Fractional-order Control Research Articles

A robust super twisting fractional-order sliding mode-based control of vehicle longitudinal dynamic subjected to a constant actuator fault

This paper deals with the design and analysis of a super twisting fractional-order sliding mode controller (ST-FOSMC) to adjust the vehicle longitudinal dynamic when braking. While vehicle loading, road types, and modeling uncertainties are time-varying parameters, the control law must be robust against these disturbances. Also, the aging of the brake plate may introduce a difference between the control output and the actuator response that should be considered. The proposed control strategy has been used to enable the anti-lock braking system (ABS) to track the desired wheel slip value despite the presence of disturbances and constant actuator fault. The design of this controller is presented and the system stability is guaranteed by applying the Lyapunov theory. We carried out a simulation example that makes a comparison between our controller and the one based on the fractional-order sliding mode control to investigate which one of them outperforms the other. The results exhibit the superiority of the super twisting fractional order controller over the traditional fractional-order sliding mode controller during the braking phase.

A New Fractional-Order Virtual Inertia Support Based on Battery Energy Storage for Enhancing Microgrid Frequency Stability

Microgrids have a low inertia constant due to the high penetration of renewable energy sources and the limited penetration of conventional generation with rotating mass. This makes microgrids more susceptible to frequency stability challenges. Virtual inertia control (VIC) is one of the most effective approaches to improving microgrid frequency stability. Therefore, this study proposes a new model to precisely mimic inertia power based on an energy storage system (ESS) that supports low-inertia power systems. The developed VIC model considers the effect of both the DC-DC converter and the DC-AC inverter on the power of the ESS used. This allows for more precise and accurate modeling of the VIC compared to conventional models. Moreover, this study proposes a fractional-order derivative control for the proposed VIC model to provide greater flexibility in dealing with different perturbations that occur in the system. Furthermore, the effectiveness of the proposed fractional-order VIC (FOVIC) is verified through an islanded microgrid that includes heterogeneous sources: a small thermal power plant, wind and solar power plants, and ESSs. The simulation results performed using MATLAB software indicate that the proposed VIC scheme provides fast stabilization times and slight deviations in system frequency compared to the conventional VIC schemes. The proposed VIC outperforms the conventional load frequency control by about 80% and the conventional VIC model by about 45% in tackling load/RESs fluctuations and system uncertainty. Additionally, the studied microgrid with the proposed FOVIC scheme is noticeably more stable and responds faster than that designed with integer-order derivative control. Thus, the proposed FOVIC scheme gives better performance for frequency stability of low-inertia power systems compared to conventional VIC schemes used in the literature.

Fractional-Order Extremum Seeking Method for Maximum Torque per Ampere Control of Permanent Magnet Synchronous Motor

Maximum torque per ampere (MTPA) control of internal permanent magnet synchronous motors (IPMSM) has become integral to high-efficiency motor drives. To minimize the influence of the traditional model-based analytical solution method on the MTPA control strategy due to the parameter variations during the motor operation, an online search MTPA method without model-based fractional-order extremum seeking control (FO-ESC) is proposed. Compared with the traditional integer-order ESC method, the Oustaloup approximation-based fractional-order calculus provides additional factors and possibilities for optimizing controller parameters to improve control performance. At the same time, the proposed approach does not require machine parameters and is thus not influenced by machine and drive nonlinearities. Simulation results show that the proposed method can ensure robust MTPA control under different loading conditions in real-time and improve the system’s dynamic response speed and steady-state accuracy.

Distributed event-triggered fractional-order fault-tolerant control of multi-UAVs with full-state constraints

Distributed event-triggered fractional-order fault-tolerant control of multi-UAVs with full-state constraints

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Analysis of different control schemes of PMSM motor and also a comparison of FOPI and PI controller for sensorless MSVPWMM scheme

This paper investigated different control Techniques of Permanent magnet synchronous motor (PMSM) drive with open loop, voltage/frequency (V/F) control, closed-loop Space Vector Pulse Width Modulation (SVPWM) control, and sensor-less Modified Space Vector Pulse Width Modulation (MSVPWMM) control with MATLAB/Simulink. The different applications of commercial use require different control schemes due to cost-effectiveness. In a small commercial application where not much precision is required, open-loop or V/F control is used, due to their easy calculation and implementation and becomes a low-cost product outcome. Where their high precision has required closed-loop control is being adopted. In this paper, closed-loop SVPWMM and sensor-less MSVPWM techniques are proposed. The algorithm has a much faster response in the switching of the inverter that is used provides better output has fewer harmonic contents. Fractional order controllers can provide more flexibility in tuning and can better adapt to complex and nonlinear systems. This often leads to improved control performance, especially in systems with unknown or time-varying dynamics. It helps to reduce steady-state error compared to integer order PI controllers. By adjusting the fractional order exponent, the system's characteristics matched better with the controller's response. Also, the FO-PI controllers allow for smoother transitions between different control modes or set points and help to reduce overshoot and rise time in dynamical systems, as they allow for more precise control of the transient response and Constant speed response available at desired load. The control techniques have been modeled and simulated in MATLAB simulation software. The proposed scheme provides efficient performance in steady-state and dynamic load conditions.

Fuzzy Gain Scheduling of the Fractional-Order PID Controller for a Continuous Stirred-Tank Reactor Process

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.

Frequency stabilization for interconnected renewable based power system using cascaded model predictive controller with fractional order PID controller

AbstractIn today's electrical grid, frequency cannot be ignored. The proliferation of renewable energy sources into a power system degrades its frequency; hence, the need for frequency regulation has been increased as a result. The second major factor is the perturbation in the load that originates the frequency fluctuation which needs to be suppressed in minimum time to avoid any system collapse. The designing of an optimal controller is indispensable because of increasing power system complexity. In order to maintain the stability of the power system, this paper presents the cascaded design of the model predictive controller with fractional order PID controller (MPC‐FOPIDN) to mitigate the frequency oscillations due to disruption in load. The combination of the predictive capabilities of model predictive control (MPC) and fractional order control enhances control abilities, making it an optimal control strategy for load frequency control (LFC). The grasshopper optimization algorithm (GOA) is applied to obtain optimal gains values for the FOPID controller. The efficacy of the controller has effectively mitigated frequency fluctuations caused by a change in demand or any uncertainty in the power system.

Disturbance Observer-Based Event-Triggered Adaptive Command Filtered Backstepping Control for Fractional-Order Nonlinear Systems and Its Application

This paper considers the disturbance observer-based event-triggered adaptive fuzzy tracking control issue for a class of fractional-order nonlinear systems (FONSs) with quantized signals and unknown disturbances. To improve the disturbance rejection ability, a fractional-order nonlinear disturbance observer (FONDO) is designed to estimate the unknown composite disturbances. Furthermore, by combining an improved fractional-order command-filtered backstepping control technique and an event-triggered control mechanism, an event-triggered adaptive fuzzy quantized control scheme is established, which guarantees the desired tracking performance can be achieved even in the presence of network constraint. Finally, the validity and superiority of the theoretic results are verified by a fractional-order horizontal platform system.

A comprehensive review on fractional-order optimal control problem and its solution

Abstract This article presents a comprehensive literature survey on fractional-order optimal control problems. Fractional-order differential equation is extensively used nowadays to model real-world systems accurately, which exhibit fractal dimensions, memory effects, as well as chaotic behaviour. These versatile features attract engineers to concentrate more on this, and it is widely used in the broad domain of science and technology. The mentioned numerical tools take the necessary optimal conditions into account, which makes it a two-point boundary value problem of non-integer order. In this review article, some numerical approaches for the approximation have been stated for obtaining the solution to fractional optimal control problems (FOCPs). Here, few numerical approaches including Grunwald-Letnikov approximation, Adams type predictor-corrector method, generalized Euler’s method, Caputo-Fabrizio method Bernoulli and Legendre polynomials method, Legendre operational method, and Ritz’s and Jacobi’s method are treated as an advanced method to obtain the solution of FOCP. Fractional delayed optimal control is selected for our investigation. It refers to a type of control problem where the control action is delayed by a fractional amount of time. In other words, the control input at a given time depends not only on the current state of the system but also on its past state at fractional times. The fractional delayed optimal control problem is formulated as an optimization problem that seeks to minimize a cost function subject to a set of constraints that represent the dynamics of the system and the fractional delay in the control input. The solution to this problem typically involves the use of fractional polynomials types, i.e. Chebyshev and Bassel polynomials.

Optimization of Robotic Arm Grasping through Fractional-Order Deep Deterministic Policy Gradient Algorithm

With the rapid development of robotics technology, robotic arm grasping has gained significant attention in the fields of automation and artificial intelligence. In this study, we propose a fractional-order deep deterministic policy gradient (DDPG) algorithm for optimizing robotic arm grasping tasks. Traditional machine learning algorithms face challenges in handling continuous action spaces, while the DDPG algorithm effectively addresses this issue. In this research, we first review the background and challenges of robotic arm grasping and provide an overview of the application of traditional reinforcement learning algorithms in grasping tasks. Subsequently, we introduce the principles and fundamental ideas of the DDPG algorithm in detail, discussing its potential for optimizing robotic arm grasping. To further enhance the performance of robotic arm grasping, we propose an improved approach based on fractional-order control. Fractional-order control exhibits unique advantages in environmental dynamics modeling and grasp posture optimization, enhancing the robustness and adaptability of robotic arm grasping. Through a series of experiments, we validate the effectiveness and superiority of the fractional-order DDPG algorithm in robotic arm grasping tasks. Our algorithm achieves significant improvements in grasping success rate and stability compared to traditional methods. The experimental results demonstrate that the fractional-order DDPG algorithm is better equipped to handle control challenges in continuous action spaces and optimize the performance of robotic arm grasping tasks.

Performance and Robustness Enhancement of Fractional Order Controller (FOC) for Electric Vehicles (EV) Using Intelligent Swarms

Performance and Robustness Enhancement of Fractional Order Controller (FOC) for Electric Vehicles (EV) Using Intelligent Swarms

Multi-objective optimization strategy for parallel tuning of multiple fractional order controllers in a PMSG based WECS

In this paper, a novel multi-objective optimization strategy is proposed for the parallel tuning of six fractional order controllers used in regulation loops of a PMSG based wind energy conversion system connected to the electric grid. The nonlinear nature of the WECS components has made controllers design challenging. To enhance the transient response of system variables, Fractional Order Proportional Integral (FOPI) controllers are considered as they are more suitable for such nonlinear physical systems. The additional parameters introduced by FOPI are normally tuned using a single objective, multi-dimensional particle swarm optimization algorithm. However, the inter-dependence of regulation loops introduces additional complexity that is solved in this work using a multi-objective optimization strategy based on a succession of Single-Objective PSO and Multi-Objective PSO. A simulation study has been conducted in order to demonstrate the higher performance and superior tracking accuracy of the proposed multi-objective optimization strategy in variable wind speed operating conditions.

Fractional-order PID controller for blood pressure regulation using genetic algorithm

In this paper, fractional order PID controller [FOPID] is designed for automatic blood pressure regulation. One of the most common problems faced by post-operative patients is abnormal blood pressure (BP). Infusion of sodium nitroprusside (SNP) into the patient reduces blood pressure by relaxing the peripheral vasculature's muscles. The patient’s BP must be continuously monitored by an expert and the correct dose has to be given to the patient. It will be difficult to give the desired dosage to a patient manually because drug sensitivity is different for different patients. So, an appropriate controller must be designed to regulate blood pressure and minimize clinical expenses. A fractional-order PID controller is proposed in this paper to regulate mean arterial pressure, and FOPID parameters are optimized as a function of minimizing integral absolute error (IAE), integral squared error (ISE), and integral time absolute error (ITAE) using genetic algorithm. The performance of the proposed system is improved in terms of undershoot, settling time, and maximum peak overshoot. A MATLAB environment was used for the simulation of the system and the implementation of the algorithm.

Power Quality Improvement Using TID based DVR Controller

The effectiveness of power utilized by electronic devices is crucial for various reasons. Firstly, high-quality power results in better efficiency, allowing devices to operate at optimal energy levels. This article aims to clarify the significance of Power Quality by highlighting the benefits of using a Dynamic Voltage Restorer (DVR) to improve power quality for electricity consumers. The proposed method employs a hysteresis voltage control system that operates with variable switching frequency to enhance DVR reliability and ease of operation. Using a Tilt Integral Derivative (TID) controller, a type of fractional order controller similar to the PID controller, voltage compensation under disturbances is achieved with satisfactory results demonstrated via simulation. The primary objective of this project is to mitigate power quality issues such as voltage swell and sag in a distribution power system by enhancing power quality with a TID controller and comparing the results with those obtained from a previously implemented PID controller, using MATLAB software. Keywords: Dynamic Voltage Restorer (DVR), Tilt Integral Derivative controller (TID), Total Harmonic Distortion, MATLAB software.

A strong secure path planning/following system based on type-3 fuzzy control, multi-switching chaotic systems, and random switching topology

This paper studies the synchronization and control of chaotic systems while proposing a novel chaotic-based path-tracking application for mobile robots (MRs) to ensure their safety and security. In security-based applications that use MRs, such as patrol MRs, the path of the MRs must be complex enough to prevent easy prediction. Multiple chaotic systems with a chaotic switching mechanism are introduced for secure path planning. The main challenges are that the dynamics of MRs are entirely unknown. The modeled dynamics of the MRs are unreliable in practice due to a broad range of uncertainties related to the parameters, operating conditions, environmental impacts, time delays, unmodeled frictions, noisy sensors, and faulty actuators. Also, the chaotic switching of reference signals between chaotic signals imposes a high dynamic perturbation. The main novelties are as follows: (1) a strong secure path is introduced for MRs. (2) A powerful fractional-order predictive controller using type-3 (T3) fuzzy-logic systems (FLSs) is developed. (3) The estimation and prediction errors of T3-FLSs are compensated by a designed parallel compensator. (4) T3-FLSs are tuned online, such that stability is ensured, and prediction accuracy is guaranteed. (5) The suggested scheme is implemented on a real-world MR, and the results demonstrate the feasibility and accuracy of the proposed method. Also, in several simulations, the efficacy of the introduced controller is examined.

Power quality improvement using rabbit optimization FOPID controlled photovoltaic- battery powered hybrid power filter

This paper presents the tuning of a fractional proportional controller (FOPI) using artificial rabbit optimization for the control of photovoltaic (PV) and battery power series active power filters along with a shunt passive filter which is known as a hybrid power filter. The PV power generation is combined into a series active filter to alleviate the problem of voltage sag and swell in the power system and also supply real power to the grid. Generally, the proportional controller is used to control the series active filter, but this is a linear controller and is not able to control the non-linear power system effectively. This problem is effectively controlled by non-linear control, i.e., a fractional-order proportional integral controller. Another problem in FOPI is finding the optimal value for proportional gain, integral gain, and fractional order. There are no standard rules for finding these values. This will make system design more complex. In this paper, artificial rabbit optimization is used to simplify the system design by finding optimal values of the FOPI controller for the series active filter and enhance the overall performance of the system. The MATLAB 2020b/Simulink environment is utilized to assess the recommended controller’s performance. According to the experimental findings, the suggested system has a total harmonic distortion (THD) value for load voltage of 0.10 % and a total harmonic distortion value for grid current of 1.87 %. The proposed artificial-rabbit optimized FOIPI controller effectively controls the system against voltage sag, swell, and non-linear loads and also obeys IEEE power quality standards.

Enhancement of a Grid-Connected DFIG Wind Turbine System Using Fractional Order PI Controllers

The wind velocities are unpredictable, and generating power with persistent speed is difficult which comprises mechanical stress at the rotor that leads to poor efficiency. So, variable wind power speed generation has ample significance with the Doubly Fed Induction Generator (DFIG). For a grid-connected DFIG, the governing of power is done conventionally by employing vector-controlled PI regulators. Yet, the performance of PI regulators depends on system parameters, which motivates the adoption of Fractional Order PI (FOPI) regulators. Presently FOPI regulators are seizing a lot of applications with the assistance of additional tuning parameters. However, tuning FOPI regulators by conventional methods is challenging. So, initially, the Particle Swarm Optimization (PSO) method was used for tuning FOPI regulators, but the disadvantages are low convergence rate, falling into local elucidation, entailing more variables to attune, and requiring a large number of iterations. Thus, this motivates introducing the Ant Lion Optimization (ALO) algorithm in this article due to its better performance and eligibility to overcome the limitations of conventional methods. Furthermore, in the validation of the proposed algorithm, the performance parameters like DC coupling capacitor voltage, rotor Speed, active power, and reactive power with PI, FOPI, PSO-FOPI, and ALO-FOPI regulators are compared and analysed using the bode plot are presented. The time response analysis of all the controllers with PI, FOPI, PSO-FOPI, and ALO-FOPI controllers were also observed with a voltage dip. Finally, the fractional order controllers with frequency response and time response analysis show superior performance in distributed generation with advanced heuristic controllers when compared to conventional controllers. The complete work has been simulated via MATLAB/ Simulation platform.

Optimized fuzzy fractional-order linear quadratic tracking control for a nonlinear system

In this paper, a novel fuzzy fractional-order Linear Quadratic Tracking (LQT) controller optimized by a Multi-Objective gray Wolf Algorithm (MOGWA) is designed for a 6 Degree-Of-Freedom (DOF) quadcopter flying system. In order to reach this end, the state-space equations would be divided into two parts, one for attitude and altitude control and another for position control. The LQT method is implemented to determine the constant parameters of the designed controller by minimizing a quadratic form related to errors and control efforts. Then, to substantially improve the performance of the linear quadratic tracking scheme, the fractional-order derivatives of the system errors are considered as the control inputs, while the MOGWA is used for optimal determination of the related orders. A fuzzy system that employs triangular and trapezoidal membership functions as well as the center average defuzzifier and singleton fuzzifier, is designed to timely regulate the gains of the controller. The introduced strategy would be applied on the nonlinear quadcopter flying system, and the related diagrams would be revealed to illustrate the efficiency and ability of the introduced fuzzy optimal fractional-order linear quadratic tracking controller.

Association of a fractional order controller with an optimal model-based approach for a robust, safe and high performing control of nonlinear systems

Association of a fractional order controller with an optimal model-based approach for a robust, safe and high performing control of nonlinear systems