Fractional Order PID Controller Research Articles

Improved Fractional-Order PID Controller of a PMSM-Based Wave Compensation System for Offshore Ship Cranes

Wave compensation technology is crucial to the safety of the ship operation and the accurate placement of load. Its compensation efficiency and the gentle change of the rope tension are particularly important. In this paper, we adopt permanent magnet synchronous machine (PMSM) as the actuator to construct the basic wave compensation system. Firstly, the motion model of ship and load under wave action is established, and the fractional-order PID (FOPID) controller for the position loop of the PMSM is introduced. Then, the parameters of FOPID are optimized by genetic algorithm-particle swarm optimization (GAPSO) algorithm, which is based on genetic algorithms (GA) and particle swarm optimization (PSO) algorithms for better compensation performance. The wave synchronization strategy is used to simulate the load, when it needs to be taken into the water. The non-linear dynamic equations of the rope are solved by Lagrange mechanics and the heave displacement is obtained by time series prediction algorithm. Finally, the effect of wave compensation and wave synchronization strategy are verified on MATLAB/Simulink. The results show that after the compensation, the crane load can follow the set height value very well, the compensation efficiency can reach more than 94%, and the wave synchronization strategy significantly reduces the change of the rope tension.

Implementation of a complex fractional order proportional-integral-derivative controller for a first order plus dead time system

<span lang="EN-US">This paper presents the implementation of a complex fractional order proportional integral derivative (CPID) and a real fractional order PID (RPID) controllers. The analysis and design of both controllers were carried out in a previous work done by the author, where the design specifications were classified into easy (case 1) and hard (case 2) design specifications. The main contribution of this paper is combining CRONE approximation and linear phase CRONE approximation to implement the CPID controller. The designed controllers-RPID and CPID-are implemented to control flowing water with low pressure circuit, which is a first order plus dead time system. Simulation results demonstrate that while the implemented RPID controller fails to stabilize the system in case 2, the implemented CPID controller stabilizes the system in both cases and achieves better transient response specifications.</span>

Spider-based FOPID controller design for temperature control in aluminium extrusion process

Abstract Based on the exit temperature in the aluminium extrusion process, the quality of the aluminium bars is obtained in the industries. Control of temperature plays a significant role to obtain the quality of the aluminium bars or rods. Problems are still encountered in the design of proper temperature control schemes in the industries. A new control scheme is presented here, to address the temperature control in the aluminium extrusion process. Spider-based fractional-order PID controller scheme is simulated for the aluminium extrusion plant using MATLAB and its toolbox. It gives the improved result for reducing the time delay, rise time and settling time in the process. Integral square error performance criteria are considered an objective function. The minimization of objective function gives good results. Comparisons of the presented control scheme with the conventional control methods are presented.

Formal Verification of Fractional-Order PID Control Systems Using Higher-Order Logic

Fractional-order PID control is a landmark in the development of fractional-order control theory. It can improve the control precision and accuracy of systems and achieve more robust control results. As a theorem-proving formal verification method, it can be applied to an arbitrary system represented by a mathematical model. It is the ideal verification method because it is not subject to limits on state numbers. This paper presents the higher-order logic (HOL) formal verification and modeling of fractional-order PID controller systems. Firstly, a fractional-order PID controller was designed. The accuracy of fractional-order PID control can be supported by simulation, comparing integral-order PID controls. Secondly, the superior property of fractional-order PID control is validated via higher-order logic theorem proofs. An important basic property, the relationship between fractional-order differential calculus and integral-order differential calculus, was analyzed via a higher-order logic theorem proof. Then, the relations between the fractional-order PID controller and integral-order PID controller were verified based on the fractional-order Grünwald–Letnikov definition for higher-order logic theorem proofs. Formalization models of the fractional-order PID controller and the fractional-order closed-loop control system were established. Finally, the stability of the fractional-order control systems was verified based on established formal models and theorems. The results show that the fractional-order PID controllers can be conducive to the control performance of control systems, and the higher-order logic formal verification method can ensure the reliability and security of fractional-order control systems.

FOPI/FOPID Tuning Rule Based on a Fractional Order Model for the Process

This paper deals with the design of a control system based on fractional order models and fractional order proportional-integral-derivative (FOPID) controllers and fractional-order proportional-integral (FOPI) controllers. The controller design takes into account the trade-off between robustness and performance as well as the trade-off between the load disturbance rejection and set-point tracking tasks. The fractional order process model is able to represent an extensive range of dynamics, including over-damped and oscillatory behaviors and this simplifies the process modelling. The tuning of the FOPID and FOPI controllers is achieved by using an optimization, as a first step, and in a second step, several fitting functions were used to capture the behavior of the optimal parameters of the controllers. In this way, a new set of tuning rules called FOMCoRoT (Fractional Order Model and Controllers Robust Tuning) is obtained for both FOPID and FOPI controllers. Simulation examples show the effectiveness of the proposed control strategy based on fractional calculus.

Global stabilization of uncertain nonlinear systems via fractional-order PID

This work presents a method that analyzes the global stabilization of fractional-order uncertain nonlinear feedback systems classes with fractional-order proportional–integral–derivative (PID) controllers. Two theorems are provided to necessary conditions for global convergence to any desired setpoints by designing controllers. The first theorem addresses a class of second-order time-varying systems controlled by fractional-order PID controllers, which extends the main result about PID (Zhao and Guo, 2017) into fractional-order systems via different analysis methods. The second theorem investigates another class of first-order time-invariant systems regulated by fractional-order proportional–integral (PI) controllers. The method is illustrated on two feedback systems with controllers to ensure the global convergence of the feedback system to desired setpoints.

Frequency regulation of hybrid shipboard microgrid system using butterfly optimization algorithm synthesis fractional‐order controller

AbstractInclusion 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.

Optimal fractional-order PID controller based on fractional-order actor-critic algorithm

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.

Fractional Order Controller Design for Wind Turbines

According to recent studies, it has been concluded that renewable electricity generation is being requested to replace all other fuels more often. In China and the USA, among renewable electricity sources, wind usage has increased significantly compared to 2020. Given these circumstances, the aim of this study was to develop a suitable speed control method for wind power systems in order to achieve maximum power generation while reducing mechanical loads. Several control strategies have been proposed in the literature, all of which offer a compromise between performance and robustness. The present research developed fractional order PID (FOPID) controllers and proved which would be the most suitable controller to address the challenges that wind turbine systems face. The parameters of the FOPID controllers (KP, KI, KD, λ and µ) were tuned with the help of the following optimization algorithms: a genetic algorithm (GA), a multi-objective genetic algorithm (MOGA) and particle swarm optimization (PSO). The results from these three turning methods were then compared to find the method that offered the best performance and system robustness.

Fuzzy fractional-order PID control for heat exchanger

Fractions have recently become widespread in technology and science. The current research looked at a fractional-order fuzzy PID controller. Furthermore, the tubular heat exchanger procedure aids in the investigation of controller behavior. The advantages of the recommended control strategy are highlighted to examine controller reactions under variations in variation and loads within the reference environment. There are additional comparisons with the conventional PID control scheme. The findings showed that the control approach performs better than a traditional PID control framework.

Frequency Regulation on an Interconnected Power System With Fractional PID Controllers Optimized Using Rao Algorithms

Developing an optimization algorithm with independent algorithm-specific parameters is crucial in tuning the controller parameters of Automatic Generation Control (AGC). In 2020, Rao developed a robust and newly proposed algorithm independent of algorithm-specific parameters with faster convergence and less computational complexities. This paper presents the AGC of a sample two-area interconnected multi-source power systems with fractional-order PID controllers optimized using the Rao algorithm. The objective function selected for tuning the optimal gain of the controller using the Rao algorithm is based on Integral Squared Error (ISE). The robustness of the Rao algorithm for parameter variations and load changes is compared with other metaheuristic algorithms such as Genetic Algorithm (GA), Grey Wolf Optimization (GWO), and Particle Swarm Optimization (PSO). The efficacy of the proposed tuning method for AGC application is validated using the dSPACE 1103 hardware-in-loop simulation.

FOPID controller design for a perturbed PHWR system using enhanced crow search algorithm

The effectiveness of a control algorithm in the operation of a Pressurized Heavy Water Reactor (PHWR) relies upon its ability to counter the step back condition accurately. This paper presents an enhanced crow search algorithm for designing a fractional-order proportional integral derivative (FOPID) controller implemented in power control loop of a PHWR under step-back condition. The proposed controller is applied on eight different interval fractional transfer function models of PHWR derived using Edge theorem as well as eight step back conditions of PHWR. Simulation results reveal excellent reference tracking capability of the proposed controller. The effectiveness of the proposed controller has been proved by performing a comparison among different error performance indices with the existing controllers in the literature.

Development of High Voltage DC Power Supply from Tesla Coil Using Hybrid Energy Sources

Background: High Voltage Direct Current (HVDC) is a well-proven technology used to transmit electricity over long distances by overhead transmission lines or submarine cables. It is also used to interconnect separate power systems, where traditional Alternating Current (AC) connections cannot be used. Objective: In this paper, an HVDC supply has been proposed with the Tesla coil using hybrid energy sources such as solar panels, batteries, and AC main supply with an AC-DC converter. Method: DC voltage is obtained from various hybrid sources and is supplied to the input of the Cockcroft-Walton (C-W) voltage multiplier circuit through DC/AC inversion. Result: The produced HVDC is provided to the Tesla coil to obtain a stable HVDC output. Fractional Order PID (FOPID) controller is used in the system for control purposes to stabilize the output voltage due to load variations. The model was designed in Matlab / Simulink environment. The simulation results show that the proposed design successfully achieved a stable 15 kV HVDC. Conclusion: The advantage of the proposed system is the availability of variable output voltage as per load requirement compared to the fixed limited output voltage generated by conventional HVDC systems.

Enhanced stability and failure avoidance of hydropower plant in contingent island operation by model predictive frequency control

The challenges of contingent island operation of hydropower plants are addressed by proposing an enhanced frequency control with advanced control algorithms. The study is based on a real power plant and considers the relevant power system in its entirety along with the load and transmission lines. Integrated transfer functions between the guide vane opening of a hydro turbine and the frequency of the associated generator were determined by in-situ identification. A model predictive controller, a fractional order PID controller, and a PID controller utilizing integral absolute error and integral time absolute error criteria were designed and developed. The performance of the proposed algorithms with the identified plant model was tested on a NI-cRIO 9049 FPGA platform. Improved frequency control in terms of setpoint change was achieved with the MPC and FOPID controllers. The MPC controller also features betters disturbance rejection compared to conventional PID controllers, which are tuned according to integral error criteria. The considered algorithms have been simulated in different operating scenarios, such as variations of active power load and transmission length. The proposed approach enhances stability and consequently avoids operational failures of hydropower plants in contingent islanding mode.

Dynamic Characteristics and Successive Start-Up Control Strategy Optimization of Pumped Storage Units under Low-Head Extreme Conditions

With inherent ‘S’ characteristics and the one-tunnel-with-two-units arrangement of the pump-turbine, hydraulic transient changes in the successive start-up process are complex, and the optimal control is difficult. This paper aims to study the dynamic characteristics and successive start-up control strategy optimization of two hydraulic couplings pumped storage units (PSUs) under low-head extreme conditions. Firstly, an accurate model of two hydraulic coupling PSUs’ successive start-up is established. Based on this model, the influence of the interval time of successive start-up on the dynamic characteristics of PSUs is carried out. It is shown that the change of the interval time of the successive start-up (ΔT) of the two PSUs has a significant impact on the dynamic response stability of the low-head start-up. If ΔT is more than 40 s, the hydraulic oscillation and speed fluctuation of the PSUs deteriorate. Secondly, with the different controller parameters for the two PSUs, a novel multi-objective optimization scheme with fractional order PID controller (FOPID) is proposed to figure out the best control scheme for the successive start-up. Furthermore, selecting the sum of the rise time (Tr) of the rotating speed of two PSUs and the sum of the integral time absolute error (ITAE) of two PSUs is the objective. Meanwhile, the optimization scheme of PID with different parameters (PIDDP) is used to compare and verify the optimization method proposed in this paper. The results for this extreme condition indicate that FOPID has more significant advantages in optimizing the instability of the successive start-up process, with the better Pareto front, and the optimized scheme has a more stable dynamic transition process of flow, water hammer pressure, and rotational speed.

Learning-based Fractional Order PID Controller for Load Frequency Control of Distributed Energy Resources Including PV and Wind Turbine Generator

Due to the ever-increasing penetration of renewable resources, Frequency control of microgrids has recently been received special consideration from researchers. The continual supply of load consumption is the major issue of standalone microgrids due to the high penetration of renewable resources. Furthermore, microgrids suffer from low inertia against load changes due to their small size and unpredictable load interruption. In addition to the above-mentioned issues, the uncertain and intermittent behaviors of renewable resources cause problems to keep the balance between load and generation sides. Hence, it is very important to consider novel control methods for keeping balance and consequently control of frequency deviation. In this research, a novel learning-based fractional-order controller is proposed to control the frequency of microgrids including micro-turbines, photovoltaic panels, and wind turbines in order to increase system stability and reduce frequency fluctuation time. The efficiency of this controller has been compared with conventional methods in the simulation and result section.

Design of Bio-Inspired Optimized Integer And Fractional Pid Controller

The PID controllers are being widely used in almost every real-time engineering problem in accordance with the increasing demand for aquick and consistent response of the system. To justify the performance of PID controllers, a mathematical model of an electric motor is considered in this paper. The complete system is simulated on MATLAB/SIMULINK with an integer and fractional-order PID controller and analyzed in terms of control characteristics. A comparative study of the various closed-loop response of the system is also carried out to compare the performance of an integer and fractional-order PID controller. The controllers used in the system are modern optimized, i.e., the particle swarm optimization technique is used to acquire a more optimized system response. The simple concept of application of integer and fractional-order PID controllers is proposed in this research article. A similar approach can be applied to various real-time problems to obtain optimized results. However, other modern optimization techniques are also available and emerging regularly that can produce a stable and optimized response to satisfy the demand for system stability.

Fractional Order PID Control Based on Ball Screw Energy Regenerative Active Suspension

A ball screw type energy regenerative active suspension under fractional order PID control is proposed and studied in order to improve the vibration damping performance of the suspension. A mathematical model of the energy regenerative actuator is established, the energy recovery power at different frequencies is measured through experiments, and then the electromagnetic torque constant, representing the proportional relationship between the output torque and current of the motor, is calculated according to the experimental results. A mathematical model of the control circuit is established and the feasibility and the superiority of the fractional order PID control are verified by simulation and experiments. To achieve a better damping effect, the fractional order PID controller of the whole vehicle suspension system is parameterized using the Beetle Antenna Search (BAS) algorithm. The results showed that the mean energy recovery power of the actuator was about 3.5091 W at a vibration frequency of 11/6 Hz, and the electromagnetic torque constant of the motor was about 0.2885. The actuator control circuit was feasible, and the root mean square value of current deviation under fractional order PID control was 1.1158 mA, which was optimized by 9.40%, compared to the PID control. The BAS algorithm effectively realized the parameter tuning of the controller, and both the tuned PID and fractional order PID controllers, achieved optimization of suspension damping performance. The optimal value of the damping performance objective function under fractional order PID control was 0.3270, which was optimized by 62.93%, compared to the PID control. In addition, all suspension performance indices under fractional order PID control were optimized to a certain extent, compared with the PID control.

Disturbance rejection based fractional order PID controller for system performance improvement of hybrid power system

AbstractThe present paper introduces a disturbance‐rejection based fractional‐order proportional‐integral‐derivative (DR‐foPID) controller as optimal control strategy for performance enhancement of hybrid power system (HPS). The two‐area HPS is equipped with various generation sources in the form of solar–thermal‐system (STS), conventional thermal, wind‐turbine‐system (WTS) and geo‐thermal power plants establishing a coordinated system frequency and tie‐line power control. In addition, electric vehicles (EVs) are integrated with the HPS to check its effect on dynamic characteristics. The controller gains are optimized using an effective bio‐geography based krill herd (BBKH) optimization technique to achieve the required performance of the HPS. This study validates the efficacy of the BBKH adjusted DR‐foPID controller for efficient operation of system dynamic characteristics. The resilience of DR‐foPID controller gains is confirmed by a sensitivity test involving large fluctuations in system load variations from their nominal values. It is also demonstrated that EVs help to increase the performance of HPS. A study involving the power management capability of EVs for improving the system performance is also demonstrated. Moreover, the effect of redox flow battery as energy storage device for system dynamic control are also illustrated. At last, a DR‐foPID controller is tested in case study on three‐area HPS.

Construction and Evaluation of a Control Mechanism for Fuzzy Fractional-Order PID

In this research, a control mechanism for fuzzy fractional-order proportional integral derivatives was suggested (FFOPID). The fractional calculus application has been used in different fields of engineering and science and showed to be improved in the past few years. However, there are few studies on the implementation of the fuzzy fractional-order controller for control in real time. Therefore, for an experimental pressure control model, a fractional order PID controller with intelligent fuzzy tuning was constructed and its results were calculated through simulation. To highlight proposed control scheme advantages, the performances of the controller were inspected under load disturbances and variations in set-point conditions. Furthermore, with classical PID control schemes and fractional order proportional integral derivative (FOPID), a comparative study was made. It is revealed from the results that the suggested control scheme outclasses other categories of the control schemes.