Fractional Order Proportional Derivative Research Articles

A Novel Fractional Order Proportional Integral-Fractional Order Proportional Derivative Controller Design Based on Symbiotic Organisms Search Algorithm for Speed Control of a Direct Current Motor

A Novel Fractional Order Proportional Integral-Fractional Order Proportional Derivative Controller Design Based on Symbiotic Organisms Search Algorithm for Speed Control of a Direct Current Motor

Spotted Hyena Optimizer enhances the performance of Fractional-Order PD controller for Tri-copter drone

AbstractIn this study, nonlinear control design is presented for trajectory tracking of Tricopter system. A Fractional Order Proportional Derivative (FOPD) controller has been developed. The performance of controlled Tri-copter system can be enhanced by suggesting modern optimization technique to optimally tune the design parameters of FOPD controller. The Spotted Hyena Optimizer (SHO) is proposed as an optimization method for optimal tuning of FOPD's parameters. To verify the performance of controlled Tricopter system based on optimal SHO-based FOPD controller, computer simulation is implemented via MATLAB codes. Moreover, a comparison study between SHO and Particle Swarm Optimization (PSO) has been made in terms of robustness and transient behavior characteristics of FOPD controller.

A Fractional-Order ADRC Architecture for a PMSM Position Servo System with Improved Disturbance Rejection

This paper proposes an active disturbance rejection control (ADRC) architecture for a permanent magnet synchronous motor (PMSM) position servo system. The presented method achieved enhanced tracking and disturbance rejection performance with a limited observer bandwidth. The model-aided extended state observer (MESO)-based ADRC was designed for the current, speed, and position loops of the PMSM position servo system. By integrating known plant information, the MESO improved disturbance estimation with a limited observer bandwidth without amplifying the noise. Additionally, a fractional-order proportional-derivative (FOPD) controller was designed as the feedback controller for the speed loop to further enhance the disturbance rejection. A simulation and experimental tests were conducted on a PMSM servo platform. The results demonstrate not only that the proposed method achieved superior tracking performance but also that the position error of the proposed strategy decreases to 2.25% when the constant disturbance was input, significantly improving the disturbance rejection performance.

A novel cascade-loop controller for load frequency control of isolated microgrid via dandelion optimizer

In fast-growing isolated microgrids (IMGs), load frequency control (LFC) ensures optimal power quality for end users. Stochastic grids, notably with renewable energy resources (RESs), require robust and intelligently designed LFC schemes. Thus, this research presents a novel cascade-loop controller combining a fractional order-proportional derivative with a filter and a fractional order-proportional tilt integral derivative (FPDN-FPTID) to improve LFC for single and multi-area IMGs. Recent dandelion optimization adjusts FPDN-FPTID controller settings. Anti-windup keeps the controller out of the non-linear zone for low inertia IMGs. It concerns various sources' maximum generating rates. The two-area IMG model shows its potential and scalability. Extensive MATLAB/Simulink simulations show that the FPDN-FPTID controller outperforms numerous published controllers, either single or cascade-loop, in minimum error criteria, undershoots/ overshoots/settling times, frequency, and tie-line power deviation following load and RES variations. Finally, the sensitivity study indicates the suggested controller stabilizes the system despite ±25 % parameter changes.

Evaluation of renewable and energy storage system-based interlinked power system with artificial rabbit optimized PI(FOPD) cascaded controller

This research work addresses automatic generation control of multiple arenas and causes under various system disturbances. Sources within arena-1 comprises thermal, bio-diesel, in arena-2 sources represent thermal elements, in arena-3 sources are thermal and hydro units. An innovative endeavor has been undertaken to employ conglomerate controller with the amalgamation of proportional-integral (PI) (integer-order) in addition fractional order proportional-derivative (FOPD). Various examination manifests the fineness of PI(FOPD) overtop additional integer order controllers from perspective concerning reduced grade of crown overshoot, expanse-of-instabilities, crown undershoot in addition to subsiding period. In determination to attain the controller’s features biologically enthused meta-heuristic artificial rabbit optimization is pragmatic. The minimum cost function value has been achieved as 0.000309 for the artificial rabbit optimization in comparison to various established optimization technique along with the proposed PI(FOPD) controller. It is likewise detected that occurrence of inexhaustible sources like realistic dish-Stirling thermal system in arena-1, geothermal power plant and precise wind turbine system styles the structure meaningfully improved related to origin structure when judged exclusively or all together. Accomplishment in presence of interline power flow controller besides combination of energy stowage elements alike redox flow battery in addition solid oxide fuel cell is as well inspected using PI(FOPD) controller, that offers with notable consequence in dynamic presentation in each cases separately. It has been clearly observed that in presence of all the renewables, in case of frequency deviation crown overshoot, crown undershoot, and subsiding period are 0.0053, 0.0131, and 24.32 respectively. These values are showing improvements in comparison to the individual presence of renewables in each arena. Similarly, with the presence of both SOFC and RFB for tie line power between arena-1 and areana-3, the crown overshoot, crown undershoot, and subsiding period are 0.00018, 0.0013, and 22.63 respectively. These values are showing improvements in comparison to the individual presence of Solid Oxide Fuel Cell without battery energy storage in each arena. Also, PI(FOPD) parameters values at nominal condition are appropriate for random pattern of disturbance needs no optimization, which justified the reliability of the suggested controller.© 2017 Elsevier Inc. All rights reserved.

Extending the admissible control-loop delays for the inverted pendulum by fractional-order proportional-derivative controller

Stabilization of the inverted pendulum by fractional-order proportional-derivative (PD) feedback with two delays is investigated. This feedback law is obtained as a combination of PD feedback with two delays and fractional-order PD feedback with a single delay. Different types of stabilizability boundaries and the corresponding geometric and multiplicity conditions are determined using the D-subdivision method. The stabilizable region is depicted in the plane of the delay parameters for given fractional derivative orders. Several special cases and the concept of delay detuning are also discussed. It is shown that the admissible delay can be slightly increased compared to the integer-order PD feedback by introducing a fractional-order feedback term.

Optimal FOPI-FOPD controller design for rotary inverted pendulum system using grey wolves’ optimization technique

The rotary inverted pendulum (RIP) has been used in various control application areas. This system can be represented as two degree of freedom (2-DOF), consisting of a rotating arm and rotating pendulum rod. RIP is an excellent example of designing a single-input multi-output (SIMO) system. Due to unstable RIP system dynamics, and its nonlinear model, multiple control techniques have been used to control this system. This paper uses integer and fractional order proportional integral-proportional derivative (PI-PD) controllers to stabilize the pendulum in the vertical direction. Constrained optimization approaches, such as the grey wolf optimization (GWO) methodology, are utilized to estimate the parametric values of the controllers. The simulation results showed that the fractional order PI-PD controller outperforms the integer order PI-PD controller with and without disturbance signal existence. A multiple results comparison has illustrated the superiority of fractional order controller over a previous work.

Utilizing controlled plug-in electric vehicles to improve hybrid power grid frequency regulation considering high renewable energy penetration

This study proposes an incorporated strategy based on energy storage systems (ESSs) like plug-in electric vehicles (PEVs) with load frequency control (LFC) to enhance the frequency stability during high penetration of renewable energy sources (RESs). Furthermore, an innovative-cascaded controller is used in the LFC loop, and PEVs are considered in the two identical areas' multi-source power grids. The proposed control structure is based on using two terms, the first term is the fractional-order-proportional-derivative (FOPD), and the second cascaded term is a fractional-order-proportional-integral (FOPI) to form the cascaded (FO-(PD-PI)) controller. Additionally, the gains of the proposed controller are well designed, utilizing an improved version of the manta ray foraging optimization algorithm (MRFO) labeled as leader MRFO (LMRFO). The effectiveness of the proposed FO-(PD-PI) controller based on the LMFRO algorithm is validated by comparing its performance with that of other control approaches such as (i.e., the proportional-integral-derivative (PID) controller, the tilt-integral-derivative (TID) controller, and the fractional-order-PID (FOPID) controller) based on different optimizers. Different load perturbation patterns, a high penetration level of RESs, and the communication delay time are broadly implemented for ensuring the superiority of the proposed controller in penalizing the power grid perturbations. Furthermore, for validating the efficiency of the proposed controller, an IEEE 39 bus is used. As a result, the proposed integrated strategy is a viable and effective control scheme for modern power grids with high-RESs penetration.

Model references frequency-domain design based fractional order PD controller for quadrotor control: attitude, altitude, and position studies

This article proposes a control strategy based on a Fractional Order Proportional Derivative (FOPD) controller to enhance the performance and robustness of quadrotors operating in trajectory tracking mode. The tuning method proposed for the FOPD controller is based on an ideal Bode transfer function in a closed loop as a fractional reference model. The latter represents the quadrotor desired closed-loop response, and its specification is the key design decision. In this study, we first appropriately set model reference parameters to realistic desired time response characteristics (i.e. overshoot and time constant). Then, the parameters of the FOPD controller are computed using the direct synthesis design approach. The dynamic model of the quadrotor is developed using Lagrange formulation. The model is used to test the performance of the proposed FOPD-based control strategy for the attitude, position, and altitude of the flying robot. The results show that the proposed controller achieved accurately set points tracking with transient responses (i.e. overshoot and time constant) that satisfactorily meet those assigned for their respective reference models. These results validate the effectiveness of our proposed control strategy. Moreover, our comparative studies of the proposed FOPD controller with the conventional PD controller show that the former satisfies better-desired design requirements.

Design of optimal cascade control approach for LFM of interconnected power system

In the present era, due to increasing power demand and complex power system structures having various load disturbances, a load frequency management (LFM) scheme is indispensable to provide uninterrupted power to consumers. This research deals with a fractional-order proportional derivative - (one + fractional order integrator) (FOPD-(1+FOI)) cascade controller as a novel control structure to ameliorate the execution of automatic generation control (AGC) for the LFM of interconnected power system (PS). The implementation of this controller is uncomplicated, and it joins the output of the FOPD controller to (1+FOI) controller, where area control error and power error are considered in the outer and inner feedback control loops, respectively. A maiden attempt of a wild horse optimizer-assisted FOPD-(1+FOI) cascade controller for AGC of considered interconnected PS has been performed in this work. To benchmark the proposed control scheme, two areas reheat thermal PS with GDB and GRC nonlinearities is chosen as the test bench. A vivid comparative analysis of six state-of-the-art control techniques is performed, and the results reveal the potency of the presented control approach. Eigenvalues-based stability assessment of interconnected PS in conjunction with the proposed controller is also performed. Finally, for the real PS implementation of the presented control architecture a new england IEEE 39 test bus is considered and analyzed.

Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases

In this paper, a delayed fractional-order predator–prey system with trans-species infectious diseases is proposed and the corresponding control strategy is implemented via fractional-order proportional-derivative (PD) control. Firstly, for the uncontrolled fractional-order predator–prey system, explicit conditions of stability and Hopf bifurcation are established by selecting time delay as the bifurcation parameter. The predator–prey system will lose its stability and a family of oscillations will emerge when the time delay passes through the critical value. Secondly, under the fractional-order PD control, the influences of the controller on the system stability and bifurcation are investigated. It is demonstrated that the Hopf bifurcation can be postponed or advanced, and the desired dynamic can be achieved by choosing appropriate control gain parameters. In addition, the impacts of fractional order and control parameters on dynamics are explored. Finally, some numerical simulations are depicted to validate the theoretical results.

Frequency regulation of a maiden structured power system with integrated renewable energy source by a fuzzy - tuned fractional order controller

ABSTRACT In this paper, a hybrid fuzzy cascaded fractional order proportional integral-fractional order proportional derivative (FCFOPI-FOPD) controller improves the frequency regulation of a renewable energy source (RES) integrated power system. The frequency response characteristics of a two-area non-linear thermal-hydro-wind model under various operating situations are explored with an emphasis on the extensive usage of renewable energy sources (RES) in modern power systems. The power system in this study is developed using an innovative combination of a standard dynamic model of the steam turbine and the actual physical position of the generation rate constraint in the power plant model. The suggested FCFOPI-FOPD hybrid controller minimizes a power system’s frequency deviation caused by specific differences in the pre-scheduled load. The effectiveness of a proposed FCFOPI-FOPD hybrid controller in alleviating system frequency variations under various perturbations was determined using MATLAB Simulink analysis. Comprehensive results show that the FCFOPI-FOPD hybrid controller outperforms the fuzzy-structured fractional order proportional integral and derivative (FOPID) and the proportional and integral controllers. The results also demonstrate that the proposed controller improves the settling time of frequency variations in area-1, area-2, and tie-line power deviation by 47%, 51%, and 66% compared to the responses obtained with the fuzzy FOPID controller.

Fuzzy Fractional-Order PD Vibration Control of Uncertain Building Structures

A new control strategy is proposed to suppress earthquake-induced vibrations on uncertain building structures. The control strategy embeds fuzzy logic in a fractional-order (FO) proportional derivative (FOPD) controller. A new improved FO particle swarm optimization (IFOPSO) algorithm is derived to adjust the initial parameters of the FOPD controller. An original fuzzy logic-FOPD (FFOPD) controller is then designed by combining the advantages of the fuzzy logic and FOPD control, to deal with large displacements on structures under earthquake excitation. Simulation experiments are carried out on uncertain building structures subjected to the effects of different kinds of seismic signals, illustrating the validity and feasibility of the proposed method.

Energy-based fuzzy supervisory non integer control for performance improvement of PMSG-Based marine energy system under swell effect and parameter uncertainties

Permanent magnet synchronous generators (PMSG) based marine current system has gained much attention due to several advantages such as high predictability, rapid response and high-power density. The performance and power integration efficiency of the above-mentioned system greatly rely on the applied control system. However, system nonlinearities, parameter variations make the controller design process a challenging task. This paper introduces passivity based fuzzy fractional order proportional integral and derivative (PID) controller for PMSG based marine current energy conversion system under swell effect and parameter uncertainties. The proposed approach combines a new passivity-based current control (PBCC) with a fuzzy fractional order PID control (FFO-PID). The proposed method is tested under the swell effect and parameter uncertainties using MATLAB/Simulink. The proposed controller exhibits robustness against swell effect, parameter changes and shows fast convergence of the system states. Furthermore, the exponential stability and error convergence of the proposed controller is analytically justified.

An Optimal Adaptive Control Strategy for Energy Balancing in Smart Microgrid Using Dynamic Pricing

Energy balancing in smart microgrid plays a vital role to improve the reliability and resolves the load shedding problem to ensure consistent energy supply. However, energy balancing is challenging due to uncertain and intermittent nature of renewable energy integrated in smart microgrid. To solve such problems, dynamic energy pricing mechanism is developed that maintain energy balance for overcoming the gap between demand and supply. Thus, the particle swarm optimization based super twisting sliding mode controller (PSO-STSMC) is developed which uses dynamic energy pricing to control renewable energy resources’ generation according to the consumers’ demand for real time closed loop energy balancing in an energy market. The proposed PSO-STSMC based model is compared with existing models like proportional integral derivative (PID) controller, proportional integral (PI) controller, proportional derivative (PD) controller, and fractional order proportional derivative (FO-PD) controller and the optimized models of the particle swarm optimization based proportional integral (PSO-PI) controller and particle swarm optimization based proportional integral derivative (PSO-PID) controller. Simulations results demonstrate that energy price regulation by PSO-STSMC consistently controls the elastic demand for real time energy balancing.

Stochastic Hopf Bifurcation of MDOF Quasi-Integrable Hamiltonian Systems with Delayed Feedback Fractional-Order PD Controller

Hopf bifurcation, as the most representative dynamic bifurcation, is closely related to the stability of many engineering structures. In this work, the stochastic Hopf bifurcation (SHB) of a controlled quasi-integrable Hamiltonian system (H.S.) of multi-degree-of-freedom (MDOF) is investigated, where the system is subjected to wide-band noise and controlled by a Fractional-order Proportional-Derivative (FOPD) controller with time delay. By decoupling FOPD control force and simplifying it without time delay, the averaged Itô differential equations of the approximated system are derived with the technique of stochastic averaging. Then, the average bifurcation parameter expression of system is obtained, which can determine the criterion of the SHB deduced by the FOPD control force. Last, an illustration of coupled Rayleigh oscillators is given to demonstrate the validity of the procedure. The influences of time delay, noise intensities and fractional order on the system SHB are discussed.

Optimal Fractional-Order Active Disturbance Rejection Controller Design for PMSM Speed Servo System.

In this paper, a fractional-order active disturbance rejection controller (FOADRC), combining a fractional-order proportional derivative (FOPD) controller and an extended state observer (ESO), is proposed for a permanent magnet synchronous motor (PMSM) speed servo system. The global stable region in the parameter (Kp, Kd, μ)-space corresponding to the observer bandwidth ωo can be obtained by D-decomposition method. To achieve a satisfied tracking and anti-load disturbance performance, an optimal ADRC tuning strategy is proposed. This tuning strategy is applicable to both FOADRC and integer-order active disturbance rejection controller (IOADRC). The tuning method not only meets user-specified frequency-domain indicators but also achieves a time-domain performance index. Simulation and experimental results demonstrate that the proposed FOADRC achieves better speed tracking, and more robustness to external disturbance performances than traditional IOADRC and typical Proportional-Integral-Derivative (PID) controller. For example, the JITAE for speed tracking of the designed FOADRC are less than 52.59% and 55.36% of the JITAE of IOADRC and PID controller, respectively. Besides, the JITAE for anti-load disturbance of the designed FOADRC are less than 17.11% and 52.50% of the JITAE of IOADRC and PID controller, respectively.

Load frequency control of a multi‐area system incorporating realistic high‐voltage direct current and dish‐Stirling solar thermal system models under deregulated scenario

A maiden attempt was made to demonstrate the impact of realistic high-voltage direct current (RHVDC) tie-line along with realistic dish-Stirling solar thermal system (RDSTS) models in multi-area load frequency control studies under a deregulated scenario. Area-1, area-2 and area-3 comprise thermal-RDSTS systems with relevant generation rate constraints. Each area includes two generation and two distribution companies. A new secondary controller with a cascaded combination of fractional order (FO) proportional derivative with filter coefficient (N) and FO-proportional-integral-derivative with filter coefficient (N) (FOPDN-FOPIDN) is proposed for the first time. The performance indices (peak magnitude, settling time and oscillations magnitude) of the proposed controller shows the dominance in comparison with the existing FOPI, PIDN and FOPIDN controllers in the policy schemes like poolco, bilateral and contract violation. A recent metaheuristic algorithm named the crow-search algorithm is successfully applied for simultaneous optimisation of the proposed FOPDN-FOPIDN controller gains and RDSTS parameters under the deregulated environment for the first time. Under the above policy schemes, the effect of RDSTS and RHVDC tie-line using FOPDN-FOPIDN controller is investigated, and the use of RHVDC tie-line with AC tie-line is explored. System dynamic response comparison with parallel AC-RHVDC tie-lines reveals better performance over AC tie-line and RHVDC tie-line when used alone.

A Two-Degree-of-Freedom Controller Design Satisfying Separation Principle With Fractional-Order PD and Generalized ESO

This article proposes a two-degree-of-freedom fractional-order proportional derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal set-speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor servo system. The GESO simplifies the control plant, estimates and actively rejects total disturbances. The FOPD controller achieves fast speed tracking with almost no overshoot. Furthermore, it is verified that the control system with the proposed FOPD-GESO controller design meets the separation principle through mathematical derivation and simulation illustration. It shows that the proposed controller breaks the inherent tradeoff on tracking performance and disturbance robustness of the typical traditional proportional–integral–derivative (PID) control. Meanwhile, a systematic scheme for designing the FOPD-GESO controller to satisfy both frequency-domain and time-domain specifications is proposed in this article. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID controller, integer-order active disturbance rejection control with a typical extended state observer, and fractional-order PID controller in terms of speed tracking, antiload disturbance, and robustness to internal uncertainties.

Stability, bifurcation prediction and optimal control of a delayed integer-order small-world network based on the fractional-order PD control policy of variable order

In this paper, a fractional-order Proportional-Derivative (PD) control policy of variable order is initially designed in solving the problems of Hopf bifurcation and optimal control on the integer-order small-world network. Firstly, the time delay of the network as a key parameter is selected as the bifurcation parameter. Meanwhile, the impact of it is considered on dynamics of the controlled network. In order to analyse the dynamics of the controlled network, two methods are used to make the equivalent transformation for it and the analysis shows that transformed networks have similar linear features near the equilibrium point when variable order is a rational number. Then, through implementing the eigenvalue analysis for the characteristic equations of transformed networks, we are able to acquire some control conditions which can enable the controlled network to be stable or occur Hopf bifurcation. The finding represents that the bifurcation dynamics of the controlled network are effectively optimized by tuning the control parameters. Finally, numerical simulation results are illustrated to prove the availability of the designed control strategy and provide some diagrams between the bifurcation threshold and the control parameters. The diagrams indicate that there is an optimal order to maximize the bifurcation threshold of the controlled network under the fixed control gains.