Integral Time Square Research Articles

Control of a fixed wing unmanned aerial vehicle using a higher-order sliding mode controller and non-linear PID controller

Unmanned aerial vehicles (UAVs) have seen a rise in use during the last few years. Such aircrafts are now a convenient way to complete dangerous, dirty, and tedious tasks. Given that their operation involves a control problem which is non-linear and coupled, it is difficult to analyse. This paper presents the modeling and control of a fixed-wing unmanned aircraft as a contribution to this field. The system’s flight dynamics is derived using Newton’s second law of motion. The system is designed to have a non-linear Proportional Integral Derivative (NPID) controller and a higher-order sliding mode controller (HOSMC). When simulating the system using MATLAB Simulink software, an external disturbance was added to test the robustness of the controllers. Five performance indices which include mean square error (MSE), integral time square error (ITSE), integral absolute error (IAE), integral time absolute error (ITAE), and integral square error (ISE), were used to compare the controllers performance. These indices are used to provide a numerical assessment of the two controllers’ performance. The outcomes demonstrate that the roll, pitch, and yaw states performed better than the super-twisting sliding mode controller. On the airspeed control, the non-linear PID performed better than the super-twisting sliding mode controller.

Comparison of the Performance of Type-1 and Interval Type-2 Fuzzy PI Controllers for Liquid Level Control in a Coupled Tank System

In this study, liquid level control in a coupled tank system is realized with PI controllers whose parameters are adapted using fuzzy logic approximation methods. Type-1 fuzzy PI control, interval type-2 fuzzy PI control and classical PI+Feedforward control methods are applied to the tank system in real time for different reference liquid levels. The performances of the controllers are compared in terms of system response parameters such as rise time, settling time and overshoot percentage. In addition, the performance evaluation of the controllers over a certain period of time is also compared by calculating integral-based concepts that express error performance metrics such as integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE). The obtained results show that the type-2 fuzzy PI controller shows the best performance, followed by type-1 fuzzy PI control and classical PI+FF controller, respectively.

Enhancing PI controller performance in grid-connected hybrid power systems

The optimal operation of a microgrid was buildup of both uncontrollable (solar, wind) and controllable (batteries, diesel generators) electrical energy sources are enclosed in this paper. By replacing controllers, the variations in wavering power supply caused by load fluctuations are managed. The objective of the research paper is to optimize these controller gain settings for effective use of electrical energy. In this paper integral time square error principle is combined along with the Cuckoo search algorithm (CSA) and particle swarm algorithm (PSA) to obtain the accurate, precise and appropriate results. It enhances the microgrid's steady-state sensitive responsiveness in comparison to trial-and-error techniques, assuring a stable supply of electricity to the load.

Speed Control for PMSM with Fast Variable-Speed Sliding Mode Control via High-Gain Disturbance Observer

Since robustness only exists on the sliding mode/surface, sliding mode control is non-globally stable. Therefore, shortening the time to reach the sliding mode is an important method of improving sliding mode robustness. However, there is an inherent contradiction between rapidity and overshoot. Therefore, ensuring rapid convergence without overshoot is a worthwhile research problem. Consequently, this paper proposes a design for a fast variable speed reaching law (FVSRL) to improve the quality of sliding mode control. The constructed approach rate is based on a variable speed term, an exponential term, and a fast term, ensuring rapid convergence without overshoot. At the same time, a high-gain disturbance observer is employed for feedforward compensation. Finally, the designed reaching law is validated by comparing it with conventional exponential approach rates and a new sliding mode reaching law, demonstrating its superior performance. Detailed comparative and quantitative analyses of the simulation results using the conventional exponential reaching law, the new sliding mode reaching law, and the FVSRL are performed, utilizing metrics such as integrated square error, integral time square error, integrated absolute error, and integral time absolute error.

Coot optimization algorithm-tuned neural network-enhanced PID controllers for robust trajectory tracking of three-link rigid robot manipulator

Robotic manipulators are nonlinear systems, multi-input multi-output, highly coupled and complicated whose performance is negatively impacted by external disturbances and parameter un-certainties. Therefore, the controllers designed for such systems must be capable of managing their complexity. The main aim of this study is to tackle the trajectory tracking issue of the three-Link Rigid Robot Manipulator (3-LRRM) based on designing three control structures using a combi-nation Neural Network (NN) with Proportional, Integral and Derivative (PID) actions named Neural Controller Like PIPD (NN-PIPD) controller, Neural Network plus PID (NN + PID) controller NN + PID controller and Elman Neural Network Like PID (ELNN-PID) controller. The parameters of the proposed controllers are adjusted utilizing the Coot Optimization Algorithm (COOA) in order to reduce the Integral Time Square Error (ITSE). A novel objective function for tuning process to produce a controller with minimum value of the chattering in the control signal is proposed. The performance of the proposed controllers is evaluated in terms of disturbance rejection, model uncertainty, fluctuating initial conditions and reference trajectory tracking. According to the simulation results proved that the suggested NN-PIPD controller outperforms all other proposed controller structures for tracking performance, stability, and robustness. As a result of the com-parison analysis the optimal controller was considered to be an NN-PIPD controller for tracking trajectory, rejecting disturbances, and parameter variation with minimizing ITSE of 0.001777.

A novel artificial hummingbird algorithm improved by natural survivor method

The artificial hummingbird algorithm (AHA) has been applied in various fields of science and provided promising solutions. Although the algorithm has demonstrated merits in the optimization area, it suffers from local optimum stagnation and poor exploration of the search space. To overcome these drawbacks, this study redesigns the update mechanism of the original AHA algorithm with the natural survivor method (NSM) and proposes a novel metaheuristic called NSM-AHA. The strength of the developed algorithm is that it performs population management not only according to the fitness function value but also according to the NSM score value. The adopted strategy contributes to NSM-AHA exhibiting powerful local optimum avoidance and unique exploration ability. The optimization ability of the proposed NSM-AHA algorithm was compared with 21 state-of-the-art algorithms over CEC 2017 and CEC 2020 benchmark functions with dimensions of 30, 50, and 100, respectively. Based on the Friedman test results, it was observed that NSM-AHA ranked 1st out of 22 competitive algorithms, while the original AHA ranked 8th. This result highlights that the NSM update mechanism provides a remarkable evolution in the convergence performance of the original AHA algorithm. Furthermore, two constrained engineering problems including the optimization of single-diode solar cell model (SDSCM) parameters and the design of a power system stabilizer (PSS) are solved with the proposed algorithm. The NSM-AHA algorithm provided better results compared to other algorithms with a value of 9.86E − 04 root mean square error for SDSCM and 1.43E − 03 integral time square error for PSS. The experimental results showed that the proposed NSM-AHA is a competitive optimizer for solving global and engineering problems.

A novel modified mountain gazelle optimizer for tuning parameter proportional integral derivative of DC motor

This article presents a modified method of mountain gazelle optimizer (MMGO) as a direct current (DC) motor control. Mountain gazelle optimizer (MGO) is an algorithm inspired by the life of the mountain gazelle animal in nature. This animal concept has five essential steps that are duplicated in mathematical modeling. This article uses two tests to get the performance of the MMGO method. The first test uses a benchmark function test with a comparison method, namely the sine tree seed algorithm (STSA) and the original MGO. The second test is the application of MMGO as a DC motor control. The simulation results show that MMGO can reduce the overshoot of conventional proportional integral derivative (PID) control by 0.447% and has a better integral time square error (ITSE) value of 5.345 than conventional PID control. Thus, the MMGO method shows promising performance.

Modeling, design and control of a 4-arm delta parallel manipulator employing type-1 and interval type-2 fuzzy logic-based techniques for precision applications

This paper presents the virtual design of a four-arm Delta parallel robot for potential applications in the food industry, specifically for the automated preparation of fast foods. Kinematic and dynamic models were developed based on the morphology of this type of robot. Cutting-edge and previously unexplored control strategies for these types of manipulators are then designed and implemented based on Fuzzy PD and Fuzzy PID configurations. Several performance indicators, such as the Integral Square Error (ISE), Integral Time Absolute Error (ITAE) and Integral Time Square Error (ITSE), were used to conduct a performance comparison of the control techniques, considering type-1 and interval type-2 fuzzy sets. In all the analyzed scenarios, the fuzzy controllers correspond to the Takagi–Sugeno–Kang model using linear functions of the inputs in the outputs. Among the main contributions of this work is the development of a detailed dynamic model of the robot in Simscape, incorporating realistic aspects that are often overlooked during analytical modeling. To ensure more accurate results, the rejection of external disturbances is thoroughly analyzed in simulations, considering elements such as time delays and control signal saturations. The results demonstrate the veracity of the proposed design for a four-arm Delta robot, both in models and in the Simscape/Simulink implementation. In the trajectory tracking task and external disturbance rejection, the superiority of the Fuzzy PID controller with interval type-2 fuzzy sets over fuzzy controllers with PD structure and over type-1 fuzzy sets is evidenced.

A novel multi-objective tuning formula for load frequency controllers in an isolated low-inertia microgrid incorporating PV/wind/FC/BESS

Load frequency control (LFC) is vital for isolated microgrids (IMGs), especially when uncertain renewable energy sources (RESs) are present. Enhancing LFC schemes relies mainly on three tracks. Adding new resources to IMG structures is the first track, designing novel controller structures for LFC schemes is the second, and the third is improving controller tuning procedures in the LFC schemes. This research suggests an innovative multi-objective formula (MOF) for controller tuning that combines a novel error criterion termed the integral-square time absolute error of frequency change with the integral-square of IMG controllers' signals. Tested IMG includes multi-sources of diesel engine generators, fuel cells, battery energy storage technologies, and RESs (like photovoltaic and wind turbines). The proposed MOF tuning is evaluated compared to four different objective functions, which are the integral-absolute error (IAE), integral-time absolute error (ITAE), integral-square error (ISE), and integral-time square error (ITSE). The proportional-integral-derivative (PID), fractional-order, and cascade PID controllers are implemented to appraise the proposed MOF extensively against all these single objectives. Statistical analyses are accomplished comprehensively to verify the effectiveness of the artificial rabbits' optimization algorithm (ARO) in competition with other recent optimization algorithms to tune different controllers utilized in the LFC schemes of the examined IMG based on tested objectives. Therefore, ARO is applied to optimize controller settings by combining system nonlinearities with IMG sources' maximal generation rate constraints. The comparative analysis considers settling times, overshoots, IAE, ITAE, ISE, and ITSE performance indices. MATLAB/Simulink simulations confirmed the ability of the suggested MOF tuning to stabilize the system and keep improving performance indices, significantly attaining the minimum settling time even for massive three-type load fluctuations. The first type is step disturbances ranging between 0.1 and 0.25 p.u, the second is varying step disturbances every 5 s, and the third is severe dynamic random load shifts from −0.2 to 0.2 p.u. In addition, the MOF outperforms other competitors' tuning formulas while adding fluctuations of RESs with load disturbances. Furthermore, the robustness analysis is conducted for the applied controllers based on the proposed MOF tuning approach by changing the IMG nominal parameters with ±25 % and adding system nonlinearities. The analysis ensured its efficacy in preserving system stability. Finally, the stability test in the frequency domain using the MATLAB/control design tool verified system stability when different LFC controllers were tuned based on the proposed MOF tuning.

Analysis and Stability Enhancement of an Inverter-Based Microgrid through the Design of an Advanced Droop Controller using a Modified PSO

Microgrids can operate in grid-tied mode and islanded mode with different load conditions. During the transition from one operating mode to another or varying load conditions, small disturbances may occur in the system, which can create transient oscillations due to the insufficient inertia of the distributed generating units (DG) of the microgrid. The droop control is mainly adapted to govern the working of the microgrid and maintain stability and power supply to the load. This paper presents an optimization-based control approach for the smooth operation of microgrids during the transition from one operating mode to another. The eigenvalue analysis and participation factors are used to find the control parameters for improving the power-sharing and stability of the microgrid. The modified PSO (MPSO) with adaptive weighted delayed velocity function (PSO-AWDV) is utilized to optimize the integral time square error (ITSE) of real and reactive power of the DGs in the microgrid. The eigenvalues analysis and time-domain simulation are presented to show the performance of the proposed approach for resistive and resistive-inductive load scenarios. The outcomes unveil that the optimized droop parameters improve the performance of DGs in microgrid by reducing overshoots in the range of 0.5% to 6% in real power, reactive power, output voltage, and currents of DGs as compared to parameters selected based on conventional approach. Moreover, the settling time for all the variables is reduced to 0.2 s with the proposed controller that enhances the steady state response of the system.

VPSA-Based Transfer Function Identification of Single DoF Copter System

In this study, an experimental set of a Single-DoF Copter system is created and transfer functions that could model the dynamics of the physical system with high accuracy were investigated. In order to model the dynamics of the physical system with the highest accuracy, the five different transfer functions have been proposed, in which the zero and pole values are determined by optimizing with the Vibrating Particle System Algorithm. Integral Square Error (ISE), Integral Time Square Error (ITSE), Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE) functions, which are widely used in the literature in determining transfer functions, are determined as fitness functions. In order to verify the transfer functions, the responses of the transfer functions and the experimental system response are presented comparatively, and their suitability was evaluated. It has been observed that the proposed method is successful in defining the transfer function of the experimental system, and the compatibility of the obtained transfer functions with the system response is between 75.407% and 98.612% accuracy.

Current source converter-based optimal power extraction and power control of a doubly fed induction generator (DFIG) using backstepping control

An improved backstepping control technique for the operation of a doubly fed induction generator (DFIG) powered by a wind turbine (WT) was developed and discussed. It is derived from a current source converter (CSC). The optimal backstepping control (BSC) settings are determined using the CSC approach, which can improve the drive by providing a more rapid dynamic response, greater precision, and stable performance. The CSC approach control function was constructed using the index criterion integral time square error (ITSE) and integral time absolute error (ITAE). With the simulation technique in the MATLAB/Simulink environment, the proposed BSC-CSC effectiveness is confirmed, and analyse the performance by using the PI and SMC control. The results indicate the goals of this work have been achieved in the form of resilience, improved dynamic system efficiency, lowering the harmonic distortion, optimization of stator power, and successfully addressing the problem of model parameter uncertainty.

Performance evaluation of dynamic voltage restorer using intelligent control algorithm

Power quality has become an important issue due to increasing applications of modern industrial and commercial sensitive equipment's. Due to high penetration of modern power electronics-based devices leads to voltage disturbances. To address the voltage disturbances the commonly employed series device called Dynamic Voltage Restorer (DVR) is used which requires an effective control technique. A control scheme namely Volterra adaptive expanded filter is developed which incorporate the higher ordered cost function. The conventional filters have like least mean square (LMS) algorithm is restricted to power error of second order. This restricts the computation of fundamental quantity from the disrupted signals and results in degradation under dynamical scenarios. The recommended approach surmount this aforesaid issue with a solution of a mixed learning of step size. This is derived from the error of second and fourth-order. The Volterra based LMS/Fourth (LMS/F) control has the merit of estimating the fundamental quantity under any power quality (PQ) scenario with less delay and low computational burden. The conventional controller like Proportional Integral (PI) has limited gain coefficients to achieve the optimized the voltage regulation. Furthermore, this is overcome by a Fractional Order PID (FOPID) with an additional coefficient of λ and γ obtain more stabilized DC and AC bus voltage by integrating with Kepler optimizer. For achieving optimal gain, an online tuning of FOPID is done with Kepler Optimizer. The Kepler is inspired by planet motion to achieve best gain values. The evaluation of FOPID is made by considering as a Fitness Function (FF) an Integral Time Square Error (ITSE). Owing to the superior performance of Kepler optimizer based FOPID under transitory state and an enhanced DVR performance is observed. The optimized FOPID has improved response in terms of less overshoot (2.9 %), undershoot (5.6 %), and fast settle time (0.104 s). To authenticate the simulating and experimental results dSPACE board is employed to validate the efficacy and accuracy of the proposed Volterra LMS/F technique.

Artificial neural network–based modelling of pacemaker and its pace tracking using discrete wavelet transform–based finite dimension repetitive controller

Efficient control of cardiac pacing is a very important aspect as it provides lifesaving regulated cardiac rhythm in this dynamic hostile environment. The foremost control objective is set to design a highly reliable and advanced control strategy to ensure the utmost accuracy in the control effort. A modified artificial neural network (ANN)–based modelling and pace tracking using finite dimension repetitive controller (FDRC) design based on internal model principle (IMP) has been presented here. This controller will not only provide accurate tracking but also minimize the control action time due to less amount of data handling through the deployment of discrete wavelet transform (DWT) in the loop of repetitive controller (RC). Finally, a case study has been propounded considering ANN model using available data sets and software to validate the control strategy and justify the control objective for optimizing the pace tracking in a pacemaker. Result of the experiment showed good accuracy as well as very low error in terms of mean-squared error (MSE), integral absolute error (IAE), integral time absolute error (ITAE) and integral time square error (ITSE). Along with that, it is observed that DWT not only benefits the handling of very less memory but also acts as an additional filter while reconstructing the signal, which serves as an added advantage of this model.

Servo and Regulatory Response of an Industrial Fluid Catalytic Cracking (FCC) Unit under Fuzzy Logic Supervisory Control

A self-tuning hierarchical controller in which a Fuzzy logic controller supervises the control actions of a conventional PID has been proposed, implemented and presented in this paper. The controller has been applied to a control study of Fluid Catalytic Cracking unit (FCCU) riser temperature, and regenerator temperature respectively. Comparison between the performance of the proposed Fuzzy-PID controller and the conventional PID was made in simulation studies of regulatory and servo performances of the two controller types. Six performance measures: Percent overshoot (OS), settling time (ST), integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE) were employed as the tools for performance comparison between the conventional PID and the Fuzzy-PID controller. For the tracking of riser temperature with a set point at 524oC, the performance indicators under PID control gave the following results overshoot (14.5%); settling time (40 seconds) Integral absolute error (8.246), integral square error (3.3); integral time absolute error(1762);integral time square error (43.77) while for the same indicators under Fuzzy-PID control the following values: overshoot (3.3%); settling time (40 seconds) ;Integral absolute error (8.811); integral square error (14.5); integral time absolute error(280),;integral time square error (31.11) .The results allude to the superiority of the fuzzy-PID scheme over the PID scheme in tracking the optimal set point of riser temperature. More so, for tracking the regenerator set point temperature of 746oC, comparative study of step response under the two schemes gave the following results in six performance indicators: overshoot (PID (12.6%) / Fuzzy-PID (6%)); settling time (PID (80 seconds) / Fuzzy-PID (20seconds)); Integral absolute error (PID (14.29) / Fuzzy-PID (8.63)); integral square error (PID(6.713). Fuzzy-PID (4.506)); integral time absolute error(PID(2858)/Fuzzy-PID(305.9)), integral time square error (PID(77.55)/Fuzzy-PID(33.05)) . Moreover, the fuzzy-PID controller also showed superior performance over the conventional PID controller in terms disturbance rejection (regulatory response) of both riser and regenerator temperature. The results from this study suggest that the application of fuzzy-PID scheme to temperature control offers good promise of improved fluid catalytic cracking unit (FCCU) operations.

Modern PID/FOPID controllers for frequency regulation of interconnected power system by considering different cost functions

This article presents frequency regulation of an interconnected three-area power system (Thermal + Wind + Hydro). Fractional Order PID (FOPID) and Proportional-Integral-Derivative (PID) controllers are applied as subsidiary regulators to control the electrical power interconnected system at the time of sudden load variation. To accomplish this study, Genetic Algorithm (GA), Grey Wolf Optimizer (GWO), Sine Cosine Inspired Algorithm (SCIA) and Atom Search Inspired Algorithm (ASIA) are implemented to optimize the secondary regulators' gains (PID and FOPID) by considering various cost functions such as Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE), Integral Square Error (ISE), and Integral Time Square Error (ITSE). Performance analysis in this work is conducted using various cost functions based on GA, GWO, SCIA and ASIA. The comparative analysis of the attained results reveals that GWO-PID and ASIA–PID settle at (83.83 s) and (30.31 s), respectively and ASIA-FOPID at (25.12 s). The controllers based on ITSE as a cost function outperform the comptrollers with other cost functions (ISE, IAE and ITAE). In addition, the ISE-based GA–PID and SCIA–PID settle at (113.92 s) and (35.1 s), respectively and SCIA-FOPID at (24.78 s). The ISE-based regulators yield improved response equated to other cost functions (ITSE, IAE and ITAE) optimized controllers. The robustness test also is carried out to validate the effectiveness of the proposed optimization techniques by changing the system parameters within ± 25% and ± 50% from their nominal values as well as changing the load pattern.

Tuning of controller parameters using Pythagorean fuzzy similarity measure for stable and time delayed unstable plants.

This paper proposes a tuning method based on the Pythagorean fuzzy similarity measure and multi-criteria decision-making to determine the most suitable controller parameters for Fractional-order Proportional Integral Derivative (FOPID) and Integer-order Proportional Integral-Proportional Derivative (PI-PD) controllers. Due to the power of the Pythagorean fuzzy approach to evaluate a phenomenon with two memberships known as membership and non-membership, a multi-objective cost function based on the Pythagorean similarity measure is defined. The transient and steady-state properties of the system output were used for the multi-objective cost function. Thus, the determination of the controller parameters was considered a multi-criteria decision-making problem. Ant colony optimization for continuous domains (ACOR) and artificial bee colony (ABC) optimization are utilized to minimize multi-objective cost functions. The proposed method in the study was applied to three different systems: a second-order non-minimum phase stable system, a first-order unstable system with time delay, and a fractional-order unstable system with time delay, to validate its effectiveness. The cost function utilized in the proposed method is compared with the performance measures widely used in the literature based on the integral of the error, such as IAE (Integral Absolute Error), ITAE (Integral Time Absolute Error), ISE (Integral Square Error), and ITSE (Integral Time Square Error). The proposed method provides a more effective control performance by improving the system response characteristics compared to other cost functions. With the proposed method, the undershoot rate could be significantly reduced in the non-minimum phase system. In the other two systems, significant improvements were achieved compared to other methods by reducing the overshoot rate and oscillation. The proposed method does not require knowing the mathematical model of the system and offers a solution that does not require complex calculations. The proposed method can be used alone. Or it can be used as a second and fine-tuning method after a tuning process.

Conditioned adaptive barrier-based double integral super twisting SMC for trajectory tracking of a quadcopter and hardware in loop using IGWO algorithm

Researchers working in the field of unmanned aerial vehicles are observing rapid developments in the field, such as the use of quadrotors to grasp, manipulate, and transport objects. These advancements are made possible through sophisticated control systems, new types of actuation and sensing technologies, and a greater understanding of the aerodynamic effects and gyroscopic moment generated by the rotating blades of the quadrotor involved. Therefore, this research work proposes four novel optimized control laws, i.e., conditioned adaptive barrier-based double integral super twisting sliding mode controller (CABDIST-SMC), BF double integral SMC (BF-DISMC), BF integral SMC, and barrier function-based SMC control laws, for attitude, heading, position, and altitude trajectory tracking of the quadcopter. The non-linear model of the quadcopter is developed using the Lagrange formalism in MATLAB ODE-45 environment, including the gyroscopic moments and aerodynamic effects, and a Lyapunov stability analysis is performed to ensure the asymptotic stability of the system. A 3D-helical complex trajectory is employed to analyze the performance and consistency of the proposed optimized controllers. For performance comparison, the proposed four variants of the SMC are compared with three traditional control strategies, i.e., backstepping SMC, optimized adaptive SMC via particle swarm optimization algorithm, and improved adaptive SMC. These traditional control strategies have also been developed and tested in MATLAB-Simulink. All the controllers are optimized using the improved grey wolf optimization algorithm, and to determine the best control law, six performance indexes, i.e., mean absolute percentage error (MAPE), root mean square error (RMSE), integral square error (ISE), integral absolute error (IAE), integral time absolute error (ITAE), and integral time square error (ITSE) are used. A hardware-in-loop (HIL) test is also performed to validate the performance of the designed novel control law. The C2000 Delfino MCU F28379D launchpad is used for performing the HIL validation test. The simulated results showed that the performance of optimized CABDIST-SMC surpassed all other control laws for altitude, heading, position, and attitude trajectory tracking. It has achieved MAPE of 0.02%, RMSE of 3.9912e−5, ISE of 3.1859e−8, IAE of 7.9823e−4, ITAE of 0.0080, and ITSE of 3.1849e−7 in case of yaw angle control. The proposed control laws have successfully passed the HIL validation test, and real-time implementation of the proposed control laws indicates no significant variations compared to the simulated results.

A robust PIλDµ controller for enhancing the width of the molten pool and the tracking of welding current in gas metal arc welding (GMAW) processes

ABSTRACT By utilizing advanced power electronic devices and digital control techniques in a high-speed welding power supply, it is possible to achieve self-regulation of the electrode contact tube to work-piece distance. This innovation offers a range of customizable features that can enhance and automate the gas metal arc welding (GMAW) process. The focus of this paper is on investigating the dynamic characteristics of a self-regulated consumable electrode, under step changes in the distance between the torch and the work-piece over time. The key components of arc welding processes have been examined, and a fractional PID (PIλDµ) regulator has been developed to maintain the welding current within a predetermined range during both the melting phase and the short-circuiting of the electrode wire. In this study, a weighted sum multi-objective fitness function is utilized to optimize the parameters of a fractional PID regulator using the Bacterial Foraging Optimization (BFO) algorithm. The fitness function incorporates various error criteria, such as Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE), Integral Time Square Error (ITSE), and Integral Square Error (ISE), each with its own assigned weight. To demonstrate the effectiveness of the proposed PIλDµ controller over a conventional PID controller, numerical simulations are performed using MATLAB/SIMULINK software. The simulations also aim to provide insights into the mechanisms that govern the changes in arc voltage and current as the arc length varies, also shedding light on the underlying mechanisms involved. Based on the simulation outcomes, it can be concluded that the automatic arc welding control system utilizing the optimal PIλDµ controller is capable of delivering excellent performance.

Fractional-order PID controller design via optimal selection strategy of frequency domain specifications

In this paper, a novel fractional-order Proportional-Integral Derivative (PID) controller design depending on optimal selection of frequency domain specifications is proposed for time delay systems. The frequency domain specification sets, namely, (i) phase margin and gain crossover frequency and (ii) phase margin and gain margin are determined so that the reference model is optimal according to three time domain performance indices, i.e. Integral Square Error (ISE), Integral Time Square Error (ITSE) and Integral Absolute Error (IAE). Here, the delayed Bode's ideal transfer function is employed in the reference model. Moreover, the stability region of the reference model is given via a theorem. In simulation studies, the proposed methodology is compared with other two different methods using the same frequency domain specifications. It is observed that the proposed optimal fractional-order PID controllers outperform according to the mentioned performance indices, and they also possess considerably acceptable performance in terms of other time domain specifications such as overshoot, settling time, etc.