Optimal Fractional Order Research Articles

Optimal Fuzzy-FOPID, Fuzzy-PID Control Schemes for Trajectory Tracking of 3DOF Robot Manipulator

The present study explores the guidance of a robotic arm along a predefined path by implementing an optimal fuzzy fractional order PID controller-based control strategy. This method serves as a means to address the nonlinearity and unpredictability of the robotic manipulator, contingent upon the fuzzy logic controller's specifications and the employment of a clonal selection algorithm. The dynamic equation of the manipulator was considered as an initial point, followed by designing a fuzzy controller for this purpose. To validate the effectiveness of this approach, it was compared to other techniques, such as Fuzzy, Fuzzy-PID, and fuzzy-FOPID controllers, with PID and FOPID controller parameters optimized using clonal selection algorithms. Simulation results reveal that the fuzzy-FOPID variant outperformed other methods under varying load conditions and model uncertainties, using SIMULINK/MATLAB 2014a.

Design an Optimal Fractional Order PID Controller for Speed Control of Electric Vehicle

Design an Optimal Fractional Order PID Controller for Speed Control of Electric Vehicle

Optimal Fractional-Order Controller for the Voltage Stability of a DC Microgrid Feeding an Electric Vehicle Charging Station

Charging stations are regarded as the cornerstone of electric vehicle (EV) development and utilization. Electric vehicle charging stations (EVCSs) are now energized via standalone microgrids that utilize renewable energy sources and reduce the stress on the utility grid. However, the control and energy management of EVCSs are challenging tasks because they are nonlinear and time-varying. This study suggests a fractional-order proportional integral (FOPI) controller to improve the performance and energy management of a standalone EVCS microgrid. The microgrid is supplied mainly by photovoltaic (PV) energy and utilizes a battery as an energy storage system (ESS). The FOPI’s settings are best created utilizing the grey wolf optimization (GWO) method to attain the highest performance possible. The grey wolf is run for 100 iterations using 20 wolves. In addition, after 80 iterations for the specified goal function, the GWO algorithm almost discovers the ideal values. For changes in solar insolation, the performance of the proposed FOPI controller is compared with that of a traditional PI controller. The Matlab/Simulink platform models and simulates the EVCS’s microgrid. The results demonstrate that the suggested FOPI controller significantly improves the transient responsiveness of the EVCS performance compared to the standard PI controller. Despite all PV insolation disruptions, the EV battery continues to charge while the ESS battery precisely stores and balances PV energy changes. The results support the suggested FOPI control’s robustness to parameter mismatches. The microgrid’s efficiency fluctuations with the insolation level and state of charge of the EV battery are discussed.

Optimal intelligent fuzzy TID controller for an uncertain level process with actuator and system faults: Population-based metaheuristic approach

For the Conical Tow-Tank Non-Interacting Level (CTTNL) prototype system, this article discusses the design of an unique optimal fractional order TID controller employing a type-1 fuzzy set. To generate a linearized model transfer function for the nonlinear CTTNL process, local linearization around the equilibrium state was performed. This work compares the performance of a fuzzy tilted-integral-derivative (FTID) controller for the CTTNL system to a traditional proportional–integral–derivative (PID) controller. The parameters of the FTID controller were optimized using the Chicken Search Optimization (CSO) algorithm in this study, and those values were used to create a PID controller. Thereafter, the FTID and PID controllers’ performance is compared. The investigation shows that the FTID controller beats the PID controller in terms of IAE, ISE, ITAE, and ITSE integral errors. The suggested controller’s fault-tolerant performance was also assessed using the fault recovery time (Frt) parameter. The FTID controller outperforms traditional PID controllers in terms of transient and steady-state performance. The fault tolerance capabilities of the FTID controller will be tested on the CTTNL system in the future, using additive and multiplicative failures. Further research will include a comprehensive examination of robustness in the context of model parameter uncertainties.

Optimal fractional order interval type-2 fuzzy controller for upside-down asymmetric multilevel inverter based dynamic voltage restorer to accurately compensate faulty network voltage

Optimal fractional order interval type-2 fuzzy controller for upside-down asymmetric multilevel inverter based dynamic voltage restorer to accurately compensate faulty network voltage

A new seismic control framework of optimal PIλDµ controller series with fuzzy PD controller including soil-structure interaction

A new framework of optimal fractional order proportional-derivative-integral (FOPID) controller series with fuzzy proportional-derivative (PD) controller, namely OFPD-FOPID controller, is proposed in this study for seismic control of structures equipped with active tuned mass damper (ATMD). Three controllers including optimal PID, optimal FOPID, and fuzzy PID (FPID) controllers are also implemented for comparison purposes. Simulation results carried out on a 15-story building show the FOPID controller than the PID and FPID controllers can remarkably reduce the maximum floor displacement, but they represent a poor performance in mitigation of the maximum floor acceleration in different soil conditions, while the proposed OFPD-FOPID controller tracking the amount of the maximum floor acceleration to estimate the optimal control force of the actuator can provide superior performance. An average reduction of 41%, 45%, and 33% in the maximum floor displacement; 36%, 33%, and 20% in the maximum inter-story drift are given by FOPID in the dense, medium, and soft soils, while it results in an increase of 45%, 52% and 24% in the maximum floor acceleration. Similarly, the proposed OFPD-FOPID controller represents an average reduction of 52%, 55%, and 45% in the maximum floor displacement; 42%, 44%, and 28% in the maximum inter-story drift in the dense, medium, and soft soils, while it also slightly reduces the maximum floor acceleration of the studied structure located on different soil conditions.

Hybrid Particle Swarm and Gravitational Search Algorithm-Based Optimal Fractional Order PID Control Scheme for Performance Enhancement of Offshore Wind Farms

This article aimed to introduce a novel application of a hybrid particle swarm optimizer and gravitational search algorithm (HPSOGSA) that can be used for optimal control of offshore wind farms’ voltage source converter connected to HVDC transmission lines. Specifically, the algorithm was used to design fractional-order proportional-integral-derivative (FOPID) controller parameters designed to minimize the system’s objective function based on an integral squared error. The proposed FOPID controller was applied to improve offshore wind farm performance under different transient conditions, and its results were compared with a PI controller that was designed using a genetic algorithm and grey wolf optimization algorithm. The fault ride-through capabilities of the proposed control strategy were also evaluated. The findings suggest that the HPSOGSA-based FOPID controller outperformed the other two methods, significantly enhancing offshore wind farm operations. The control strategy was thoroughly tested using MATLAB/Simulink under various operating scenarios.

A new algorithm for fetal heart rate detection: Fractional order calculus approach.

A new modified Pan-Tompkins' (mPT) method for fetal heart rate detection is presented. The mPT method is based on the hypothesis that optimal fractional order derivative and optimal window width of the moving average filter would enable efficient estimation of fetal heart rate from surface abdominal electrophysiological recordings with relatively low signal-to-noise ratios. The algorithm is tested on signals recorded from the abdomen of pregnant women available from the PhysioNet Computing in Cardiology Challenge database. Fetal heart rate detection is performed on 10-s long segments selected by the estimation of signal-to-noise ratios (the extravagance of the fetal QRS peak to its surroundings and to the whole signal; and the mean ratio of fetal and maternal QRS peaks) and on the manually selected segments. The best results are obtained via criteria based on the extravagance of the fetal QRS peak to its surroundings that reached average sensitivity of 97%, positive predictive value of 97%, error rate of ∼3.5%, and F1 score of 97%. The obtained averaged optimal parameters for mPT are 0.51 for fractional order and 24.5ms for the window width of the moving average filter. Proposed mPT algorithm showed satisfactory performance for fetal heart rate detection. Further adaptations of the presented mPT method could be used for peak detection in noisy environments in biomedical signal analysis in general.

Optimal self-tuning fractional order fuzzy load frequency control considering sustainable energy sources and electric vehicle

Considering uncertainties associated with sustainable energy sources in modern power systems, one of the main obstacles for load frequency control (LFC) is that various publications regard the parameters of FOPID controllers as fixed after optimisation. To tackle this challenge, an adaptive control structure may be a viable option for LFC. In this paper, in a two-zone hybrid power system that includes a thermal power plant, green energy sources, fuel cells, and plug-in electric vehicles, an optimal self-tuning fractional order fuzzy (OSTFOF) controller for LFC is proposed. Pathfinder algorithm (PFA) has been utilised for optimal tuning of parameters of the OSTFOF controller, including the upper bands of output membership functions, the input scaling factors, and the order of integral and derivative operators. In the proposed controller, the values of proportional, integral, and derivative gains are adaptively obtained. In the thermal power plant, non-linear factors, such as governor dead band (GDB) and generation rate constraint (GRC), are considered. Four different scenarios have been considered to evaluate the performance of the proposed OSTFOF controller, and results have been compared with PI, PID, and FOPID controllers. The simulations’ results indicate the excellent performance indices of the suggested OSTFOF controller compared to other controllers.

Optimal tuning fractional order PID based on marine predator algorithm for DC motor

DC motors are a popular topic because they are widely applied in various electronic equipment. So, this requires a control that is fast and reliable. The development of optimized control methods is growing rapidly with the discovery of several new methods. Marine predator algorithm (MPA) is an optimization method based on marine life between living things. This article discusses the application of the MPA method for optimizing fractional order PID (FOPID) control on DC motors. The implementation of the FOPID controller is also difficult because the fractional calculus operators of the FOPID controller cannot be directly implemented in numerical calculations. The method proposed in this article is the FOPID-MPA method. To get a performance test of the proposed method, this study uses several comparison methods, namely the seagull optimization algorithm (ASO), chimp optimization algorithm (ChOA), and sine tree seed algorithm (STSA). This study also uses a variation of the reference speed to get the performance of the proposed method. From the experiment it is known that the FOPID-MPA method gives the best performance. The FOPID-MPA method has an overshoot value of 4.34% compared to the PID-MPA method in case study 1 and has an integrated of time-weighted-squared-error (ITSE) value of 7.44% better than the PID-MPA method in case study 2.

Bearing failure diagnosis at time-varying speed based on adaptive clustered fractional Gabor transform

For bearing fault diagnosis at time-varying speed with tachometer-free and non-resampling, the crucial process is to obtain a high-resolution time-frequency representation and extract fault features. However, current multi-component non-stationary signal feature extraction methods based on time-frequency transform suffer from fixed parameter settings and insufficient resolution for low signal-to-noise ratio signals. To address these issues, a novel adaptive clustered fractional Gabor transform is proposed and applied to extract bearing fault features at time-varying speed. Firstly, the grey wolf optimization is utilized to adaptively search for the optimal fractional order and Gauss window length based on the maximum spectral kurtosis and the generalized time-bandwidth product to achieve the most adequate fractional Gabor spectrum (FrGS). Then, the Clustering by Fast Search and Find of Density Peaks algorithm reconstructs the sparse representation of the FrGS, remapping multi-component signals into single-component clusters. Bearing fault diagnosis is achieved by matching the relative order of each cluster with the bearing fault characteristic coefficients. Simulation signals validate the superiority of the feature extraction method, and experimental signals validate the feasibility of the bearing fault diagnosis method.

Optimal Fractional Order Proportional Integral Controller for Dual Star Induction Motor Based on Particle Swarm Optimization Algorithm

Optimal Fractional Order Proportional Integral Controller for Dual Star Induction Motor Based on Particle Swarm Optimization Algorithm

Design of an Optimal Fractional Complex Order PID Controller for Buck Converter

Dynamic and robust controllers are the inherent requirement of power electronic converters, which are subjected to dynamic variations and nonlinearities. The effectiveness of fractional order controllers in non-linear system control has been well-established by studies in the past few decades. Various forms of fractional order controllers have been used in power-electronic control. Recent research indicates that complex order controllers, extensions of fractional controllers, are more robust against uncertainties and non-linearities than their integer and fractional order counterparts. Though complex order controllers have been employed in various nonlinear plants, they have not been extensively tested on power electronic applications. Also, the design and tuning of the controller is difficult. This paper investigates the effectiveness of a complex order PID controller on a typical power electronic DC-DC buck converter for the first time. Two types of complex order controllers of the form PI^{a+ib}D^c and PI^{a+ib}D^{c+id} were designed for a power electronic buck converter. The complex order controllers were implemented in Simulink and the optimal tuning of the complex order controller parameters for various performance indices was performed using different optimization algorithms. The Cohort Intelligence algorithm was found to give the most optimal results. Both the complex controllers showed more robustness towards uncertainties than the linear and fractional PID controllers. The PI^{a+ib}D^c controller gave the smoothest and fastest response under non-linearities. The dynamic performance of the complex order controller is the best and can be expected to be useful for more power electronic applications.

Fractional-order modeling and optimal control of a new online game addiction model based on real data

The spread of online games has become more and more serious in recent years, which not only endangers the healthy growth of young people, but also has a certain potential harm to society. Therefore, how to effectively control the spread of games has become an urgent problem to be solved. To solve this problem, a new fractional model of online game addiction is developed in this paper. In the aspect of qualitative analysis, the non-negativity and boundedness of the model solutions are demonstrated. All equilibria and basic reproduction number are solved. The global asymptotic stability of all equilibria are proved by constructing ingenious Lyapunov functions. In terms of quantitative analysis, different from previous fractional order literature, we use a new method to fit the real data of game users in China from 2010 to 2021, and obtain the optimal fractional order α=0.98942 and model parameters. The estimated results show that the value of the basic reproduction number during this period is R0=7.1045. By setting different values of the parameters, the effects of all parameters on the model are shown. With the Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) techniques, the influence of all parameters in the basic reproduction number R0 are quantified and the means to control the spread of the game were generalized: isolation and treatment. Finally, the Fractional Euler Method (FEM) and the fractional Forward Backward Sweep Method (FBSM) are used together to solve the fractional optimal control problem and the optimal control strategy is determined. The results of this paper provide a new research idea for parameter estimation of fractional equation, and a more reliable result for controlling the spread of online games.

Transport of coupled particles in fractional feedback ratchet driven by Bounded noise

In this paper, the transport of coupled particles in fractional feedback potential driven by two bounded noises is investigated. The mean velocity of coupled particles is calculated versus the fractional order, barrier height, noise intensity, coupling intensity and static length. The results suggest that compared with the integer order feedback potential, the fractional order situation can affect the switching frequency of the feedback potential, and thereby regulate the transport speed of coupled particles. Therefore, a new quantity Cf is specially introduced to quantify the feedback switch frequency. In addition, the superposition of bounded noises on the coupled particles will lead to the increase of mean velocity. It is worth noting that for a definite noise intensity, an optimal fractional order can be found to bring the particles reach the maximum velocity. Once the fractional order is greater than the optimal value, the mean velocity will drop sharply to near zero. Furthermore, our results also show that the optimal static length can increase the transport velocity when the coupling coefficient is properly selected. This can provide theoretical basis for the treatment of diseases caused by neurotransmitter transport disorder.

Optimal fractional-order proportional–integral–derivative control enabling full actuation of decomposed rotary inverted pendulum system

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.

Synchrosqueezing-Based Short-Time Fractional Fourier Transform

A novel synchrosqueezing transform to the time-frequency representation based on short-time fractional Fourier transform for strong time-varying signals is proposed in this paper. To finely describe the local characteristics of nonstationary signal in the short-time fractional Fourier transform domain, a new instantaneous frequency estimator, a new instantaneous fractional frequency estimator and the corresponding energy reassignment operators are given by time-fractional frequency basis. The discrete implementation and signal reconstruction of the proposed method are investigated. Furthermore, the calculation of the optimal fractional order, computational complexity and limitation of the proposed method are discussed. Various strong time-varying signal experiments and time-frequency spectrum energy attenuation gradient extraction experiments of real synthetic aperture radar (SAR) images are conducted to verify the effectiveness and superiority of the proposed method over some advanced time-frequency analysis methods in energy concentration, time-frequency localization, signal reconstruction and clutter suppression.

An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption

<abstract> <p>In this paper, we propose an optimal fractional-order accumulative Grey Markov model with variable parameters (FOGMKM (1, 1)) to predict the annual total energy consumption in China and improve the accuracy of energy consumption forecasting. The new model is built upon the traditional Grey model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The particle swarm optimization algorithm (PSO) is used to determine the number of optimal fractional order and nonlinear parameters. An experiment is conducted to validate the high prediction accuracy of the FOGMKM (1, 1) model, with mean absolute percentage error (MAPE) and root mean square error (RMSE) values of 0.51% and 1886.6, respectively, and corresponding fitting values of 0.92% and 6108.8. These results demonstrate the superior fitting performance of the FOGMKM (1, 1) model when compared to other six competitive models, including GM (1, 1), ARIMA, Linear, FAONGBM (1, 1), FGM (1, 1) and FOGM (1, 1). Our study provides a scientific basis and technical references for further research in the finance as well as energy fields and can serve well for energy market benchmark research.</p> </abstract>

An Optimal Fractional Order PIλDµ For Robotic Manipulators Control Under Constrained Torque

An Optimal Fractional Order PIλDµ For Robotic Manipulators Control Under Constrained Torque

Huizhou GDP forecast based on fractional opposite-direction accumulating nonlinear grey bernoulli markov model

<abstract><p>In this paper, a fractional opposite-direction accumulating nonlinear grey Bernoulli Markov model (FOANGBMKM) is established to forecast the annual GDP of Huizhou city from 2017 to 2021. The optimal fractional order number and nonlinear parameters of the model are determined by particle swarm optimization (PSO) algorithm. An experiment is provided to validate the high fitting accuracy of this model, and the effect of prediction is better than that of the other four competitive models such as autoregressive integrated moving average model (ARIMA), grey model (GM (1, 1)), fractional accumulating nonlinear grey Bernoulli model (FANGBM (1, 1)) and fractional opposite-direction accumulating nonlinear grey Bernoulli model (FOANGBM (1, 1)), which proves the robustness of the opposite-direction accumulating nonlinear Bernoulli Markov model. This research will provide a scientific basis and technical references for the economic planning industries.</p></abstract>