Modeling and analysis of fractional order DC-DC converter

Fractional-order electromagnetic modeling and identification for PMSM servo system

An accurate electromagnetic model is essential for an optimal controller tuning of the high-performance servo system. This paper proposes a fractional-order electromagnetic model of a permanent magnet synchronous motor (PMSM) servo system and an identification methodology of this model. The reason why the investigated electromagnetic model should be a fractional-order one is addressed with a detailed explanation. The influence of voltage source inverter nonlinearity, which may cause system identification error, is analyzed. An improved inverter nonlinearity model and compensation method are proposed to promote the accuracy of the model parameter identification. Compared with the existing typical electromagnetic models of the PMSM servo system, the current open-loop and closed-loop experiments prove that the proposed fractional-order electromagnetic model with time delay is more accurate for the actual physical system. The effectiveness of the proposed nonlinearity modeling and compensation scheme of the inverter is also verified on an experimental PMSM servo system.

Continuous Adaptive Finite-Time Sliding Mode Control for Fractional-Order Buck Converter Based on Riemann-Liouville Definition

This study proposes a continuous adaptive finite-time fractional-order sliding mode control method for fractional-order Buck converters. In order to establish a more accurate model, a fractional-order model based on the Riemann-Liouville (R-L) definition of the Buck converter is developed, which takes into account the non-integer order characteristics of electronic components. The R-L definition is found to be more effective in describing the Buck converter than the Caputo definition. To deal with parameter uncertainties and external disturbances, the proposed approach combines these factors as lumped matched disturbances and mismatched disturbances. Unlike previous literature that assumes a known upper bound of disturbances, adaptive algorithms are developed to estimate and compensate for unknown bounded disturbances in this paper. A continuous finite-time sliding mode controller is then developed using a backstepping method to achieve a chattering-free response and ensure a finite-time convergence. The convergence time for the sliding mode reaching phase and sliding mode phase is estimated, and the fractional-order Lyapunov theory is utilized to prove the finite-time stability of the system. Finally, simulation results demonstrate the robustness and effectiveness of the proposed controller.

Design of Adaptive Fractional-Order Fixed-Time Sliding Mode Control for Robotic Manipulators

In this investigation, the adaptive fractional-order non-singular fixed-time terminal sliding mode (AFoFxNTSM) control for the uncertain dynamics of robotic manipulators with external disturbances is introduced. The idea of fractional-order non-singular fixed-time terminal sliding mode (FoFxNTSM) control is presented as the initial step. This approach, which combines the benefits of a fractional-order parameter with the advantages of NTSM, gives rapid fixed-time convergence, non-singularity, and chatter-free control inputs. After that, an adaptive control strategy is merged with the FoFxNTSM, and the resulting model is given the label AFoFxNTSM. This is done in order to account for the unknown dynamics of the system, which are caused by uncertainties and bounded external disturbances. The Lyapunov analysis reveals how stable the closed-loop system is over a fixed time. The pertinent simulation results are offered here for the purposes of evaluating and illustrating the performance of the suggested scheme applied on a PUMA 560 robot.

DSP-HIL Comparison between IM Drive Control Strategies

Due to their high robustness and simple maintenance, induction motors (IM) are commonly applied in household appliances and industry. Recently, advanced control techniques are being applied to traditional controllers such as field-oriented control (FOC) and torque control (DTC). Dynamic performance improvement, hardware simplification and software resource reduction are some of the characteristics reported by these advanced techniques, where a comparison of the new proposal with a traditional structure is generally reported for its validation. However, an assessment between advanced techniques is usually missing. Therefore, we evaluated the traditional FOC and DTC with two additional advanced control modifications, fuzzy and predictive. The resulting six structures were numerically evaluated using MATLAB SIMULINK in a 5 HP four-pole three-phase IM and practically validated using hardware-in-the-loop (Typhoon HIL 402 and DSP TMS320F28035). Speed, torque, phase current and flux response are reported for the six controllers and practical insights are summarized.

Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter

Fractional-order (FO) differential equations are more and more frequently applied to describe real-world applications or models of phenomena. Despite such models exhibiting high flexibility and good fits to experimental data, they introduce their inherent inaccuracy related to the order of approximation. This article shows that the chosen model influences the dynamic properties of signals. First, we calculated symbolically the steady-state values of an FO inertia using three variants of the Oustaloup filter approximation. Then, we showed how the models influence the Nyquist plots in the frequency domain. The unit step responses calculated using different models also have different plots. An example of FO control system evidenced different trajectories dependent on applied models. We concluded that publicized parameters of FO models should also consist of the name of the model used in calculations in order to correctly reproduce described phenomena. For this reason, the inappropriate use of FO models may lead to drawing incorrect conclusions about the described system.

Fractional-order modeling and control of pneumatic-hydraulic upper limb rehabilitation training system1

In this paper, by replacing the integral mass flow equation to fractional-order mass flow equation, the fractional-order mathematical model of 2DOF pneumatic-hydraulic upper limb rehabilitation training system is established. A new 2DOF fractional-order fuzzy PID (FOFPID) controller is designed, to provides a new reference for improving the control accuracy of the pneumatic system. In the design of the controller, the weight parameters of the input terms are transformed into the weight parameters of the error, and the input, which are analyzed to improve the accuracy of the controller design. The parameters of the control system are determined by multi-objective particle swarm optimization. To prove the effectiveness of the proposed control method, the experimental research was carried out by building the experimental platform of pneumatic-hydraulic upper limb rehabilitation training system. The results show that the 2DOF FOFPID controller has better performance than other designed controllers under different working conditions.

Modeling and Analysis of the Fractional-Order Flyback Converter in Continuous Conduction Mode by Caputo Fractional Calculus

In order to obtain more realistic characteristics of the converter, a fractional-order inductor and capacitor are used in the modeling of power electronic converters. However, few researches focus on power electronic converters with a fractional-order mutual inductance. This paper introduces a fractional-order flyback converter with a fractional-order mutual inductance and a fractional-order capacitor. The equivalent circuit model of the fractional-order mutual inductance is derived. Then, the state-space average model of the fractional-order flyback converter in continuous conduction mode (CCM) are established. Moreover, direct current (DC) analysis and alternating current (AC) analysis are performed under the Caputo fractional definition. Theoretical analysis shows that the orders have an important influence on the ripple, the CCM operating condition and transfer functions. Finally, the results of circuit simulation and numerical calculation are compared to verify the correctness of the theoretical analysis and the validity of the model. The simulation results show that the fractional-order flyback converter exhibits smaller overshoot, shorter setting time and higher design freedom compared with the integer-order flyback converter.

Fractional-order time-sharing-control-based wireless power supply for multiple appliances in intelligent building

The wired power transmission is usually adopted to supply power for the devices in the traditional buildings. With the development of intelligent buildings, the way of wired power supply would greatly increase the complexity and consumption of laying the lines. To improve the flexibility of power supply and reduce the cost of wiring, wireless power transfer technology has been used in smart buildings. However, it remains a fundamental challenge to create a simple wireless power transfer system in which power can be wirelessly transferred to multiple appliances. Therefore, this paper proposes a wireless power transfer scheme based on fractional-order time-sharing control for a variety of household appliances in intelligent building. In the proposed scheme, only one fractional-order capacitor in the transmitter is needed to realize the time-sharing resonant charging. In contrast, the traditional multiple-receiver systems require complicated control scheme, for example, controlling a plurality of sets of series-parallel capacitors through a series of relay switches. To demonstrate the method, a 150 W LED TV with 300 kHz and a 5 W mobile phone charger with 127 kHz serve as the actual loads. The experimental results show that the proposed system can supply power to the TV and the mobile phone by a time-sharing way wirelessly.

Fractional-order autonomous circuits with order larger than one

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Two kinds of new fractional-order autonomous circuits are proposed.

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The fractional-order autonomous circuits are based on fractional-order elements with order larger than one.

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The operating frequency or resonant frequency of the circuits can be changed by adjusting the resistance.

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The current and voltage of the circuits can be controlled by adjusting the orders of fractional-order elements.

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The available simulations verify the effectiveness of the theoretical analysis.

Fractional-order circuit is a kind of circuit which contains fractional-order elements. It has been proved that the fractional-order circuit has some characteristics which are hard to be achieved by integer-order circuits, such as higher degree of freedom in circuit design. For integer-order circuits, there are not only non-autonomous circuits, but also autonomous circuits. Since there are many applications of integral-order autonomous circuits in real world, it is also necessary to explore fractional-order autonomous circuits. However, few research focuses on fractional-order autonomous circuits. Therefore, this paper proposes two kinds of fractional-order autonomous circuits based on fractional-order elements with order larger than one. The corresponding mathematical models are also established based on fractional calculus and their characteristics are analyzed based on circuit theory. Finally, circuit simulation are performed to verify the correctness of theoretical analysis.

A modified modeling and dynamical behavior analysis method for fractional-order positive Luo converter

Compared to the integer-order modeling, the fractional-order modeling can achieve higher accuracy for designing and analyzing the DC-DC power converters. However, its applications in pulse width modulation (PWM) converters are limited due to the computational complexities. In this paper, a modified fractional-order modeling methodology for DC-DC converters is proposed, and its effectiveness is verified on the fractional-order positive Luo converters. Instead of using fractional-order calculus, the proposed methodology analyzes the harmonic components of the PWM converters by utilizing the non-linear vector differential equations of the periodically time-variant system. The final solution of the state variables is composed of two parts: the steady-state solution and the transient solution. The approximate steady state solution can be obtained by using the equivalent small parameter (ESP) method and the harmonic balance theory, while the main part of the transient solution can be obtained according to the explicit Grünwald-Letnikov (GL) approximation. In addition, the influence of the fractional orders on the performance of the DC-DC converters, and on the dynamic behaviors of the fractional-orders systems are also discussed in this paper. Compared to the conventional fractional-order numerical models, the proposed model is able to present the time-domain information more precisely, which helps to better reveal and analyze the non-linear behaviors of the DC-DC converters. The effectiveness of the work is demonstrated by the simulation and experimental results of the equivalent circuits built with fractional-order components.

Complex dynamics and control of a novel physical model using nonlocal fractional differential operator with singular kernel

Fractional calculus (FC) is widely used in many interdisciplinary branches of science due to its effectiveness in describing and investigating complicated phenomena. In this work, nonlinear dynamics for a new physical model using nonlocal fractional differential operator with singular kernel is introduced. New Routh-Hurwitz stability conditions are derived for the fractional case as the order lies in [0,2). The new and basic Routh-Hurwitz conditions are applied to the commensurate case. The local stability of the incommensurate orders is also discussed. A sufficient condition is used to prove that the solution of the proposed system exists and is unique in a specific region. Conditions for the approximating periodic solution in this model via Hopf bifurcation theory are discussed. Chaotic dynamics are found in the commensurate system for a wide range of fractional orders. The Lyapunov exponents and Lyapunov spectrum of the model are provided. Suppressing chaos in this system is also achieved via two different methods.

Fractional-Order Chaotic Memory with Wideband Constant Phase Elements

This paper provides readers with three partial results that are mutually connected. Firstly, the gallery of the so-called constant phase elements (CPE) dedicated for the wideband applications is presented. CPEs are calculated for 9° (decimal orders) and 10° phase steps including ¼, ½, and ¾ orders, which are the most used mathematical orders between zero and one in practice. For each phase shift, all necessary numerical values to design fully passive RC ladder two-terminal circuits are provided. Individual CPEs are easily distinguishable because of a very high accuracy; maximal phase error is less than 1.5° in wide frequency range beginning with 3 Hz and ending with 1 MHz. Secondly, dynamics of ternary memory composed by a series connection of two resonant tunneling diodes is investigated and, consequently, a robust chaotic behavior is discovered and reported. Finally, CPEs are directly used for realization of fractional-order (FO) ternary memory as lumped chaotic oscillator. Existence of structurally stable strange attractors for different orders is proved, both by numerical analyzed and experimental measurement.

Accurate Constant Phase Elements Dedicated for Audio Signal Processing

This review paper introduces real-valued two-terminal fully passive RC ladder structures of the so-called constant phase elements (CPEs). These lumped electronic circuits can be understood as two-terminal elements described by fractional-order (FO) dynamics, i.e., current–voltage relation described by non-integer-order integration or derivation. Since CPEs that behave almost ideally are still not available as off-the-shelf components, the correct behavior must be approximated in the frequency domain and is valid only in the predefined operational frequency interval. In this study, an audio frequency range starting with 20 Hz and ending with 20 kHz has been chosen. CPEs are designed and values tabularized for predefined phase shifts that are commonly used in practice. If constructed carefully, a maximum phase error less than 0.5° can be achieved. Several examples of direct utilization of designed CPEs in signal processing applications are provided.

Adaptive Neuro-Fuzzy Sliding Mode Controller

A novel adaptive sliding mode controller using neuro-fuzzy network based on adaptive cooperative particle sub-swarm optimization (ACPSSO) is presented in this article for nonlinear systems control. The proposed scheme combines the advantages of adaptive control, neuro-fuzzy control, and sliding mode control (SMC) strategies without system model information. An adaptive training algorithm based on cooperative particle sub-swarm optimization is used for the online tuning of the controller parameters to deal with system uncertainties and disturbances. The algorithm was derived in the sense of Lyapunov stability analysis in order to guarantee the high quality of the controlled system. The performance of the proposed algorithm is evaluated against two well-known benchmark problems and simulation results that illustrate the effectiveness of the proposed controller.