Fractional Order Fuzzy PID Controller Research Articles

Fractional Order Fuzzy PID Control of Automotive PEM Fuel Cell Air Feed System Using Neural Network Optimization Algorithm

The air feeding system is one of the most important systems in the proton exchange membrane fuel cell (PEMFC) stack, which has a great impact on the stack performance. The main control objective is to design an optimal controller for the air feeding system to regulate oxygen excess at the required level to prevent oxygen starvation and obtain the maximum net power output from the PEMFC stack at different disturbance conditions. This paper proposes a fractional order fuzzy PID controller as an efficient controller for the PEMFC air feed system. The proposed controller was then employed to achieve maximum power point tracking for the PEMFC stack. The proposed controller was optimized using the neural network algorithm (NNA), which is a new metaheuristic optimization algorithm inspired by the structure and operations of the artificial neural networks (ANNs). This paper is the first application of the fractional order fuzzy PID controller to the PEMFC air feed system. The NNA algorithm was also applied for the first time for the optimization of the controllers tested in this paper. Simulation results showed the effectiveness of the proposed controller by improving the transient response providing a better set point tracking and disturbance rejection with better time domain performance indices. Sensitivity analyses were carried-out to test the robustness of the proposed controller under different uncertainty conditions. Simulation results showed that the proposed controller had good robustness against parameter uncertainty in the system.

Robust type-2 fuzzy fractional order PID controller for dynamic stability enhancement of power system having RES based microgrid penetration

The increased penetration of renewable energy sources (RES) based microgrid (MG) to the power system can affect the system stability due to the difference in dynamic characteristics of this kind of MG from the conventional generators. The reduction in system inertia caused by these power electronics interfaced renewable power generations introduces a negative effect in the dynamic stability of the system and may cause ensuing instability problems. On the other hand, power injection of RES based MG improves the damping performance with the reduction of transmission line congestion and power loss. Thus it becomes imperative to analyze the new dynamic stability concerns and control performance of a power system in the context of increased MG penetration. This study thoroughly investigates the impact of RES based MG penetration on the dynamic stability and control of a multi-machine multi-area system under varying operating conditions. The design of a novel type-2 fuzzy fractional order PID based power system stabilizer (PSS) using a meta-heuristic hybrid algorithm is presented in this paper for improving the electromechanical oscillation damping performance of the power system to enhance the dynamic stability. The large bandwidth, memory effect and flat phase contribution in the frequency response of fractional-order PID controllers are exploited to make the controller perform well against a wide range of system uncertainties in the presence of an MG. First, the parameter tuning problem of the type-2 fuzzy fractional order PID controller is transformed to an optimization problem that is solved using a hybrid algorithm by combining a dynamic genetic algorithm (DGA) with a bacteria foraging algorithm (BFA). The capability of the proposed controller in damping the low-frequency oscillations in the system with various MG penetration ratios is assessed through non-linear time-domain simulations and some performance indices under different disturbances and operating conditions.

A novel application of ALO-based fractional order fuzzy PID controller for AGC of power system with diverse sources of generation

The operation and control of the modern power system has become complex and difficult due to the incessant penetration of nonconventional energy sources integrated to the power grid and the structural variation of power system with continuing escalation of power demand in recent years. This entails the implementation of intelligent control strategy for satisfactory operation of the power system. Hence, a fractional order fuzzy proportional integral derivative (FOFPID) controller is suggested in this article for automatic generation control of two unequal area interconnected power system with diverse generating units such as thermal, hydro, diesel and wind power plants. The dynamic performance of the system is investigated by using proportional integral derivative (PID), fractional order PID (FOPID), fuzzy PID (FPID) and fractional order fuzzy PID (FOFPID) controllers separately. The parameters of these controllers are optimised by using ant lion optimiser algorithm with integral time absolute error as the objective function. The supremacy of the proposed controller is established by contrasting the results with FPID, FOPID and PID controllers. It is also observed that FPID controller gives superior result than PID and FOPID controllers. Further it is found that the result of FOPID controller is better than the integer order PID controller. Finally robustness analysis is performed to confirm the robustness of the proposed controller against parametric variations and random loading of the system.

A novel optimized fractional-order hybrid fuzzy intelligent PID controller for interconnected realistic power systems

This article presents a novel hybrid fractional-order intelligent proportional-integral-derivative (PID) controller integrated with a fractional-order fuzzy PID controller for load frequency control of a realistic interconnected two-area power system, where each area is powered from a different source. The strategy presented here involves incorporating a damping controller based on a thyristor-controlled series capacitor in the system. In doing so, the parameters of the current controller are optimized via craziness-based particle swarm optimization. The effectiveness of the strategy presented here in load frequency control is validated by extensive simulation examples. The results are compared with a recently published technique based on a fractional-order PID controller. Finally, the sensitivity analysis of the plant is studied by varying the plant parameters and operating load conditions from their prescribed values. It is observed that the current controller is a robust controller and performs satisfactorily with variations in system parameters and load patterns.

Design and simulation of self-tuning fractional order fuzzy PID controller for robotic manipulator

Two-link robotic manipulator system is completely nonlinear and time-varying multi-input-multiple output. In this research, the fractional order fuzzy PID (FOFPID) controller is proposed in order to control the robotic manipulator position. Since real control systems are generally nonlinear systems, therefore, better control of these systems requires the usage of an adaptive or nonlinear controller. So we applied a fuzzy system in order to determine the coefficients of a FOPID controller based on particle swarm optimization (PSO) algorithm. In definition of fitness function for this optimization, we considered integral of absolute error (IAE) and integral of absolute change in controller output (IACCO). Finally, in order to compare this controller with the FPID controller, numerical simulations were performed on the robotic manipulator. The results demonstrate that the overshoot of FOFPID controller is less than the FPID and proposed controller has less oscillations amplitude, totally, its performance is better than the FPID controller.

Modeling and Oil Contamination Influence Control of a Vehicle Mounted and Unbalanced Barrel Pitching System

The vehicle mounted and unbalanced barrel pitching system is a typical kind of high precision electrohydraulic servo system. The key to system control is not only to overcome the influence of external interference such as unbalanced torque and road fluctuation, but also to suppress the influence of internal parameters’ change induced by oil contamination. Firstly, the overall model of barrel pitching system is established and its sensitivity analysis is conducted, and then the correction link and the pressure difference feedback loop are respectively designed to suppress the influence of unbalanced torque and road fluctuation. Secondly, the influence of oil contamination is categorized and the core decay parameters are determined, and then the fractional order fuzzy PID controller is designed. Finally, the simulation model of MATLAB/Simulink is built and the system simulation is carried out. The results show when the given angle is fixed on 25°, the setting time is reduced to 0.2 s, and the maximum steady state error is only 0.000132 rad. Thus, the presented method is effective for barrel pitching system’s control, and the service life of the equipment can be prolonged under the same required accuracy.

Design and simulation of self-tuning fractional order fuzzy PID controller for robotic manipulator

Design and simulation of self-tuning fractional order fuzzy PID controller for robotic manipulator

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers.

Fractional order fuzzy PID optimal control in copper removal process of zinc hydrometallurgy

The copper removal process is the first stage of purification in zinc hydrometallurgy. Due to its dynamic characteristics and complex reaction mechanism, a robust and effective controller to maintain high quality and stability of the outlet-ion-concentration is in great need. In this paper, a fractional order fuzzy proportional integral derivative (FOFPID) controller based on fuzzy logic is proposed to meet this challenge. The proposed work is conducted through a combination of three novel interdependent efforts. First, controller design problem is transformed into a nonconvex optimization problem. Second, a novel method named state transition algorithm (STA) is employed to solve the aforementioned optimization problem. Furthermore, in order to evaluate the performance of the proposed control strategy, the response performance of the system is analyzed. Finally, further tests are carried out to evaluate the performance of FOFPID controller, where disturbances caused by the measurement, flow rate, and inlet-ion-concentration are all taken into account. The simulation results demonstrate the superiority of the FOFPID controller in copper removal process over the competing FOPID and manual control in the same application environment.

An expert 2DOF fractional order fuzzy PID controller for nonlinear systems

This work presents a generic two-degree-of-freedom fractional order fuzzy PI-D (2DOF FOFPI-D) controller dedicated to a class of nonlinear systems. The control law for proposed scheme is derived from basic 2DOF fractional order PID controller in discrete domain. Expert intelligence is embedded in overall derived control law by utilizing formula-based fuzzy design methodology. The controller structure comprises of fractional order fuzzy PI (FOFPI) and fractional order derivative filter to handle multiple issues and provides flexibility in design and self-tuning control feature. Further, the proposed scheme is compared with its integer order counterpart and 2DOF PI-D controller for coupled nonlinear 2-link robotic arm in real operating environment. The parameters of designed controllers are optimally tuned using multi-objective non-dominated sorting genetic algorithm-II for attaining low variation in control effort and error index. Intensive simulation studies are performed to analyze trajectory tracking, model uncertainty, disturbance due to cogging, sensor noise and noise as well as disturbance rejection simultaneously. Results demonstrate the superior performance of 2DOF FOFPI-D controller as compared to other designed controllers in the facets of different operating conditions.

Efficient control of integrated power system using self-tuned fractional-order fuzzy PID controller

The integrated power system (IPS) uses various autonomous generation and energy storage systems like aqua electrolyzer, battery, diesel engine, flywheel, fuel cell, solar photovoltaic, ultracapacitor, wind turbine, etc. These may be switched on/off and may run at higher/lower power outputs, at different times. Additionally, IPS is also subjected to parameter variations of its components and the load. As a result, the frequency of an IPS fluctuates from the nominal desired value and therefore it requires a robust controller to accomplish the above-mentioned task. In this work, a self-tuned fractional-order fuzzy PID (STFOFPID) controller, tuned using cuckoo search algorithm, is investigated for efficient control of IPS. STFOFPID is essentially a Takagi–Sugeno model-based fuzzy adaptive controller comprising of non-integer-order differ-integral operators. To assess the relative performance of STFOFPID controller, it is compared with its integer-order counterpart on the basis of their respective objective function value defined as the sum of integral of squared error and integral of squared deviation of controller output. Intensive LabVIEW-based simulation studies have indicated the robustness and hence superiority of STFOFPID controller over its integral counterpart.

Fuzzy Fractional-Order PID Controller for Fractional Model of Pneumatic Pressure System

This article presents a fuzzy fractional-order PID (FFOPID) controller scheme for a pneumatic pressure regulating system. The industrial pneumatic pressure systems are having strong dynamic and nonlinearity characteristics; further, these systems come across frequent load variations and external disturbances. Hence, for the smooth and trouble-free operation of the industrial pressure system, an effective control mechanism could be adopted. The objective of this work is to design an intelligent fuzzy-based fractional-order PID control scheme to ensure a robust performance with respect to load variation and external disturbances. A novel model of a pilot pressure regulating system is developed to validate the effectiveness of the proposed control scheme. Simulation studies are carried out in a delayed nonlinear pressure regulating system under different operating conditions using fractional-order PID (FOPID) controller with fuzzy online gain tuning mechanism. The results demonstrate the usefulness of the proposed strategy and confirm the performance improvement for the pneumatic pressure system. To highlight the advantages of the proposed scheme a comparative study with conventional PID and FOPID control schemes is made.

Online tuning of fractional order fuzzy PID controller in smart seismic isolated structures

This paper aims at designing an adaptive fractional order fuzzy proportional–integral-derivative controller for seismic control of smart base-isolated structure by means of variable friction dampers (VFD). One main challenge occurs when large displacement of the isolator happens due to near-field motions. To overcome this challenge, a solution is to use VFDs. However, the floor accelerations of the superstructure can increase because of sudden changes in the damper friction force of VFDs. Therefore, a suitable control strategy is desired to handle the displacement of isolator without any increase in superstructure acceleration responses during both far-field and near-field earthquakes. First, a sub-level fractional order fuzzy PID (FOFPID) controller is designed to reduce the isolator displacement without significant increase in roof acceleration based on a multi-objective optimization algorithm. Using an adaptive strategy, the fuzzy rule weights of the FOFPID controller are then tuned on-line based on information sensed from both the earthquake and the building responses. Considering nine important performance criteria and several real-data earthquakes, numerical studies are carried out for a benchmark base-isolated structure equipped with VFDs. Simulation results show the superior performance of the proposed controller in mitigation of seismic responses of base-isolated structure against various types of earthquakes in comparison with other controllers presented in previous researches.

Fractional order fuzzy PID controller for wind energy‐based hybrid power system using quasi‐oppositional harmony search algorithm

In this study, a novel fuzzy logic control scheme is investigated for the frequency and power control of an isolated hybrid power system (HPS) (IHPS) and HPS-based two-area power system. The studied IHPS comprises of various autonomous generation systems such as wind energy, diesel engine generator and an energy storage device (i.e. capacitor energy storage device). A novel fractional order (FO) fuzzy proportional-integral-derivative (PID) (FO-F-PID) controller scheme is deployed and the various tunable parameters of the studied model are tuned by quasi-oppositional harmony search (HS) (QOHS) algorithm for improved performance. The QOHS algorithm (based on standard HS algorithm) accelerates the convergence speed by combining the concept of quasi-opposition in the basic HS framework. This FO-F-PID controller shows better performance over the integer order-PID and F-PID controller in both linear and non-linear operating regimes. The proposed FO-F-PID controller also shows stronger robustness properties against loading mismatch and different rate constraint non-linarites than other controller structures.

Adaptive fractional order fuzzy proportional–integral–derivative control of smart base-isolated structures equipped with magnetorheological dampers

The current semi-active or even active control strategies have been developed to address a few drawbacks, such as unwanted large displacements created at the base level and system deficiency in adaptation to different types of seismic excitations, in the base isolation systems. In this article, two control strategies, multi-objective modified clipped optimal and adaptive fractional order fuzzy proportional–integral–derivative, are proposed for semi-active control of a smart base-isolated structure equipped with a magnetorheological damper. The main objective is to reduce the displacement of isolation system without allowing significant increase in the acceleration of superstructure for both far-field and near-field earthquake excitations. Using proper fitness functions, the weighting matrices of the multi-objective modified clipped optimal controller are tuned using multi-objective optimization. Then, the parameters of the fractional order fuzzy proportional–integral–derivative controller are obtained. Next, the fuzzy rule weights of the fractional order fuzzy proportional–integral–derivative controller are updated online based on the values of ground motion and structural responses using an adaptive strategy. For comparison, two control cases in which the magnetorheological damper is in passive mode, passive-off and passive-on, are considered. Numerical simulations show that the proposed adaptive fractional order fuzzy proportional–integral–derivative controller better mitigates the seismic responses of a base-isolated structure excited by a range of real-data earthquakes.

AGC of restructured multi-area multi-source hydrothermal power systems incorporating energy storage units via optimal fractional-order fuzzy PID controller

Owing to nonlinear structure and uncertain load demand characteristics, expert and intelligent automatic generation control (AGC) is inevitable for coherent operation and control of electric power system. Hence, in this paper, to mitigate the frequency and power deviations efficiently under sudden load demand conditions, a novel fractional-order fuzzy PID (FOFPID) controller is suggested in AGC of restructured multi-area multi-source hydrothermal power systems. The parameters of FOFPID controller are optimized by utilizing bacterial foraging optimization algorithm. The controller is implemented on restructured two- and three-area systems. It is observed that the advocated method shows superiority over fuzzy PID, fractional-order PID and conventional PID control schemes. Energy storage units such as redox flow batteries (RFB) which show extremely long charge–discharge life cycle and outstanding quick response to alleviate the system oscillations under disturbances have further been incorporated into the studied systems to analyze their efficacy in boosting AGC performance. Analysis of results reveals that with RFB, system transient performance improves significantly. It is also observed that the obtained results satiate the AGC requirement under different power transactions taking place in a deregulated market in the presence/absence of appropriate generation rate constraint treated for thermal and hydro plants. Finally, the robustness of the presented approach is demonstrated against the wide variations in the system parameters and initial loading condition.

Hybridized ABC-GA optimized fractional order fuzzy pre-compensated FOPID control design for 2-DOF robot manipulator

The robotic manipulator is an extremely nonlinear, multi-input multi-output (MIMO), highly coupled, and complex system wherein the parameter uncertainties and external disturbances adversely affect the performance of this system. From this, it necessitates that the controllers designed for such system must overcome these complexities. In this paper, we develop a novel fractional order fuzzy pre-compensated fractional order PID (FOFP-FOPID) controller for 2-degree of freedom (2-DOF) manipulator dealing with trajectory tracking problem. In order to optimize the controller’s parameters while minimizing integral of time absolute error (ITAE), a metaheuristic optimization technique, viz., artificial bee colony-genetic algorithm (ABC-GA) is presented. The efficacy of our proposed controller is demonstrated by comparing it with some existing controllers, such as integer order fuzzy pre-compensated PID (IOFP-PID), fuzzy PID (FPID), and conventional PID controllers. Furthermore, the robustness analysis for proposed controllers is also investigated for parameter variations and external disturbances. The simulation results indicate that FOFP-FOPID controller can not only guarantee the best trajectory tracking but also ameliorate the system robustness for parameter variations as well as external disturbances.

A novel interval type-2 fractional order fuzzy PID controller: Design, performance evaluation, and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.

AGC performance enrichment of multi-source hydrothermal gas power systems using new optimized FOFPID controller and redox flow batteries

Redox flow batteries (RFB) showcase extremely long charge-discharge life cycle and outstanding quick response to alleviate the oscillations under sudden disturbances in power system. The assimilation of energy storage units in power system can curtail the oscillations energetically by contributing fast active power compensation. Hence, in this paper, RFB are tried to integrate into multi-source power systems and their efficacy in boosting automatic generation control (AGC) performance is executed. A new fractional order fuzzy PID (FOFPID) controller is employed to enhance the system performance. FOFPID controller parameters are optimized maidenly by utilizing imperialist competitive algorithm (ICA). The controller is designed and implemented on more realistic single/two-area multi-source hydrothermal gas system with/without RFB. The potency of FOFPID is established by contrasting its responses with optimal and lately developed hSFS-PS, DE, TLBO and IPSO optimized controllers. To check the efficacy of the approach, the study is further conducted under the presence of important non-linearites like GDB and GRC. Analysis of results reveals that the advocated approach with/without RFB improves the system performance significantly in comparison to the prevalent methods. The robustness of the method is demonstrated against wide variations in system parameters under the presence/absence of RFB/GDB-GRC and at higher and variable step load demands.

BFOA-scaled fractional order fuzzy PID controller applied to AGC of multi-area multi-source electric power generating systems

Abstract In the fast developing world of today, automatic generation control (AGC) plays an incredibly significant role in offering inevident demand of good quality power supply in power system. To deliver a quality power, AGC system requires an efficient and intelligent control algorithm. Hence, in this paper, a novel fractional order fuzzy proportional-integral-derivative (FOFPID) controller is proposed for AGC of electric power generating systems. The proposed controller is tested for the first time on three structures of multi-area multi-source AGC system. The gains and fractional order parameters such as order of integrator (λ) and differentiator (µ and γ) of FOFPID controller are optimized using bacterial foraging optimization algorithm (BFOA). Initially, the proposed controller is implemented on a traditional two-area multi-source hydrothermal power system and its effectiveness is established by comparing the results with FOPID, fuzzy PID (FPID) and PI/PID controller based on recently published optimization techniques like hybrid firefly algorithm-pattern search (hFA-PS) and grey wolf optimization (GWO) algorithm. The approach is further extended to restructured multi-source hydrothermal and thermal gas systems. It is observed that the dynamic performance of the proposed BFOA optimized FOFPID controller is superior to BFOA optimized FPID/FOPID/PID and differential evolution (DE)/genetic algorithm (GA) optimized PID controllers. It is also detected that the dynamic responses obtained under different power transactions with/without appropriate generation rate constraint, time delay and governor dead-zone effectively satisfy the AGC requirement in deregulated environment. Moreover, robustness of the suggested approach is verified against wide variations in the nominal initial loading, system parameters, distribution company participation matrix structure and size and position of uncontracted power demand.