithm involves a balanced structure in terms of explorative and exploitative phases, which was confirmed via performing related analysis on unimodal and multimodal benchmark functions. Non-parametric statistical test has also showed the better capability of the proposed algorithm. Due to its enhanced capability, the proposed algorithm helped achieving optimum values of FOPID parameters such that a better closed-loop output voltage control performance of the buck converter in terms of time and frequency domain responses as well as disturbance rejection have been achieved. The proposed LFDSA-based FOPID controller also tested against other capable and reported state-of-the-art algorithm and the results have also verified the superior capability of the LFDSA over other approaches. [ABSTRACT FROM AUTHOR]

Aiming at the problems of nonlinearity and inaccuracy in the model of the pneumatic control valve position in the industrial control process, a valve position control method based on a fractional-order PID controller is proposed. The working principle of the pneumatic control valve is analyzed, and its mathematical model is established. In order to improve the accuracy of the model, an improved biogeography-based optimization algorithm is proposed to tune the parameters of the fractional-order PID controller in view of the wide range and high complexity of the fractional-order PID controller. The initialization of the chaotic graph, the adjustment of the migration model, and the improvement of the migration operator and the mutation operator are introduced to improve the algorithm optimization ability, which is used for the model identification of the control valve control system. The simulation and experimental results clearly show that, compared with the integer-order PID controller, the designed fractional-order PID controller has faster response speed and control accuracy, which can better meet the requirements of pneumatic control valve position control. [ABSTRACT FROM AUTHOR]

This research presents a fractional order (FO) controller for frequency control in microgrid. Four intelligent methodologies, namely, Grasshopper optimization algorithm (GOA), Gravitational search algorithm (GSA), Genetic algorithm (GA), and Particle swarm optimization (PSO), are used for optimization-based tuning of FO controller. The proposed microgrid consists of wind turbine, solar photo voltaic system, aqua electrolyser, flywheel, ultra-capacitor, battery storage system, diesel engine, and fuel cell. GOA is employed to tune the parameters of the controllers. Application of GOA-based two-/multi-stage fractional order PID controller i.e., FOPID-(1 + PI) controller in frequency control for microgrid is a novel work. GOA-optimized FOPID-(1 + PI) controller unveils best results over the conventional PID/FOPID controller in terms of settling time, peak undershoot/overshoot, and performance index. Examination of dynamic responses for abrupt changes in load request divulges the pre-eminence of the proposed controller strategy with others. The robustness study implies that GOA-optimized fractional controller operates superbly and robustly under nonlinearities and perturbation in system parameters. In order to demonstrate the ascendancy of GOA, its results in terms of statistical parameters and performance index are compared with the results of GA, PSO, and GSA. [ABSTRACT FROM AUTHOR]

Due to factors such as uneven guide rails and airflow disturbance in the hoistway, high-speed elevators may experience significant vibrations during operation. This paper proposes an optimized fractional-order PID (FOPID) method to suppress vibrations of high-speed elevators. First, an accurate horizontal vibration model is established for the elevator car, in which the car frame and body are separate. Then, taking the control cost and the system performance as objective functions, we obtained an optimized FOPID controller based on multi-objective genetic algorithm optimization. Finally, the effectiveness of the controller in reducing elevator vibration was verified through numerical simulation. The results indicate that the horizontal acceleration controlled by the FOPID controller is reduced by about 68% compared to the case without a controller and about 25% compared to the conventional PID controller.

Fractional-order proportional integral derivative (FOPID) controllers are becoming increasingly popular for various industrial applications due to the advantages they can offer. Among these applications, heating and temperature control systems are receiving significant attention, applying FOPID controllers to achieve better performance and robustness, more stability and flexibility, and faster response. Moreover, with several advantages of using FOPID controllers, the improvement in heating systems and temperature control systems is exceptional. Heating systems are characterized by external disturbance, model uncertainty, non-linearity, and control inaccuracy, which directly affect performance. Temperature control systems are used in industry, households, and many types of equipment. In this paper, fractional-order proportional integral derivative controllers are discussed in the context of controlling the temperature in ambulances, induction heating systems, control of bioreactors, and the improvement achieved by temperature control systems. Moreover, a comparison of conventional and FOPID controllers is also highlighted to show the improvement in production, quality, and accuracy that can be achieved by using such controllers. A composite analysis of the use of such controllers, especially for temperature control systems, is presented. In addition, some hidden and unhighlighted points concerning FOPID controllers are investigated thoroughly, including the most relevant publications. [ABSTRACT FROM AUTHOR]

There is a continuous effort to develop efficient control mechanisms for power converters as it is a challenging task due to nonlinear nature of such systems. As part of the ongoing effort in the related field, a novel control method is presented in this paper. The proposed method with this study involves a fractional order proportional-integral-derivative (FOPID) controller and the development of a novel metaheuristic algorithm for tuning in order to achieve optimum performance of a buck converter system. In terms of the metaheuristic algorithm, an improved version of the hunger games search (IHGS) algorithm is developed by enhancing the intensification and the diversification abilities of the hunger games search (HGS) algorithm with the aid of Nelder-Mead simplex method and the random learning mechanism, respectively. Several classical unimodal, multimodal, and fixed dimensional benchmark functions along with CEC2019 test suite are used to confirm the improved structure of the developed IHGS algorithm. A novel objective function is also constructed in this study by modifying the structure of the performance index known as integral of squared error. The novel IHGS algorithm together with the novel objective function are proposed as an efficient tool to design a FOPID controller employed in a buck converter system. The proposed method's superiority for the operation of a buck converter system is confirmed comparatively with transient and frequency responses along with robustness analysis in terms of parametric uncertainties and measurement noise along with input and load voltage fluctuations using the best performing methods of artificial ecosystem optimization algorithm based PID, Lévy flight distribution algorithm based PIDA and Harris hawks optimization algorithm based FOPID controllers. The other capable approaches reported in the literature are also used to further confirm the excellent ability of the proposed method for controlling a buck converter system.

This paper presents an adaptive Fractional Order PID (FOPID) controller for improving the performance of a Brushless DC (BLDC) motor using Artificial Bee Colony (ABC) algorithm. BLDC motor is desired to operate at various speed and load conditions with enhanced performance and robust speed control. In practice, the effect of longer settling time, fluctuation of steady-state error, power fluctuation and nonlinearity characteristics of the BLDC motor drive result in poor controllability. To overcome the problems, an optimized FOPID controller using the ABC algorithm in a self-tuned regulator structure is proposed to minimize the given objective function to satisfy the inequality constraints. It is also interesting to note that the usage of Hall Effect sensors has many limitations due to the failure of its components, poor reliability, need special mechanical arrangements for mounting and electrical noise aspects. In order to avoid such issues, a Kalman Filter is designed for estimating the speed of the motor. The simulation is carried out for the proposed ABC tuned FOPID controller and the results are compared with conventional genetic algorithm and modified genetic algorithm tuned FOPID controllers. The results indicate that the proposed ABC tuned controller is superior in terms of time-domain characteristics, control effort, and specified performance indices. Further to show the usefulness of the proposed method, an experimental model is developed and validated for the selected operating conditions with the required comparison.

A novel procedure for the realization of a fractional-order PID loop-shaping controller, suitable for precision control of mechatronic systems, is introduced in this work. Exploiting appropriate tools, the controller function is approximated as a whole, leading to a simple form of integer-order approximation, when compared to the case where each intermediate part of the PID transfer function is approximated. This leads to a direct implementation, composed of conventional active and passive elements. Simulation and experimental results, derived from the OrCAD PSpice simulator and a Field-Programmable Analog Array respectively, verify the efficient functionality of the proposed implementation procedure. • A curve-fitting based procedure is used for the realization of a fractional-order PID loop-shaping controller • The complete controller transfer function is approximated in one step. • The order of the approximation function is independent of the number of product terms in the fractional-order transfer function. • The complexity of the realization topology is significantly reduced compared to term-by-term implementations. • Experimental results using a Field-Programmable Analog Array (FPAA) show a very efficient design. [ABSTRACT FROM AUTHOR]

Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results.

Aiming at the problems of nonlinearity and inaccuracy in the model of the pneumatic control valve position in the industrial control process, a valve position control method based on a fractional-order PID controller is proposed. The working principle of the pneumatic control valve is analyzed, and its mathematical model is established. In order to improve the accuracy of the model, an improved biogeography-based optimization algorithm is proposed to tune the parameters of the fractional-order PID controller in view of the wide range and high complexity of the fractional-order PID controller. The initialization of the chaotic graph, the adjustment of the migration model, and the improvement of the migration operator and the mutation operator are introduced to improve the algorithm optimization ability, which is used for the model identification of the control valve control system. The simulation and experimental results clearly show that, compared with the integer-order PID controller, the designed fractional-order PID controller has faster response speed and control accuracy, which can better meet the requirements of pneumatic control valve position control.

In paper industries, Multiple Stage Evaporator (MSE) is used to concentrate black liquor. Due to the energy intensive nature of MSE, the global energy scenario stresses on optimizing its energy efficiency. Moreover, the necessity of a tight control of product quality demands superior understanding of system dynamics for controller design. This paper presents a robust fractional‐order Proportional–Integral–Derivative (FOPID) controller for concentration control of black liquor in Heptad's effect MSE. First, the steady‐state unknown process parameters are estimated by solving the nonlinear steady‐state model. Thereafter, these optimal process parameters are utilized to simulate the nonlinear dynamic model to obtain the transfer functions. By using these transfer functions, the FOPID controller is designed whose parameters are tuned via Water Cycle Algorithm (WCA). The competence of WCA toward controller tuning is validated by comparing with other optimization techniques (Genetic Algorithm [GA], Simulated Annealing [SA], Particle Swarm Optimization [PSO], and Krill Herd [KH]). Moreover, the performance of the proposed FOPID controller in concentration control, set‐point tracking, and noise suppression is validated by comparing with conventional PID, two‐degree of freedom‐PID (2‐DOF‐PID), and Internal Model Control (IMC) controllers. The results demonstrate that FOPID controller reduces the Integral Square Error (ISE) by 91.05%, 89.81%, and 78.84%, respectively, with respect to PID, 2‐DOF‐PID, and IMC. Also, the proposed FOPID controller improves the system transience with high robustness. [ABSTRACT FROM AUTHOR]

Fractional-order proportional integral derivative (FOPID) controllers are becoming increasingly popular for various industrial applications due to the advantages they can offer. Among these applications, heating and temperature control systems are receiving significant attention, applying FOPID controllers to achieve better performance and robustness, more stability and flexibility, and faster response. Moreover, with several advantages of using FOPID controllers, the improvement in heating systems and temperature control systems is exceptional. Heating systems are characterized by external disturbance, model uncertainty, non-linearity, and control inaccuracy, which directly affect performance. Temperature control systems are used in industry, households, and many types of equipment. In this paper, fractional-order proportional integral derivative controllers are discussed in the context of controlling the temperature in ambulances, induction heating systems, control of bioreactors, and the improvement achieved by temperature control systems. Moreover, a comparison of conventional and FOPID controllers is also highlighted to show the improvement in production, quality, and accuracy that can be achieved by using such controllers. A composite analysis of the use of such controllers, especially for temperature control systems, is presented. In addition, some hidden and unhighlighted points concerning FOPID controllers are investigated thoroughly, including the most relevant publications.

In this study, a fractional-order proportional–integral–derivative (FOPID) controller was used for controlling the speed of direct current (DC) motor. The parameters of the controller have optimally been adjusted using a new meta-heuristic algorithm, namely the opposition-based (OBL) hybrid manta ray foraging optimization (MRFO) with simulated annealing (SA) algorithm (OBL-MRFO-SA). The proposed novel OBL-MRFO-SA algorithm aims to improve the original MRFO algorithm in two ways. Firstly, it provides MRFO a better exploration capability with the aid of opposition-based learning. In this way, it can avoid local minimum stagnation. Secondly, it enables MRFO to have a better exploitation capability with the aid of hybridization using simulated annealing algorithm. The hybridization helps accelerating the convergence rate of MRFO. A time domain objective function which takes the performance criteria (maximum overshoot, steady-state error, rise time and settling time) into account has been used to design the FOPID based speed control system for DC motor with OBL-MRFO-SA algorithm. The performance of the proposed novel algorithm has been assessed through various analyses such as time and frequency domain simulations, robustness and load disturbance rejection. Compared to other state-of-the-art optimization algorithms, OBL-MRFO-SA has shown superior exploration and exploitation capabilities. The performance of the developed algorithm has also been demonstrated to be better by using a physical setup. [ABSTRACT FROM AUTHOR]

The performance of the robotic manipulator is negatively impacted by outside disturbances and uncertain parameters. The system's variables are also highly coupled, complex, and nonlinear, indicating that it is a multi-input, multi-output system. Therefore, it is necessary to develop a controller that can control the variables in the system in order to handle these complications. This work proposes six control structures based on neural networks (NNs) with proportional integral derivative (PID) and fractional-order PID (FOPID) controllers to operate a 2-link rigid robot manipulator (2-LRRM) for trajectory tracking. These are named as set-point-weighted PID (W-PID), set-point weighted FOPID (W-FOPID), recurrent neural network (RNN)-like PID (RNNPID), RNN-like FOPID (RNN-FOPID), NN+PID, and NN+FOPID controllers. The zebra optimization algorithm (ZOA) was used to adjust the parameters of the proposed controllers while reducing the integral-time-square error (ITSE). A new objective function was proposed for tuning to generate controllers with minimal chattering in the control signal. After implementing the proposed controller designs, a comparative robustness study was conducted among these controllers by altering the initial conditions, disturbances, and model uncertainties. The simulation results demonstrate that the NN+FOPID controller has the best trajectory tracking performance with the minimum ITSE and best robustness against changes in the initial states, external disturbances, and parameter uncertainties compared to the other controllers., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Jasim Mohamed, Oleiwi, Azar and Mahlous.)

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This paper presents a state‐dependent self‐tuning fractional control strategy for a DC‐DC buck converter in order to enhance its output voltage regulation and disturbance attenuation capability. The proposed control scheme primarily employs a ubiquitous proportional‐integral‐derivative (PID) controller, where gains are optimally selected using a linear‐quadratic state‐space tuning approach. The optimal PID controller is then augmented with fractional‐order integral and derivative operators in order to improve the controller's degrees‐of‐freedom as well as the system's overall time‐domain performance. The fractional controller's robustness against bounded exogenous disturbances, contributed by the input fluctuations and load‐step transients, is further enhanced by adaptively modulating the fractional‐orders of the integro‐differential operators as a smooth nonlinear function of controlled‐variable's error‐dynamics. An online dynamic adjustment law, comprising of a zero‐mean Gaussian function of error and its derivative, is used to individually update the two fractional orders after every sampling interval. The error derivative is evaluated by measuring the output capacitor's current in order to compensate the noise injected by parasitic impedance. The other controller parameters are tuned via particle‐swarm‐optimization algorithm. The proposed self‐adaptive control strategy renders rapid transits, minimum transient recovery time, and minimal fluctuations around steady state in the response. Its efficacy is validated through hardware in‐the‐loop experiments conducted on a buck converter prototype. [ABSTRACT FROM AUTHOR]

Switch reluctance motor is suitable for an electric vehicle driving system, which has the advantages of simple structure, high reliability of system and wide range of speed adjustment. In order to reduce the torque ripple of the system and improve the dynamic performance, a strategy of direct instantaneous torque control (DITC) based on a fractional-order proportion integration differentiation (PID) controller is proposed. According to the mathematical characteristics of the fractional-order controller, the form of the fractional-order speed loop controller is determined. Also, the parameters of the speed regulator are designed using the frequency-domain design theory of the control system. Then, the fractional-order controller is discretised. Compared with the traditional proportion integration (PI) controller, the fractional-order controller can have a better control effect. Simulation experimental results of the system show that the DITC control method has effectively reduced the torque ripple and the fractional-integral controller has reduced the overshoot and adjustment time and improved the robustness and disturbance resistance of the system.