FOPI Controller Research Articles

Fractional Order Controller for Non-linear Current Control Technique

linear and Non-Linear controller shows their best performance under different power quality conditions. However, under sub transient condition these controller shows sluggish performance. This paper introduces the application of Fractional order [FO] controller in real world power system phenomena. FO-controller based on proportional integral control action was used here for grid interconnection of inverter. Different power quality issues such as Real & Reactive Power exchange between renewable source and grid have been presented here. Matlab Simulink model was developed for a real-world grid connected model in order to check the robustness of the controller. A comparison between the PI controller and FO-PI controller was presented in this paper.

Impact of ultra‐capacitor on automatic generation control of electric energy systems using an optimal FFOID controller

Automatic generation control (AGC) acts as a significant part in alleviating dynamic oscillations and sustaining constancy in frequency and scheduled tie-line power to establish the reliable, secure, and stable operation of electric energy systems under dynamic conditions. AGC needs energy storage system (ESS) and elevated expert, intelligent, and flexible control strategies to ensure generation-demand balance in modern complex structured energy systems following inconsistent load demands. Hence, this paper utilizes a new fuzzy fractional order integral derivative (FFOID) controller along with ultra-capacitor (UC) ESS to solve AGC issue in energy systems effectively. The imperialist competitive algorithm is employed to tune the output scaling factors like integral, derivative, and noninteger order of integrator/derivative of FFOID controller using ISE performance index. Initially, the technique is applied on a one-area nonreheat thermal system. Then, to demonstrate its competency and scalability, the study is boosted to prevalent two-area nonreheat thermal, two-area multisource multi-unit hydrothermal, and three-area reheat thermal energy system models. The advantage of the proposed controller is demonstrated by juxtaposing the outcomes with those offered by various best claimed intelligent control approaches expressed in the contemporary literature and fuzzy proportional integral (FPI)/fuzzy FO PI (FFOPI) controller. The UC with the FFOID controller outperforms other methods. The robustness analysis proves that parameters of the utilized controller acquired at nominal situation are healthy enough and necessarily not needed to retune under broad alterations in the system loading/parameters, size/position of load perturbation, and under the appearance of system constraints and random load pattern with/without noise.

Fractional order controllers for throughput and product quality control in a grinding mill circuit

This paper presents the design and application of a multiple-input–multiple-output fractional order proportional-integral (MIMO FOPI) controller to a grinding mill circuit. The MIMO FOPI controller parameters are tuned using an off-line optimization process based on Particle Swarm Optimization (PSO). Its performance is compared to a single-input–single-output fractional order proportional-integral (SISO FOPI) controller designed and tuned using the same procedure based on PSO. The results show that the MIMO FOPI achieves better results compared to the SISO FOPI controller in most of the cases simulated, even in the presence of hardness and composition variations in the processed ore, and also in the presence of process noise.

Load mitigation of a class of 5-MW wind turbine with RBF neural network based fractional-order PID controller

In variable-pitch wind turbines, pitch angle control is implemented to regulate the rotor speed and power production. However, mechanical loads of the wind turbines are affected by the pitch angle adjustment. To improve the performance and at the same time alleviate the mechanical loads, a gain-scheduling fractional-order PID (FOPID), where a trained RBF neural network chooses its parameters is proposed. The database, which the RBF neural network is trained based on, is created via optimization of a FOPID in several wind speeds with chaotic differential evolution (CDE) algorithm. The simulation results are compared to an RBF based PID controller that is designed via the same method, a conventional gain-scheduling baseline PI controller developed by NREL, an optimal RBF based PI controller, and a FOPI controller. The simulations indicate that the RBF based FOPID improves the control performance of the benchmark wind turbine in comparison to the other controllers, while the applied loads to the structure are mitigated. To validate the performance and robustness, all controllers are implemented on FAST wind turbine simulator. The superiority of the proposed FOPID controller is depicted in comparison to the other controllers.

Electronically reconfigurable two-path fractional-order PI/D controller employing constant phase blocks based on bilinear segments using CMOS modified current differencing unit

This work introduces a versatile type of electronically controllable bilinear transfer segments, i.e. two ports allowing independent electronic control of zero and pole of transfer function, based on modified current differencing unit (MCDU) active element. These proposed bilinear transfer segments serve for construction of fractional-order constant phase block (φα = ±15° and ±36°, i.e. orders α = ±1/6 and ± 2/5, tested in our case) representing electronically controllable integrator or differentiator (in dependence on current demand) as a part of novel two-path system of the fractional-order proportional-integral or derivative (FOPI/D) controller. The example of design procedure employs four bilinear transfer segments, electronically controllable proportional path and summing stage. Cadence IC6 Spectre simulation results (TSMC 0.18 μm CMOS process) in both frequency and time domain are performed in order to confirm expected behavior of the system. An application of the proposed FOPI controller in control of linear voltage regulator is also demonstrated and performance improvements of the proposed design are discussed.

Disturbance observer based speed control of PMSM using fractional order PI controller

In this paper, fractional order PI &#x0028 FOPI &#x0029 control is developed for speed control of permanent magnet synchronous motor &#x0028 PMSM &#x0029. Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM. All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer &#x0028 NLDO &#x0029 to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB &#x002F SIMULINK and results are presented.

Normalized Robust FOPID Controller Regulation Based on Small Gain Theorem

In this paper, a normalized robust FOPID controller regulation algorithm is proposed. Only one parameter k is necessary to be tuned in the controller regulation process, so the proposed control algorithm is convenient to be applied on both fractional-order systems and integer-order systems. A robustness evaluation function is constructed based on the small gain theorem. Larger robustness evaluation function value will help the system achieve better robustness performance. Another parameter, β, is also available to serve as a tuning knob when larger robust evaluation function value is needed. Therefore, the controlled systems can be stabilized and can achieve quite satisfactory robust control performance using the proposed algorithm. The corresponding robust analysis results are obtained according to different conditions in the discussion. For a special case of widely used fractional-order systems, the FOPI and FOID controllers are presented based on the same tuning scheme together with their robustness discussion. Some examples are shown to verify the robustness of systems controlled by the proposed algorithm.

Enhancement of DFIG performance at high wind speed using fractional order PI controller in pitch compensation loop

Doubly fed induction generator (DFIG) has been widely applied in wind farms. Meanwhile, DFIG control at high wind speeds has become an important issue. In this regard, the main task of pitch angle control loop is too important by the wind speed increase above the middle speeds (e. g. 12 m/s) to limit DFIG active power and rotor speed and to control the machine performance. In this study, a fractional order PI controller (FOPI) is designed and applied for the pitch angle compensation control loop to improve the DFIG performance at the high wind speed of 18 m/s. Due to using the fractional order coefficient as an extra control variable in the FOPI controller function in comparison with the PI controller, a preferable control scheme would be realized in the pitch angle control by the wind speed increase to high values. In this regard, the various simulation results for monitoring the active power and rotor speed are obtained in the multi machine test system including the DFIGs considering high wind speed operating mode via using MATLAB/SIMULINK software. In addition, different kinds of transient faults are considered to evaluate the performance of the proposed FOPI controller, instead of the conventional PI controller. The results validate the advantage of using the FOPI control scheme in the pitch angle control loop for promoting the DFIG active power and rotor speed profiles.

Design and real time implementation of sliding mode supervised fractional controller for wind energy conversion system under sever working conditions

Wind energy conversion system (WECS) is increasingly taking the place to be the most promised renewable source of energy, which obliges researchers to look for effective control with low cost. Thus, this paper proposes to build a suitable controller for speed control loop to reach the maximum power point of the wind turbine under sever conditions and to ensure the stability of the outer voltage regulation loop to meet high range of load variations. In literature, a major defect of the well-used conventional PI controller is the slow response time and the high damping. Nowadays, intelligent controllers have been used to solve the drawbacks of the conventional ones but they demand high speed calculators and expensive cost. Moreover, many solutions proposed the fractional order PI controller (FO-PI) by extending the order of integration from integer to real order. The FO-PI controller presents also some weakness in steady state caused by the approximation methods. The idea of this paper is to propose a Sliding Mode Supervised Fractional order controller (SMSF) which consists of conventional PI controller, FO-PI controller and sliding mode supervisor (SMS) that employs one of the controllers to ensure good steady and transient states. WECS laboratory prototype is built around real-time dSPACE cards and evaluated to verify the validity of the developed SMSF. The results clearly fulfill the requirements, confirm its high performance in steady and transient states and demonstrate its feasibility and effectiveness.

Design of Dual Mode Fractional Order PI Controllers Based Type-III SVC Model for Multi Wind-Diesel Isolated Hybrid Power Systems

This paper presents the design of dual-mode Fractional order controller based type-III SVC model for isolated multi wind-diesel hybrid power systems. In conventional SVC type-III model the VAR regulator output is based upon proportional plus integral terms. Generally, the gains of the controllers are selected on the basis of a typical load; also these controllers, employed in type-III SVC model, do not eliminate the conflict between the static and dynamic accuracy. Hence, this paper proposes the advantage of dual mode concept and FOPI controllers on a new design of dual mode FOPI controller based type-III SVC model for isolated multi wind-diesel hybrid power systems. The simulation results show the proposed dual mode FOPI controller based type-III SVC model as having better responses than the conventional type-III SVC model. It is also found that the proposed model is found less sensitive to system parameter variation and robust under different operating conditions of the power systems.

Hybrid Optimization Based FOPI Controller Design with Real-Time Validation

A hybrid optimization technique has been adopted for the tuning of fractional-order PI controller parameters for satisfying a predefined set of gain and phase margin specifications. The algorithm aims at determining a set of optimal controller parameters by minimizing an objective function framed using the equations defining the margins and corresponding cross-over frequencies. Further, the integrated controlled system has been implemented on a digital signal processor advanced control engineering (dSPACE DS1103) platform and the fractional controller design scheme has been experimentally validated in time and frequency domain for its real-world applicability.

Fractional Order Controller for Controlling Power System Dynamic Behavior

AbstractSeveral power system networks exhibit bifurcation, chaos and instability behavior for some specific values of initial conditions and parameters. Angle and voltage instability behavior of power system is prone to such specific values and parameter variation. This paper proposes fractional order proportional integral controller (FOPI) based state feedback for precise and robust control of such undesirable behavior. This paper proposes first ever use of FOPI for precise rotor angle control leading to instability in power system dynamic behavior. FOPI controller is applied on generator connected to IEEE‐14 bus benchmark model. The ripple frequency of turbine torque is chosen as one of the cause of instability behavior of power system, which has the potential possibility to push system behavior to chaos and instability mode. The proposed FOPI controller design will inhibit the dynamic behavior of power system to safe and stable bounds. Proposed strategy can be applied to other large power system models as well due to its simplicity in design philosophy. Several phase plane trajectories with and without FOPI controller are used to support the viewpoint.

Optimal fractional order PI control applicability for enhanced dynamic behavior of on-grid solar PV systems

This paper aims at finding the optimal gain scheduling of the conventional Proportional Integral (PI) and the Fractional Order (FOPI) through the use of the advanced meta-heuristic optimization techniques in PV-grid connected systems. Therefore, the hybridization of the optimization techniques with both PI and FOPI controllers is proposed for attaining an optimal dynamic performance through a specific criterion. This latter is a function of different response characteristics such as the settling time, maximum overshoot, steady state error and execution time. Based on the proposed criterion, the meta-heuristic technique that provides the best enhanced dynamic performance can be simply identified. For this purpose, a comprehensive state of art of the on-grid PV system performance dilemma is initially discussed. The problem of designing current and voltage regulators for the PV-grid connected system is addressed, seeking for an adequate dynamic behavior. Then, different metaheuristic optimization techniques such as Artificial Bee Colony (ABC), Cuckoo Search (CS), Grey Wolf Optimizer (GWO), Mine Blast Algorithm (MBA), Whale Optimization Algorithm (WOA) and Moth Swarm Algorithm (MSA) are employed for determining the optimal PI/FOPI controller gains, forming a hybrid optimal FOPI or PI control. From the numerical simulation analysis of Matlab™/Simulink results, the significant dynamic behavior enhancement of the overall on-grid PV system is illustrated using PI/FOPI controllers optimally tuned with the proposed meta-heuristic algorithms considering solar irradiation variation conditions. The impact of the optimized PI and FOPI controllers on the overall system dynamic responses is explicitly analyzed while using different meta-heuristic algorithms through qualitative and quantitative comparisons.

Tuning strategy of fractional‐order proportional integral controllers for permanent magnet synchronous motor servo system based on enhanced stochastic multi‐parameters divergence‐based optimisation algorithm

This study concentrates on the study of optimisation-based tuning method of fractional-order proportional integral (PIλ or FOPI) controller, and the application of FOPI controller in permanent magnet synchronous motor servo drive system. The main contribution lies in two aspects: (i) A practical FOPI tuning method is proposed. The tuning method formulates a non-linear optimisation problem by maximising the closed-loop bandwidth with constraints on complementary sensitivity, and gain and phase margin. Compared with the existing FOPI tuning strategies, the proposed method is suitable for both integer order and fractional order control systems and, it fully considers the stability requirement of the servo system. (ii) An enhanced stochastic multi-parameters divergence-based optimisation (SMDO) algorithm is presented to solve the non-linear optimisation problem in the FOPI tuning. The enhanced SMDO has the advantages of easy to implement, effective for fast convergence to minima, stochastic in nature and simple adaption to real-time application. Compared with the traditional SMDO method, enhanced SMDO owns faster convergence speed and better global search ability. Experiments are presented to demonstrate the effectiveness of the proposed tuning method and enhanced SMDO algorithm.

Design of fractional-order PI controllers and comparative analysis of these controllers with linearized, nonlinear integer-order and nonlinear fractional-order representations of PMSM

Mathematical model of permanent magnet synchronous motor (PMSM), which is also popularly known as sinusoidal BLDC motor, is highly nonlinear. Speed control of this motor is a cascade control structure which has two distinct loops: an inner current control loop and outer speed control loop. In this paper, we present the design of fractional proportional-integral (PI) controller using small-signal model of PMSM. The basic scheme used for speed control is field-oriented control wherein constant torque angle control is obtained by zero direct-axis current. This requires three PI controllers: one for direct-axis current to keep at zero; another for quadrature axis current to maintain at maximum; and the third for the speed to keep at the reference level. In this paper, we have replaced all three PI controllers with fractional-order (FO) PI controllers, where order of integrator is fractional. These three FOPI controllers are tested on integer-order nonlinear model as well as fractional-order nonlinear model of PMSM using MATLAB simulink and FOMCON toolbox. The comparative analysis shows superior performance of the FOPI controllers for FO PMSM.

Craziness Particle Swarm Optimization based FOPI Controller for liquid level control of HCT

Craziness Particle Swarm Optimization based FOPI Controller for liquid level control of HCT

Stability regions of closed loop system with One Non-Integer Plus Time Delay plant by fractional order PID controller

In this paper, a simple method for finding the stability region of feedback control system with One Non-Integer Plus Time Delay (NIOPTD-I) plant and fractional order Proportional Integral Derivative (FOPID) controller is presented. Analytical expressions for finding the asymptotic stability regions in (X, Y, Z) space are derived using D-partition method. Stability regions are obtained for various fractional orders of P\(I^{\lambda }D{^\mu }\) controller in the range of (0, 2). Fractional order parameters are chosen such that larger stability region in positive direction than integer order parameters is obtained. Controller tuning parameters are chosen from the obtained stability region. The use of proposed FOPID controller for the NIOPTD-I plant increases the stability region and also the degree of freedom increases from three to five in comparison to FOPI controller. Knowledge of these stability regions makes design of controller easier. Effectiveness of the proposed method is illustrated with examples, which shows better control performance.

Design, Analysis and Performance Evaluation of Fractional Order Proportional Integral for Three Interacting Tank Process in Frequency Domain considered as Third Order System

Conventional Integer order Proportional Integral Derivative (IOPID) are the workhorse for the control of almost 90% of the Industrial processes due to its structural simplicity. With the application of fractional calculus in the field of control engineering, Fractional Order (FO) PID controllers are gaining popularity since it requires a slight modification of the integer order PID controller. Tuning of the Integer Order PID controller parameters are by well known techniques like Ziegler Nichols method, Cohen Coon Method, etc mostly time domain based and few frequency techniques are also available. In the present research work, an attempt has been made to tune the FOPI controller using Frequency domain specifications. Frequency domain specifications considered for the design includes the Phase Margin specification, Gain crossover frequency specification and robustness to gain variations. The proposed control schemes are applied to three interacting tank process represented as third order system and verified under servo, regulatory, servo-regulatory response and robustness conditions. Comparison of the time domain performance indices are performed to guarantee the superiority of the proposed scheme.

Fuzzy Fractional Order Proportional Integral Controllers for UAV Lateral Attitude Control System

This article is based on the theory of fractional calculus control, and put forward a kind of fractional order PI controller design method for lateral attitude control system of unmanned aerial vehicle (UAV) model. And the unit step response of the control system is analyzed in the simulation to improve the UAV flight control system stability and robustness. Use the controller parameter tuning method and combined with fuzzy reasoning to design IOPID controller, FOPI controller and fuzzy fractional order PI controller. Then, by exploiting Matlab, the frequency domain response and unit step response characteristics of the different control systems can be plotted. The results verified that the designed fuzzy fractional order controller for the attitude control system is effective.

Robust Fractional Order Proportional Integral Control for Large Time-Delay System

In this paper, a new control method for large time delay system is proposed. Firstly, the decreasing time delay controller is used to remodel large delay time plant into small delay time plant. Then, a fractional robust proportional-integral controller (FOPI) is designed, using the phase margin and cut-off frequency at a specified point in the Bode plot of flat robust conditions, to guarantee the desired control performance and the robustness of the high order system to the gain order system. For comparison between the fractional order proportional integral controller and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. The simulation results indicates that the both designed controllers work efficiently. Furthermore, the FOPI controller makes the large time-delay system get better control effect, the system has high robustness, adaptive ability and anti-jamming ability.