Robust Fractional Order Research Articles

Fixed-Time Robust Fractional-Order Sliding Mode Control Strategy for Grid-Connected Inverters Based on Weighted Average Current

Fixed-Time Robust Fractional-Order Sliding Mode Control Strategy for Grid-Connected Inverters Based on Weighted Average Current

Fractional finite-time control for robust tracking of nonlinear systems subject to Hölder disturbances with application to UAVs

The aim of the present article is to design a robust fractional-order (FO) finite-time (FnT) control able to tackle Hölder disturbances of second-order nonlinear systems. First, a novel sliding manifold with Arc-Tangent function is suggested for second nonlinear systems. It has been proven that the system states globally converge to the origin in FnT using the proposed sliding mode variable. To ensure a FnT stability of the sliding variable, a robust control is developed. By using fractional operators, a uniformly continuous control law is designed to tackle Hölder disturbances. Furthermore, the suggested approach is shown to be resistant to matched Hölder disturbances and uncertainties that are continuous but not necessarily differentiable. Moreover, the FnT stability of quadrotors using the proposed control, that is our second result. The quadrotor simulations analysis demonstrates the practicality of the proposed FnT controller in the presence of Hölder disturbances.

Humanoid Head Camera Stabilization Using a Soft Robotic Neck and a Robust Fractional Order Controller.

In this paper, a new approach for head camera stabilization of a humanoid robot head is proposed, based on a bio-inspired soft neck. During walking, the sensors located on the humanoid's head (cameras or inertial measurement units) show disturbances caused by the torso inclination changes inherent to this process. This is currently solved by a software correction of the measurement, or by a mechanical correction by motion cancellation. Instead, we propose a novel mechanical correction, based on strategies observed in different animals, by means of a soft neck, which is used to provide more natural and compliant head movements. Since the neck presents a complex kinematic model and nonlinear behavior due to its soft nature, the approach requires a robust control solution. Two different control approaches are addressed: a classical PID controller and a fractional order controller. For the validation of the control approaches, an extensive set of experiments is performed, including real movements of the humanoid, different head loading conditions or transient disturbances. The results show the superiority of the fractional order control approach, which provides higher robustness and performance.

Investigation of the Robust Fractional Order Control Approach Associated with the Online Analytic Unity Magnitude Shaper: The Case of Wind Energy Systems

This paper investigates the development of a novel analytic approach for computing Unity Magnitude (UM) shapers that deviates from established numerical methodologies. The experimental validation on a test bench confirms the practicality and benefits of the suggested UM shaper technique. The study extends the use of UM shapers to improve the control of wind conversion systems (WCSs), particularly those including hybrid excitation synchronous generators (HESGs), demonstrating their adaptability and versatility. Experimental validation guarantees real-world application, confirming the suggested UM shapers’ trustworthiness. Strict management is still required to assure the system’s efficiency and dependability. In reality, the dynamic equations of a turbine, as well as those of an HESG, are substantially nonlinear; most system parameters are very uncertain; and, finally, a WCS is always impacted by disturbance sources such as load variations, harmonics, and mechanical vibrations. Robust control measures must be used to overcome these issues. A CRONE controller (Robust Fractional Order Control) of the second generation is created. A comparative study performed on the Simulink platform reveals substantial gains brought about by UM shapers in real-world circumstances. The study demonstrates the effectiveness of UM-shaped inputs in mechanical stabilization and Maximum Power Point Tracking (MPPT), emphasizing both theoretical soundness and practical advantages. The analytic equations for UM shapers in undamped and damped systems, offered together with a real-time algorithm, contribute to the optimization of wind conversion systems.

Robust fractional-order sliding mode tracker for quad-rotor UAVs: Event-triggered adaptive backstepping approach under disturbance and uncertainty

In this paper, tracking control of the quad-rotor UAVs in the presence of exterior perturbations and dynamical uncertainties is accomplished using an event-triggered adaptive backstepping fractional-order sliding mode control scheme. For this reason, tracking errors are considered as the difference between the actual and desired states of the quad-rotor system. Moreover, event-triggering errors are defined as the difference between tracking errors at time ti and tracking errors at time t. Afterward, a dynamical model of the quad-rotor system under external disturbance and model uncertainty is obtained based on the tracking errors’ states. Then, the fractional-order sliding mode surface based on the tracking errors and virtual control inputs is proposed to guarantee the convergence of desired tracking errors. Hence, to avoid the complexity in the control process, the virtual control inputs are presented as fractional-order integral-type laws to avoid high derivatives of virtual control inputs. In addition, the event-triggering condition is applied for backstepping fractional-order sliding mode control to prevent frequent periodic action of control inputs. Moreover, employing the backstepping control procedure and the Lyapunov stability concept, the convergence of fractional-order sliding surfaces is guaranteed. Later, the fractional-order adaptive laws are designed to estimate the unknown upper bounds of perturbations and uncertainties. Finally, to demonstrate the efficiency of the control algorithm recommended in this paper, the simulation results on MATLAB/Simulink environment are presented. A comparison between the control method in this paper and another existing technique is prepared to prove the productivity of performance of the offered control method on the quad-rotor system.

Robust Fractional Low‐Order Multiple Window STFT for Infinite Variance Process Environment

Mechanical fault vibration signal is a typical non‐Gaussian process, they can be characterized by the infinite variance process, and the noise within these signals may also be the process in complex environments. The performance of the traditional cross‐term reduction algorithm is compromised, sometimes yielding incorrect results under the infinite variance process environment. Several robust fractional lower order time–frequency representation methods are proposed including fractional low‐order smoothed pseudo Wigner (FLOSPW), fractional low‐order multi‐windowed short‐time Fourier transform (FLOMWSTFT), and improved fractional low‐order multi‐windowed short‐time Fourier transform (IFLOMWSTFT) utilizing fractional low‐order statistics and short‐time Fourier transform (STFT) to mitigate cross‐terms, enhance time–frequency resolution, and accommodate the infinite variance process environment. When compared to traditional methods, simulation results indicate that they effectively suppress the pulse noise and function effectively in lower mixed signal noise ratio (MSNR) in an infinite variance process environment. The efficacy of the proposed time–frequency algorithm is validated through its application to mechanical bearing outer ring fault vibration signals contaminated with Gaussian noise and subjected to an α infinite variance process.

Robust Fractional Order PID Controller Coupled with a Nonlinear Filtered Smith Predictor for Solar Collector Fields

This work introduces a Fractional Order PID (FOPID) controller associated with a nonlinear Filtered Smith Predictor (FSP) to control a Solar Collector Field (SCF) system. The combined approach enhances the control performance by decoupling model uncertainties. First, the FOPID addresses linear model uncertainties through optimal robust design across the operational conditions, while the FSP compensator adeptly manages the system’s varying time delays. Rigorous tuning in the frequency domain considering closed-loop, robustness, and disturbance rejection performances is developed using a bi-level optimization approach to obtain the FOPID control parameters. Experimental results of the FOPID + nonlinear FSP demonstrate low rise time for reference tracking and robust stability across several operating conditions, even in the face of high-frequency disturbances in the solar irradiance due to passing clouds. Moreover, the nonlinear FSP effectively handles variations in time delays undergone by the water flow variation during the experiment. The achieved outcomes of the overall control structure, comprising the FOPID + FSP, demonstrate a promising approach for SCF system control, obtaining robust behavior in the presence of model uncertainties and disturbances while offering satisfactory reference tracking capabilities across an extensive range of plant operations.

A Fractional Order Tilt Integral Controller Based Load Frequency Control with Dispersed Generation and Electric Vehicle

The elevated level of entrance of decentralized power sources with their Intermittent and volatility gives us a accost task to control load frequency, moreover this quandary is getting worsen up with the Involvement of electric vehicles in the rundown. This paper presents a censorious robust fractional order operative established tilt integral derivative controller (FOTID) for regulating the frequency. To emulate distributed power sources a linearized model of a wind power plant is considered and a small signal model of EV is developed. With the consideration dynamic nature of EV & wind power plants, the dynamic pursuance of the envisaged FOTID controller is investigated by comparing them with integral order PID controller, Fractional order PID controller, sliding mode controller under various conditions. The transfer function model of proposed controllers is derived and the robustness of the proposed FOTID controller is examined by conducting detailed simulation studies.

Fractional Order Control of Continuum Soft Robots: Combining Decoupled/Reduced-Dynamics Models and Robust Fractional Order Controllers for Complex Soft Robot Motions

Continuum soft robots are made up of soft material components (referred to as continuum), rigid components, actuators, and sensors. By structurally deforming the continuum, a motion of the entire system is initiated. To capture the interaction of the actuators on the soft material deformation and the corresponding sensor readings, mathematical models involving geometrical, material, and inertia parameters of the physical system must be set up to predict its complex physical behavior.

Modeling and Robust Fractional Order Fuzzy Sliding Mode Two Time Scale Controller Design for Synchronous Generator of ACP1000 Nuclear Power Plant in LabVIEW

Modeling and Robust Fractional Order Fuzzy Sliding Mode Two Time Scale Controller Design for Synchronous Generator of ACP1000 Nuclear Power Plant in LabVIEW

A Robust Fractional-Order Control Scheme for PV-Penetrated Grid-Connected Microgrid

This article presents a new cascaded control strategy to control the power flow in a renewable-energy-based microgrid operating in grid-connected mode. The microgrid model is composed of an AC utility grid interfaced with a multi-functional grid interactive converter (MF-GIC) acting as a grid-forming converter, a photovoltaic (PV) power-generation system acting as grid-feeding distributed generation unit, and various sensitive/non-sensitive customer loads. The proposed control strategy consists of a fractional order PI (FO-PI) controller to smoothly regulate the power flow between the utility grid, distributed generation unit, and the customers. The proposed controller exploits the advantages of FO (Fractional Order) calculus in improving the steady-state and dynamic performance of the renewable-energy-based microgrid under various operating conditions and during system uncertainties. To tune the control parameters of the proposed controller, a recently developed evaporation-rate-based water-cycle algorithm (ERWCA) is utilized. The performance of the proposed control strategy is tested under various operating conditions to show its efficacy over the conventional controller. The result shows that the proposed controller is effective and robust in maintaining all the system parameters within limits under all operating conditions, including system uncertainties.

Robust Fractional Order Speed Controllers for Induction Motor Under Parameter Variations and Low Speed Operating Regions

This brief describes the two unique Fractional Order (FO) speed controllers’ FOPI and FO[PI] design and validation for the induction motor drive. The detuning of the conventional PI controller issues under machine parameter variations and low speed operating regions are overcome by the proposed two types of FO speed controllers. This brief presents the novel FO controller design procedure for the Voltage Source Inverter (VSI) fed IM. The actual FO VSI fed IM transfer function model is identified using the chirp signal injection method with the Hardware-In-Loop (HIL) system for the laboratory prototype. The parameter variation is subjected to different stator winding resistance machines of the same rating. The rotor inertia change of up to eight times the no-load value is incorporated to investigate the robust performance of these speed controllers under dynamic operating conditions. The performance of the designed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$FOPI$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$FO[PI]$ </tex-math></inline-formula> controllers are analyzed at low speeds. The results show the supremacy of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$FO[PI]$ </tex-math></inline-formula> controller over the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$FOPI$ </tex-math></inline-formula> and PI under the same stability boundary limits. The experimental validation of these controllers is provided.

Robust fractional-order fast terminal sliding mode control of aerial manipulator derived from a mutable inertia parameters model

The coupling disturbance between the manipulator and the unmanned aerial vehicle (UAV) deteriorates the control performance of system. To get high performance of the aerial manipulator, a robust fractional order fast terminal sliding mode control (FOFTSMC) strategy based on mutable inertia parameters is proposed in this paper. First, the dynamics of aerial manipulator with consideration of the coupling disturbance is derived by utilizing mutable inertia parameters. Then, based on the dynamic model, a robust FOFTSMC algorithm is designed to make the system fly steadily under coupling disturbance. Furthermore, stability analysis is conducted to prove the convergence of tracking errors. Finally, comparative simulation results are given to show the validity and superiority of the proposed scheme.

Robust Fractional Order Flow Control in an Oil Pipeline

The robust fractional order oil flow control in an oil pipeline is addressed in this paper. An experimental identification based on a step like input was developed which yielded a second order transfer function with a zero and a time varying time delay. Controllers are subsequently designed with nominal phase margin and zero steady state error of the closed-loop step response specifications, plus robust damping expressed in terms of a maximum allowed variation of the phase margin of ±10% around the nominal value. We have considered integer and fractional order controllers. Rules to tune the parameters of these controllers have been obtained and a condition to get minimum phase closed-loop systems has been derived. We have shown that PI controllers verifying the three design conditions often yield undesired nonminimum phase closed-loop systems. This is avoided using the proposed fractional order controllers. Simulations carried out in this paper illustrate these results.

Design an Optimal Fractional Order PI Controller for Congestion Avoidance in Internet Routers

The main problem that degrade data transition in communication networks is the congestion, to achieve stable TCP network, an active queue management (AQM) is used for controlling congestion and saving regular queue length .In this paper, a robust Fractional Order PI (FOPI) controller is suggested to control the AQM system, Gray Wolf Optimization Algorithm (GWO) is used for tuning of the controller gains and the Integral Time Absolute Error (ITAE) is adopted as a fitness function for monitoring system response by minimizing its error value until reach an efficient and robust response. The transient analysis is used for comparing the suggested controller with two conventional controllers (PI &amp; PID) to show the efficient behavior of suggested controller, then a robustness analysis is applied by adding disturbances positive and negative signals with value 150 packets at different time(15 sec, 30 sec) to the system also varying the queue size after each 40 sec to see the system response , the controller overcomes the disturbances signals with less than 3.5 sec and faces the queue size varying values and returning the system response to its desired value efficiently.

Robust fractional order PID controller synthesis for the first order plus integral system

The fractional order PID (FOPID) controller has been found to have the potential to provide more flexibility in the design options than the integer order PID (IOPID) controller. However, in the FOPID controller design practice, investigations are still required in selecting the achievable design specifications and controller parameters. In order to obtain a practical tuning method for the FOPID controller, taking the first order plus integral systems as the plants, the complete achievable regions of the design specifications are collected and analyzed. In addition, the selectable integral and derivative orders of the FOPID controller are also collected and modeled. With the prior knowledge obtained, a synthesis method for the FOPID controller is proposed to make the control system achieve the desired flat-phase characteristic. To verify the effectiveness of the proposed method, the synthesis method is applied to design the FOPID controller for the permanent magnet synchronous motor (PMSM) speed servo system. Simulation and experimental results show that system with the FOPID controller can achieve satisfying tracking performance and disturbance rejection performance.

Design of an improved robust fractional order PID controller for magnetic levitation system based on atom search optimization

Design of an improved robust fractional order PID controller for magnetic levitation system based on atom search optimization

Robust yaw control of autonomous underwater vehicle based on fractional-order PID controller

Autonomous underwater vehicles (AUVs) have broad applications owing to their small size, low weight, strong ability to operate autonomously, and ability to replace humans in dangerous operations. AUV motion control systems can ensure stable operation in complex ocean environments and have attracted significant research attention in marine science and technology. The main difficulties with AUV motion control include the large uncertainties of dynamic and hydrodynamic characteristics and time delay of the signal transmission channel. In this study, we propose a robust fractional-order proportional–integral–derivative (FOPID) controller design for an AUV yaw control system. First, a three-dimensional stability region analysis method is proposed to achieve fractional orders. Unlike other stability region analysis methods, the proposed method is supported by theory instead of observation. Then, the other parameters are optimized according to the robust design specifications with respect to the parameter uncertainties. Therefore, the controlled system can tolerate different parameter uncertainties and fulfill transient performance specifications while maintaining system stability. The simulation results illustrate the superior robustness and transient performance of the proposed control algorithm.

An effective Smith predictor based fractional-order PID controller design methodology for preservation of design optimality and robust control performance in practice

In this study, an optimal and robust fractional order PID (FOPID) controller design approach is suggested for Smith predictor based FOPID (SP-FOPID) control system design. This new design approach considers continued fraction expansion (CFE) based approximate models in the optimal design task of FOPID controllers, and this approach preserves the design optimality in control applications. For this purpose, an inverse controller loop shaping design methodology is performed in order to approximate the frequency response of a Bode’s ideal loop reference model, and robust performance CFE based FOPID controller models are obtained by solving a multi-objective optimisation problem via a genetic algorithm. Thus, the suggested algorithm can deal with several controller realisation concerns in the design task of FOPID controllers and overcome real-world controller performance issues related with model approximation errors and signal saturation boundaries of electronic hardware. Illustrative design examples demonstrate that the suggested design scheme can preserve design optimality and improve practical control performance in practice.

Development of Prototype Fractional Order Controller for a Grid-Tied Photovoltaic System

This paper presents design of a robust fractional order proportional-integral (FO-PI) prototype controller for a grid connected photovoltaic (PV) system. The robustness in face of parameter variation is handled by designing a suitable controller considering sensitivity function, gain margin and phase margin for both inner and outer control loops. As FO-PI controller is not yet available in physical form and due to complexity involved in grid-tied PV system, we propose an alternative way of hardware implementation of inner loop FO-PI controller by using fractor through RC ladder network. Firstly, an emulator circuit of the inner current loop comprising the FO-PI controller (including fractor and the proportional gain) along with the transfer function of inverter and filter is developed and the response is verified through a real-time simulator (OPAL-RT). Finally, the FO-PI part of the emulator circuit is interfaced with the PC target to form a hardware-in-loop (HIL) by employing OPAL-RT. The performance of the complete system is verified through OPAL-RT simulator. The result shows the improved robustness by the proposed control design method.