Design and Application of Fractional Order PIλDµ Controller in Grid-Connected Inverter System

2017 ◽  
Author(s):  
Zhifeng Pan ◽  
Xiaohong Wang ◽  
Thi Thu Giang Hoang ◽  
Ying Luo ◽  
Yangquan Chen ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Frequency Domain Analysis ◽  
Discretization Method ◽  
Vector Method ◽  
Practical Applications ◽  
Three Phase ◽  
Grid Connected Inverter ◽  
Fractional Order Controller ◽  
Two Parameters

In comparison with the traditional controller PID, the fractional order controller PIλDμ is added with two parameters (μ and λ), that increases the flexibility of the controller. The larger adjustable space makes it more favorable to the control of the nonlinear system like the three-phase grid-connected inverter. However, since the fractional calculus operator is an irrational function on the complex plane, it can’t be implemented directly in simulation or in practical applications. In this paper, the advantages of the fractional order controller PIλDμ will be analyzed, then the fractional calculus operator is fitted by the frequency domain analysis method. Based on the vector method, the fractional order controller PIλDμ of the grid-connected inverter is designed. Simultaneously, the optimal controller parameters are searched with the ITAE and IAE as the performance index. And finally, the results are compared with those of the traditional controller PID. In consideration of the defects of fractional algorithm and single discretization method, a hybrid discretization method is proposed in order to ensure that the discretized controller can keep the same time-domain response and frequency characteristics as the designed controller. The experimental results show that the proposed method has the dynamic and static characteristics better than the traditional controller PID, which proves that the application of fractional order controller in three-phase grid-connected inverter is effective and feasible.

FRACTIONAL CALCULUS BASED STABILIZATION TECHNIQUE APPLIED TO SUPPRESS CHAOS IN CHAOTIC CIRCUITS

2010 ◽  
Vol 24 (24) ◽  
pp. 4861-4879
Author(s):  
MOHAMMAD SALEH TAVAZOEI ◽  
MOHAMMAD HAERI ◽  
SAEID JAFARI
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Chaotic Oscillations ◽  
Practical Applications ◽  
Stability Theorems ◽  
Single Input ◽  
Chaotic Circuits ◽  
The Stability ◽  
Linearized Model ◽  
Stabilization Technique

This paper deals with a new fractional calculus based method to stabilize fixed points of single-input 3D systems. In the proposed method, the control signal is determined by fractional order integration of a linear combination of the system linearized model states. The tuning rule for this method is based on the stability theorems in the incommensurate fractional order systems. The introduced technique can be used in suppression of chaotic oscillations. To evaluate the performance of the proposed technique in practical applications, it has been experimentally applied to control chaos in two chaotic circuits.

Chaotic Modeling of Ferroresonance with Single-Phase Open in a Three-Phase System and Its Fractional-Order Control

2021 ◽  
Vol 31 (08) ◽  
pp. 2150118
Author(s):  
Ali̇ Durdu ◽  
Yilmaz Uyaroğlu
Keyword(s):  
Power Systems ◽  
Fractional Order ◽  
Chaotic System ◽  
Single Phase ◽  
Duffing Oscillator ◽  
Phase System ◽  
Fractional Order Control ◽  
Practical Applications ◽  
Mathematical Expressions ◽  
Three Phase

In this study, a chaos-theoretic method is proposed to model the case of ferroresonance that can occur under nominal conditions in power systems, and the factors that determine the types of ferroresonance to occur are examined. In the ferroresonance chaotic system modeled in Matlab environment, the length of the transmission line and the breaker capacities in the circuit are fixed and its relationship with the transformer efficiency is investigated. In the proposed chaotic modeling, considering the situations that may occur in practical applications, the ferroresonance situations that occur when the single-phase remains open in the three-phase system are examined. In the study, ferroresonance, which occurs when one phase is open in a three-phase system, is analyzed by considering the situations that may happen during practical implementations. The similarity between the mathematical expressions obtained from the systems that create ferroresonance and Duffing oscillator is evaluated. In the chaotic system, fundamental ferroresonance, subharmonic ferroresonance, and chaotic ferroresonance situations are created depending on the transformer loss. Additionally, ferroresonance that occurs when the chaotic system is of fractional-order is analyzed, and it is observed that results of ferroresonance with different fractional-order values are not different. The results show that transformer loss is a significant element to determine the type of ferroresonance in power transformers. Also, when the chaotic system is operated in the fractional-order setting, the ferroresonance cases that occur are re-examined, and it is observed that the system can exit from the chaotic situation and prevent the formation of ferroresonance when fractional-order control is applied. According to the results, the fractional-order method can be used to control ferroresonance.

scholarly journals Experimental Assimilation of Various Tuning Rules with Fractional Order Controller in Inverted Pendulum

2019 ◽  
Vol 8 (6S2) ◽  
pp. 753-757
Keyword(s):  
Fractional Order ◽  
Pid Control ◽  
Pid Controller ◽  
Inverted Pendulum ◽  
Control Parameters ◽  
Controller Tuning ◽  
Tuning Methods ◽  
Fractional Order Controller ◽  
Two Parameters ◽  
Tuning Rules

Modified pendulum is a commonplace trial territory for the investigation of control hypotheses. The adjusting of a reversed pendulum by moving a truck along a flat track is a commonplace issue in the zone of control. So as to improve the capacity of PID controller reacting for the heap unsettling influence, controller tuning guidelines assume fundamental job. This work engaged with enhancement of the PID control parameters for controlling the pendulum in upstanding position particularly with the best heartiness and contrasting it tentatively and ideal settings of a fragmentary PIλDμ controller which can satisfy five distinctive plan details for the shut circle framework, exploiting the fragmentary requests, λ and μ. Since these partial controllers have two parameters more than the customary PID controller improves the presentation of the framework. The pendulum has been adjusted in the upstanding position utilizing the two techniques and the exploratory outcomes are analyzed and announced. The recreation just as exploratory aftereffects of ordinary PID controller demonstrate that the arrangement of new and tuned controller parameters are furnishing the outcomes with better shut circle execution thought about than other tuning methods. And furthermore the control ability and the framework execution furnished by fragmentary request PID controller with the determined new arrangement of parameters has been tentatively demonstrated that the partial request PID controller gives controller execution relatively superior to the customary one along these lines it isn't just controlling the ongoing framework with better adjustment and following control yet additionally have heartiness to aggravations

Research on High Precision and Stability of Three-Phase Rectifier Based on Fractional PIλ Order Controller

2011 ◽  
Vol 130-134 ◽  
pp. 2489-2494
Author(s):  
Fei Yu ◽  
Yi Ming Zhang
Keyword(s):  
Fractional Order ◽  
Control Strategy ◽  
Closed Loop ◽  
Pso Algorithm ◽  
Closed Loop Control ◽  
Loop Control ◽  
Three Phase ◽  
The Stability ◽  
Fractional Order Controller ◽  
Deep Exploration

According to the demand of transmitter for deep exploration, this paper presents a strategy of current double closed loop control based on fractional order controller, which used to improve the tracing performance and anti-interference capability of the current regulating loop, also the stability of load current. And also presents a modified GA-PSO algorithm to get the parameters of fractional order controller. Results show that modified GA-PSO algorithm has faster convergence speed and higher accuracy, new control strategy using in three-phase PWM voltage rectifier has remarkably improved the stability and anti-interference capability of system.

scholarly journals Design of Low-Voltage FO-[PD] Controller for Motion Systems

2021 ◽  
Vol 11 (2) ◽  
pp. 26
Author(s):  
Rafailia Malatesta ◽  
Stavroula Kapoulea ◽  
Costas Psychalinos ◽  
Ahmed S. Elwakil
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Degrees Of Freedom ◽  
Low Voltage ◽  
Laplacian Operator ◽  
Practical Applications ◽  
Operational Transconductance Amplifiers ◽  
Significant Research ◽  
Analog Implementation ◽  
Fractional Order Controller

Fractional-order controllers have gained significant research interest in various practical applications due to the additional degrees of freedom offered in their tuning process. The main contribution of this work is the analog implementation, for the first time in the literature, of a fractional-order controller with a transfer function that is not directly constructed from terms of the fractional-order Laplacian operator. This is achieved using Padé approximation, and the resulting integer-order transfer function is implemented using operational transconductance amplifiers as active elements. Post-layout simulation results verify the validity of the introduced procedure.

Mkhitar Djrbashian and his contribution to Fractional Calculus

2020 ◽  
Vol 23 (6) ◽  
pp. 1797-1809
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Approximation Theory ◽  
Fractional Derivatives ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Modern Theory ◽  
Survey Paper ◽  
The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

scholarly journals Optimal Fractional PID Controller for Buck Converter Using Cohort Intelligent Algorithm

2021 ◽  
Vol 4 (3) ◽  
pp. 50
Author(s):  
Preeti Warrier ◽  
Pritesh Shah
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Power Converters ◽  
Buck Converter ◽  
Optimization Techniques ◽  
Superior Performance ◽  
Computational Time ◽  
Optimization Approach ◽  
Response Characteristics ◽  
Fractional Order Controller

The control of power converters is difficult due to their non-linear nature and, hence, the quest for smart and efficient controllers is continuous and ongoing. Fractional-order controllers have demonstrated superior performance in power electronic systems in recent years. However, it is a challenge to attain optimal parameters of the fractional-order controller for such types of systems. This article describes the optimal design of a fractional order PID (FOPID) controller for a buck converter using the cohort intelligence (CI) optimization approach. The CI is an artificial intelligence-based socio-inspired meta-heuristic algorithm, which has been inspired by the behavior of a group of candidates called a cohort. The FOPID controller parameters are designed for the minimization of various performance indices, with more emphasis on the integral squared error (ISE) performance index. The FOPID controller shows faster transient and dynamic response characteristics in comparison to the conventional PID controller. Comparison of the proposed method with different optimization techniques like the GA, PSO, ABC, and SA shows good results in lesser computational time. Hence the CI method can be effectively used for the optimal tuning of FOPID controllers, as it gives comparable results to other optimization algorithms at a much faster rate. Such controllers can be optimized for multiple objectives and used in the control of various power converters giving rise to more efficient systems catering to the Industry 4.0 standards.

scholarly journals Analysis of Three-Phase Wye-Delta Connected LLC

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3606
Author(s):  
Jing-Yuan Lin ◽  
Chuan-Ting Chen ◽  
Kuan-Hung Chen ◽  
Yi-Feng Lin
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Operation Time ◽  
Time Domain Analysis ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Complete Analysis ◽  
Plane Analysis ◽  
Analysis Methods ◽  
Three Phase

Three-phase wye–delta LLC topology is suitable for voltage step down and high output current, and has been used in the industry for some time, e.g., for server power and EV charger. However, no comprehensive circuit analysis has been performed for three-phase wye–delta LLC. This paper provides complete analysis methods for three-phase wye–delta LLC. The analysis methods include circuit operation, time domain analysis, frequency domain analysis, and state–plane analysis. Circuit operation helps determine the circuit composition and operation sequence. Time domain analysis helps understand the detail operation, equivalent circuit model, and circuit equation. Frequency domain analysis helps obtain the curve of the transfer function and assists in circuit design. State–plane analysis is used for optimal trajectory control (OTC). These analyses not only can calculate the voltage/current stress, but can also help design three-phase wye-delta connected LLC and provide the OTC control reference. In addition, this paper uses PSIM simulation to verify the correctness of analysis. At the end, a 5-kW three-phase wye–delta LLC prototype is realized. The specification of the prototype is a DC input voltage of 380 V and output voltage/current of 48 V/105 A. The peak efficiency is 96.57%.

Sign in / Sign up

Export Citation Format

Share Document