Fractional Order PID Controller Research Articles

Neural network-based robot nonlinear output feedback control method

In order to improve the accuracy of robot terminal pose tracking and the anti-interference performance of robot nonlinear motion path control, a nonlinear output feedback control method based on neural network is proposed. Construct the coordinate transformation matrix of the connecting rod, calculate the linear and angular velocity of the nonlinear motion of the robot, then calculate the sum of the kinetic energy of each connecting rod of the robot, and establish the motion equation of the robot. The structure of BP neural network is analyzed, and the motion equation is solved by BP neural network. Finally, a Fractional Order PID controller is designed and BP neural network is constructed to control the nonlinear motion equation of the robot to complete the output feedback control of the robot. The experimental results show that the end attitude tracking error of this method is the smallest, and it best fits the actual nonlinear trajectory of the robot. It shows that this method can accurately track the end posture of the robot, and can still effectively control the trajectory of the robot in the interference environment.

Gaussian RBFNN method for solving FPK and BK equations in stochastic dynamical system with FOPID controller

Solving the Fokker–Planck–Kolmogorov (FPK) equation and the Backward-Kolmogorov (BK) equation is a crucial task to obtain the transient response of stochastic dynamical systems. Fractional order PID (FOPID) is a new efficient controller to change the system response to be the expected one. Therefore, in this paper, the Gaussian Radial Basis Functions Neural Network (RBFNN) is proposed to solve FPK and BK equations, to obtain the transient probability density function and the reliability function for a generalized Van der Pol system under a FOPID controller. The values of the different fractional orders are analyzed to discuss the performance of the FOPID controller. A data collection strategy is adopted to deal with the associated boundary conditions by way of a one-time Monte-Carlo simulation and uniform distribution in our Gaussian RBFNN method. The advantage of this method is that the solution process of FPK and BK equations is converted into solving algebraic equations. Numerical results with regard to the transient system response prove that the Gaussian RBFNN is efficient and accurate in getting the solutions of FPK and BK equations. The order of the fractional integration and the fractional derivative are critical parameters to control the system response. Moreover, we conclude that the fractional order parameters in a FOPID controller can indeed enhance the system’s response to a certain extent and lead to bifurcation.

Fuzzy Fractional Order Proportional Integral Derivative Controller Design for Higherorder Time Delay Processes

Process control is the interested domain of interest as the industrial high-order applications require an effective control mechanism with higher robustness. Since the conventional method of proportional integral derivative (PID) controller remains inadequate for the higher-order processes, this research concentrates on the fuzzy fractional-order controllers, that more and more attention nowadays in various research areas of science and engineering specifically, on the areas of tuning, design, implementation, and analysis of these controllers. Accordingly, this research marks a milestone for the control industry through introducing a robust controller, fuzzy fractional-order (FO) PI[Formula: see text]D[Formula: see text] (fuzzy FOPID) for higher-order applications with dead time. The fractional-order controller requires the fractional orders for the derivative term [Formula: see text] and integral term [Formula: see text]. The results of the proposed fuzzy FOPID controller is analyzed and compared with the comparative methods, such as a proportional integral derivative (PID) controller and fractional order PID controller (FOPID). Accordingly, the time-domain specifications are evaluated in the presence/absence of the disturbances is analyzed and in addition, the time domain optimal integral metrics are determined. Simulations are carried out using MATLAB/SIMULINK.

Grey wolf optimization based fractional order PID controller in SSSC on damping low frequency oscillation in interconnected multi-machine power system

Grey wolf optimization based fractional order PID controller in SSSC on damping low frequency oscillation in interconnected multi-machine power system

Fractional-Order Control of Fluid Composition Conductivity

Dialysis refers to the procedure of removing waste products and excess fluids from the blood stream. This is the main form of treatment for both acute and chronic renal failure. The need for hemodialysis process optimization is increasing. More than 10% of adults are affected by chronic kidney disease, and it is the nineth leading cause of deaths worldwide. Critically ill patients are particularly at risk, and their mortality is significantly affected by the hemodialysis procedures. This is the reason why the design and control of the hemodialysis process is studied by many researchers. The present paper proposes a fractional-order control of the fluid composition conductivity in this process. Fractional-order PI and PID controllers are designed with different imposed performances in order to establish the best performing controller for this medical process. The proposed fractional-order controllers are compared to the classical controller’s results in different real-world scenarios, including process parameter changes, flow changes, and priming sequences. The results are compared with a classical PID controller used in current clinical practice. The simulation results show the robustness and advantages of the proposed fractional-order PID controller over other controllers. These results could improve the clinical use of the hemodialysis process.

Solar PV Combined Efficient Torque Control of BLDC Motor Using Salp Swarm Optimization

This study provides an efficient torque and speed control method for brushless DC (BLDC) motor utilizing a fractional order proportional integral derivative (FOPID) controller based on the multiverse optimization algorithm and salp swarm optimization (SSO). When combined with a solar photovoltaic (PV) system and a voltage boosting architecture, standard PID controllers regulated the BLDC drive parameters due to their simplicity and improved steady-state performances. A solar PV system with a specific power range is chosen for the best output solution on the output side. The MPPT method employed is the incremental conductance approach for tracking maximum power from the source. However, it has a problem with unpredictability owing to load changes. The PID controller tuning also relates to the structure’s parametric uncertainties. Therefore, precise control methods may be offered with the aid of the FOPID controller to address the aforementioned issues. Simulation results of the proposed MVO and SSO-based FOPID controller for BLDC speeds run in the Matlab Simulink platform. To confirm the adaptability of the suggested control scheme for BLDC motor, the outcomes are interrelated using genetic algorithm, gray wolf, and PSO-based FOPID controllers.

Modified Fractional Order PID Controller for Load Frequency Control of Four Area Thermal Power System

This paper presents the development of a modified Fractional Order Proportional Integral Derivative (FOPID) controller to mitigate frequency deviation in a four-area thermal power system. Change in load demand and noisy power system environment can cause frequency deviation. Reducing high-frequency deviation is very paramount in load frequency control. This is because large frequency deviation can cause the transmission line to be overloaded, which may damage transformers at the transmission level, damage mechanical devices at the generating stations and also damage consumer devices at the distribution level. The conventional PID has been widely used for this problem. However, the parameter values of the various generating units of the power system like generators, turbines and governors keep changing due to numerous on/off witching in the load side. As such, it is essential that the control strategy applied should have a good capability of handling uncertainties in the system parameters and good disturbance rejection. Fractional order PID controller is known to give a higher phase margin resulting in very good disturbance rejection, robustness to high-frequency noise and elimination of steady-state error. A four-area power system was designed, and FOPID was used as the supplementary controller to mitigate frequency deviation. Ant Lion Optimizer (ALO) algorithm was used to optimize the gains of the FOPID controller by minimizing Integral Square Error (ISE) as the objective function. Results obtained outperformed other designed methods available in the literature in terms of reducing frequency deviation, tie-line power deviation and area control error.

Frequency Control Strategy for Grid-tied Virtual Power Plant Using SSA-tuned Fractional Order PID Controller

This paper investigates the frequency control strategy of the Virtual Power Plant (VPP), with the structure of an independent control area that includes diverse Distributed Energy Resources. The proposed VPP system comprises generating units such as Solar PV, Archimedes Wave Energy Conversion, Biodiesel driven Generator, and Plug-in Hybrid Electric Vehicle, which are interconnected to conventional thermal power plant. Centralized control strategy is adopted for frequency control studies, by considering the communication time delays. Fractional order Proportional Integral Derivative (FOPID), Proportional Integral Derivative (PID), and Proportional Integral (PI) controllers are employed to perform the control action on generating units to perform the frequency control. Tuning of the controllers is done using optimization algorithms such as Particle Swarm Optimization, Firefly Algorithm, Grasshopper Optimization Algorithm, Ant Lion Optimizer, Sine Cosine Algorithm, and Salp Swarm Algorithm (SSA). By comparative analysis, SSA algorithm is proved to outperform the other algorithms in terms of minimizing the objective function of Integral of Squared Error of the deviations in system frequencies and tie-line power. The system is also investigated under various scenarios of generation and load disturbances to study the comparative performance of the FOPID controller over PID and PI controllers. Results prove the superiority of SSA-tuned FOPID controller over PID and PI controllers in terms of providing better system responses. Sensitivity test has been conducted on the system without resetting nominal controller gain values and the proposed SSA-tuned FOPID controller is proved to be robust against the uncertainties in the load and parameters of our system.

A Numerical Implementation of Fractional-Order PID Controllers for Autonomous Vehicles

In the context of reaching the best way to control the movement of autonomous cars linearly and angularly, making them more stable and balanced on different roads and ensuring that they avoid road obstacles, this manuscript chiefly aims to reach the optimal approach for a fractional-order PID controller (or PIγDρ-controller) instead of the already classical one used to provide smooth automatic parking for electrical autonomous cars. The fractional-order PIγDρ-controller is based on the particle swarm optimization (PSO) algorithm for its design, with two different approximations: Oustaloup’s approximation and the continued fractional expansion (CFE) approximation. Our approaches to the fractional-order PID using the results of the PSO algorithm are compared with the classical PID that was designed using the results of the Cohen–Coon, Ziegler–Nichols and bacteria foraging algorithms. The scheme represented by the proposed PIγDρ-controller can provide the system of the autonomous vehicle with more stable results than that of the PID controller.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems: A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work. Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants. Also, in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative (FOPID) controller. To the best of the authors' knowledge, no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain, time-constants, and time delay. The three primary contributions of this study are as follows: i) a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractional-order control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system; ii) an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis; and iii) two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction. Finally, four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Cascaded Fractional Model Predictive Controller for Load Frequency Control in Multiarea Hybrid Renewable Energy System with Uncertainties

The rapid utilization of electricity has forced the stability of the power system for continuous operation. Due to difference in demand and generation, the frequency reference point changes that needs to be restored to its locus point for the stable operation of the power system. Therefore, a novel efficient control design is propounded to counter the phenomena of load frequency control. The designing of cascaded fractional model predictive controller coupled with fractional-order PID controller (CFMPC-FOPID) is designed for an efficient response of the power system under load disruption and system parameter variations. The controller is optimized by sooty tern optimization algorithm to identify the optimal parameters of the controller. The controller is tested under power mixing of renewable energy sources (i.e., PV and wind) and under varying load scenarios in multiarea hybrid power system. The proposed controller has effectively handled the frequency disruption under distinct load change by stabilizing it in 1.34 sec, 0.60 sec, and 0.41 sec for area-1 with an average time of 0.78 sec, and for area-2, the stabilizing time is 1.40 sec, 0.89 sec, and 0.56 sec with an average time of 0.95 sec, whereas the average time for MPC/PI, DSA-FOPID, GWO: PI-PD, and SCA: FOPI-FOPID is 7.67 sec, 4.68 sec, 1.77 sec, and 4.72 sec, respectively, for area-1 and 6.47 sec, 5.13 sec, 3.45 sec, and 5.02 sec, respectively, for area-2. The outcome result justifies the superiority of the studied technique.

Fractional Order PID Optimal Control Method of Regional Load Frequency Containing Pumped Storage Plants

The pumped storage unit has good adjustment characteristics of a fast power response and convenient start and stop, which provides support for the safe and stable operation of the power system. To this end, this paper proposes a fractional order PID (FOPID) optimization control method for the regional load frequency of pumped-storage power plants. Specifically, based on IEEE standards, this paper established a single-region model of pumped storage. Then, a fractional order PID (FOPID) controller was designed, and the parameters of the controller were optimized via using the chaos particle swarm optimization (CPSO) algorithm. The effectiveness of the proposed method is verified by example simulation in the two-zone model of the pumped storage based on IEEE standards. The results of the example show that the proposed method exhibits stronger robustness and stability in the regional load frequency control.

An improved sine cosine algorithm with heterogeneous subpopulations for global optimization and fractional order PID controller design

An improved sine cosine algorithm with heterogeneous subpopulations for global optimization and fractional order PID controller design

Robust Motion Planning in Robot-Assisted Surgery for Nonlinear Incision Trajectory

In the era of digital OTs (operating theatres), the developments in robot-assisted surgery (RAS) can greatly benefit the medical field. RAS is a method of technological advancement that uses robotic articulations to assist in complicated surgeries. Its implementation improves the ability of the specialized doctor to perform surgery to a great extent. The paper addresses the dynamics and control of the highly non-linear 3DOF surgical robot manipulator in the event of external disturbances and uncertainties. The integration of non-linear robust SMC (sliding mode control) with a smoothing mechanism, a FOPID (fractional-order proportional integral derivative) controller, and a fuzzy controller provides a high degree of robustness and minimal chatter. The addition of fuzzy logic to the controller, named intelligent fuzzy-SFOSMC (smoothing fractional order sliding mode controller) improves the system’s performance by ruling out the disturbances and uncertainties. The prototype model is developed in a laboratory and its outcomes are validated on OP5600, a real-time digital simulator. Simulation and experimental results of the proposed fuzzy-SFOSMC are compared with conventional controllers, which illustrates the efficacy and superiority of the proposed controller’s performance during the typical surgical situations. The proposed fuzzy-SFOSMC outperforms conventional controllers by providing greater precision and robustness to time-varying nonlinear multi-incision trajectories.

Robust H[formula omitted]-PID control Stability of fractional-order linear systems with Polytopic and two-norm bounded uncertainties subject to input saturation

This paper deals a type of H∞ proportional–integral–derivative (PID) control mechanism for a type of structural uncertain fractional order linear systems by convex Polytopic and two-norm bounded uncertainties subject to input saturation which mainly focuses on the case of a fractional order α such that 0<α<1. The Gronwall–Bellman lemma and the sector condition of the saturation function are investigated for system stability analysis and stabilization. The main strategy of the presented strategy is to restore fractional order PID controller design under input saturation problem from static output feedback controller design. Unlike existing strategies, non-iterative strategy is used to get optimal output feedback based on the LMI. On the premise of a linear matrix inequality algorithm, the SOF control laws can be obtained. After that, the fractional-order PID controller is recovered from the SOF controller. A numerical example is provided in order to show the validity and superiority of the proposed method.

Intelligent Fractional Order Sliding Mode Based Control for Surgical Robot Manipulator

In the era of digital OT (Operating Theatre), the developments in Robot-Assisted Surgery (RAS) can greatly benefit the medical field. RAS is a method of technological advancement that uses surgical robots to assist complicated surgeries. Its implementation improves the ability of the specialised doctors to perform surgery to a great extent. This paper addresses the dynamics and control of the highly non-linear 3DOF surgical robot manipulator in the occurrence of external disturbances and uncertainties. The integration of non-linear robust SMC (Sliding Mode Control) with smoothing mechanism, FOPID (Fractional-Order Proportional Integral Derivative) controller and fuzzy controller provides a high degree of robustness and minimal chatter. The addition of type-2 fuzzy logic to the controller, named intelligent T2F-SFOSMC (Type-2 Fuzzy-Smoothing Fractional Order Sliding Mode Controller), improves the system’s performance by ruling out the disturbances and uncertainties. The prototype model is developed in a laboratory and its outcomes are validated on OP5600: a real-time digital simulator. The simulation results and experimental results of the proposed T2F-SFOSMC are compared with conventional controllers, which illustrates the efficacy and superiority of the proposed controller’s performance during the typical situation of surgery. The proposed T2F-SFOSMC outperforms conventional controllers by providing greater precision, stability and robustness to time-varying nonlinear multi-incision trajectory.

Fractional‐order PID and internal model control‐based dual‐loop load frequency control using teaching–learning optimization

AbstractA load frequency controller is essential to counter load disturbances and minimize unscheduled power flow between interlinked areas of a power system. Hence, this paper proposes a fractional‐order proportional‐integral derivative (FOPID)‐based dual‐loop control approach for load frequency control of multi‐area nonreheated thermal power systems (NRTPS) using teaching–learning optimization (TLO). A stability equation‐based predictive model is used with internal model control in the internal loop of the proposed approach, whereas the external loop contains TLO‐based FOPID controller. The proposed method is tested on two‐area and three‐area NRTPSs under various operating conditions. It is validated from the simulation results that the proposed approach improves the system response substantially compared to the well‐known existing techniques. The robustness of the proposed method is also demonstrated by performing sensitivity analysis with parametric uncertainties, random load disturbances, generation rate constraints, and governor dead zone.

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.

Data-driven Koopman fractional order PID control of a MEMS gyroscope using bat algorithm

Data-driven Koopman fractional order PID control of a MEMS gyroscope using bat algorithm

Time delay margin for islanded microgrid with parameter uncertainty using fractional order proportional‐integral‐derivative controller

AbstractIn this article, an islanded microgrid (MG) consisting of the diesel generator (DEG), the photovoltaic panel (PV), the wind turbine generator (WTG), the battery energy storage system (BESS), and the control unit is considered. In the islanded MGs, the control signals are exchanged on the open communication network, which results in the time delays in the input and the output of the islanded MG central controller (MGCC). The time delay has a destructive effect on the islanded MG stability. Thus, finding the maximum allowable time delay bound (MADB) is a significant issue. Since it is shown that the fractional order systems have larger stability region and more robustness rather than the corresponding integer order systems, in this research, we propose the fractional order proportional‐integral‐derivative (FOPID) controller as the MGCC to achieve a larger MADB value. As another innovation, in this article, a method is presented in which the MADB of the islanded MG system is determined considering the parametric uncertainties related to the damping coefficient (D) and the inertia constant (H). It is shown that the percentage improvement in the MADB of the uncertain MG system with the designed FOPID controller over the integer order proportional‐integral‐derivative (IOPID) controller is 9.64%. The accuracy of the proposed method is verified by simulation results in Matlab.