Integral Square Error Research Articles

Maximum Energy Density for Evaluation of the Dynamic Accuracy of LVDT Sensors Applied in the Energy Industry

This paper presents a proposal in which the maximum energy density criterion is used to evaluate the dynamic accuracy of LVDT (Linear variable differential transformer) sensors for applications in the energy industry. The solutions proposed in the paper are based on a mathematical model of the LVDT sensor, represented by its frequency response. The mathematical foundations required for the synthesis of such a model and the formulae and algorithm necessary to determine the maximum energy density for the integral-square error criterion are presented. Numerical and simulation calculations are performed using MathCad 15 and MATLAB R2014a programs. The solutions presented in this paper can constitute a basis for the selection of LVDT sensors for applications in the energy industry, with a view to achieving accurate diagnostic measurements.

Analyzing the performance of metaheuristic algorithms in speed control of brushless DC motor: Implementation and statistical comparison.

A brushless DC (BLDC) motor is likewise called an electrically commutated motor; because of its long help life, high productivity, smaller size, and higher power output, it has numerous modern applications. These motors require precise rotor orientation for longevity, as they utilize a magnet at the shaft end, detected by sensors to maintain speed control for stability. In modern apparatuses, the corresponding, primary, and subsidiary (proportional-integral) regulator is broadly utilized in controlling the speed of modern machines; however, an ideal and effective controlling strategy is constantly invited. BLDC motor is a complex system having nonlinearity in its dynamic responses which makes primary controllers in efficient. Therefore, this paper implements metaheuristic optimization techniques such as Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Accelerated Particle Swarm Optimization (APSO), Levy Flight Trajectory-Based Whale Optimization Algorithm (LFWOA); moreover, a chaotic map and weight factor are also being applied to modify LFWOA (i.e., CMLFWOA) for optimizing the PI controller to control the speed of BLDC motor. Model of the brushless DC motor using a sensorless control strategy incorporated metaheuristic algorithms is simulated on MATLAB (Matrix Laboratory)/Simulink. The Integral Square Error (ISE) criteria is used to determine the efficiency of the algorithms-based controller. In the latter part of this article after implementing these mentioned techniques a comparative analysis of their results is presented through statistical tests using SPSS (Statistical Package for Social Sciences) software. The results of statistical and analytical tests show the significant supremacy of WOA on others.

Neuro-modelling and fuzzy logic control of a two-wheeled wheelchair system

Two-wheeled wheelchairs have been used as alternatives for the elderly and disabled people to perform physical activities due to their restriction of movement. Significant challenges posed by two-wheeled wheelchairs control due to their inherent instability, resembling that inverted pendulum system. This research addresses these challenges by developing a dynamic non-linear model and stability control using computational algorithms. A neural network-based Nonlinear Autoregressive model with Exogenous Inputs (NARX) was developed, capturing and behaving similar to the complex dynamics of the wheelchair system with the identification on the experimental input–output data. Ensuring stable and responsive control, design of optimized PD-type and PID-type fuzzy logic controllers using Particle Swarm Optimization (PSO) were established and were tested under a simulation environment. The performance was evaluated across various metrics, including Integral Squared Error (ISE), Integral Absolute Error (IAE), Mean Squared (MSE), and Integral Time Absolute Error (ITAE). The result demonstrates that the PSO Optimized PID-type fuzzy logic controller with scaling factor from MSE index performance come out as best overall, significantly outperforms PD-type fuzzy logic controller, reducing its settling time by 12.5% to 35 s, minimizing overshoot to 0.81°, and achieving a negligible steady-state error of 0.046%. These results highlight the significant of integrating fuzzy logic control and PSO to the neural network model in enhancing the stability and performance of two-wheeled wheelchair systems, offering user safety and comfort.

Decentralized fractional-order PIλ control applied to a TITO distillation column: a comparative study with PID and MPC

This paper investigates the use of fractional-order PIλ (FO-PI) controllers and compares their performance with classical integer-order PID (IO-PID) and fractional-order PID (FO-PID) controllers for a two-input, two-output (TITO) distillation column. Additionally, a comparative study between FO-PI and model predictive control (MPC) is conducted on the same multivariable system. While fractional control in multivariable systems has been explored, evaluations of global performance metrics—such as integral square error (ISE), integral absolute value of error (IAE), integral time weighted absolute error (ITAE), integral time weighted square error (ITSE), and integral of manipulated variables (IU)—compared to IO-PID and MPC are still scarce. This work addresses this gap by examining these metrics alongside the steps necessary for fractional control design, including Laplace numerical inversion and controller tuning. The results demonstrate that the FO-PI controller shows superior performance compared to FO/IO-PID and MPC controllers. The global relative gain indexes show improvements, with FO-PI achieving gains of 36.9% to 59.9% compared to FO/IO-PID, and a reduction of 19% to 44.1% in global index compared to MPC. The distillation column dynamics were modeled using transfer functions, allowing for a detailed comparison of control strategies. The studies conducted in this work indicate that fractional-order controllers (FO-PI) show promise in controlling the dynamics of the TITO distillation column, as evidenced by simulations and comparison with integer-order (IO-PID) and fractional-order (FO-PID) control strategies, as well as with MPC control. The study highlights the potential benefits of using fractional controllers for a classical multivariable system, allowing to advance the state of the art of this type of control approach.

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.

Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined.

Enhanced frequency control of a hybrid microgrid using RANFIS for partially shaded photovoltaic systems under uncertainties

Nowadays environmental concerns and fossil fuel limitations, as well as economic benefits and technical issues such as reliability lead conventional distribution networks to smart microgrids, where the renewable energy resources are merged with the grids. Nevertheless, the systems face new challenges due to the intermittent nature and uncertainties in the distributed generations, which cause frequency fluctuations in the microgrid. The photovoltaic cells are the main part of the contemporary microgrids. Although the photovoltaic (PV) systems depend on solar irradiance, and temperature and are affected by the partial shading phenomenon they could contribute to improving the microgrid frequency stability with a proper control scheme. In this paper, the frequency control strategy is designed for a hybrid stand-alone microgrid, which is robust against load disturbances, variations in weather conditions, and uncertainties in the microgrid parameters. The proposed intelligent control scheme relies on the Recurrent Adaptive Neuro Fuzzy Inference System (RANFIS). The Whale Optimization Algorithm (WOA) is employed to optimize the RANFIS controller structure and generate the parameters of membership functions. In this multi-objective optimization, the objectives are settling time (ST), overshoot (Osh), and Integral Square Error (ISE). The simulation results verify the high robustness and performance of the proposed RANFIS controller, compared to other controllers, during various operational circumstances, as well as the sporadic behavior of renewable energy resources (RES) such as fluctuations in solar radiation and certain uncertainties in the microgrid parameters.

A Novel Spotted Hyena Optimizer for the Estimation of Equivalent Circuit Model Parameters in Li-Ion Batteries

Li-ion batteries possess significant advantages like large energy density, fast recharge, and high reliability; hence, they are widely adopted in electric vehicles, portable electronics, and military and aerospace applications. Albeit having their merits, accurate battery modeling is subjected to problems like prior information on internal chemical reactions, complexity in problem formulation, a large number of unknown parameters, and the need for extensive experimentation. Hence, this article presents a reliable Spotted Hyena Optimizer (SHO) to determine the equivalent circuit parameters of lithium-ion (Li-ion) batteries. The methodology of the SHO is derived from the living and hunting tactics of spotted hyenas, and it is efficiently applied to solve the battery parameter estimation problem. Nine unknown battery model parameters of a Samsung INR 18650-25R are determined using this method. The model parameters estimated are endorsed for five different datasets with various discharge current values. Further, the effect of parameter range and its selection is also emphasized. Secondly, for validation, various performance metrics such as Integral Squared Error, mean best, mean worst, and Standard Deviation are evaluated to authenticate the superiority of the proposed parameter extraction. From the computed results, the SHO algorithm is able to explore the search area up to 89% in the case of larger search ranges. The chosen model and range of the SHO precisely predict the behavior of the proposed Li-ion battery, and the results are in accordance with the catalog data.

Design and implementation of Golden Eagle optimized cascaded PI and LQR controller for PFC SEPIC converter in EV charging

This research article focuses on designing and implementing a single ended primary inductor converter (SEPIC) for an AC-DC converter, followed by an electric vehicle (EV) charger. It improves the high-power factor at the AC supply with minimum harmonic distortion. The Golden Eagle optimization techniques are adapted to optimize the tuning of Proportional-Integral (PI) and Linear Quadratic Regulator (LQR) controller parameters for better converter performance. The optimization is designed based on the eagle knowledge of hunting methods at various angles of spiral trajectories in capturing the animal. The SEPIC converter is designed and derived from the state space model by state space averaging, and the reduced model is obtained through the moment matching method to reduce computational complexity. The Golden Eagle Optimize the parameters of KP and KI of the PI controller and weighing matrix Q of the linear quadratic controller. The fitness function of the proposed optimization is the sum of the Integral Absolute error (IAE) and Integral Square error (ISE). The proposed optimization is implemented using MATLAB/SIMULINK software, and the simulation outcomes demonstrate an improved settling time, fast recovery against input and output variations, Total Harmonic Distortion (THD) of 1.75 %, and enhanced stability.

Speed Control for PMSM with Fast-Terminal Super-Twisting Sliding Mode Controller via Extended State Disturbance Observer

Since robustness is only maintained on the sliding-mode surface, sliding mode control is inherently non-globally stable. Therefore, reducing the time to reach the sliding mode is crucial for enhancing sliding mode robustness. To improve the performance of conventional super-twisting reaching law (CSTRL) further, we propose a fast-terminal super-twisting reaching law (FTSTRL) designed to improve the quality of sliding mode control. This approach incorporates a terminal term and an exponential term with the CSTRL to ensure rapid convergence. The effectiveness of the designed FTSTRL is validated by comparing it to the CSTRL and a new sliding mode reaching law, demonstrating its superior performance. Finally, integrated square error (ISE), integrated time square error (ITSE), integrated absolute error (IAE), and integrated time absolute error (ITAE) are employed for detailed comparative and quantitative analyses of the simulation results.

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.

Combustion Control of Ship’s Oil-Fired Boilers Based on Prediction of Flame Images

This study proposes and validates a novel combustion control system for oil-fired boilers aimed at reducing air pollutant emissions through flame image prediction. The proposed system is easily applicable to existing ships. Traditional proportional combustion control systems supply fuel and air at fixed ratios according to the set steam load, without considering the emission of air pollutants. To address this, a stable and immediate control system is proposed, which adjusts the air supply to modify the combustion state. The combustion control system utilizes oxygen concentration predictions from flame images via SEF+SVM as control inputs and applies internal model control (IMC)-based proportional-integral (PI) control for real-time combustion control. Due to the complexity of modeling the image-based system, IMC filter constant tuning through experimentation is essential for achieving effective control performance. Experimental results showed that optimal control performance was achieved when the filter constant λ was set to 1.5. In this scenario, the peak overshoot Mp was reduced to 0.19245, and the Integral of Squared Error (ISE) was minimized to 10.1159, ensuring a stable response with minimal oscillation and maintaining a fast response speed. The results demonstrate the potential of the proposed system to improve combustion efficiency and reduce emissions of air pollutants. This study provides a feasible and effective solution for enhancing the environmental performance of marine oil-fired boilers. Given its ease of application to existing ships, it is expected to contribute to sustainable air pollution reduction across the maritime environment.

Comparison between Genetic Algorithms of Proportional–Integral–Derivative and Linear Quadratic Regulator Controllers, and Fuzzy Logic Controllers for Cruise Control System

One of the most significant and widely used features currently in autonomous vehicles is the cruise control system that not only deals with constant vehicle velocities but also aims to optimize the safety and comfortability of drivers and passengers. The accuracy and precision of system responses are responsible for cruise control system efficiency via control techniques and algorithms. This study presents the dynamic cruise control system model, then investigates a genetic algorithm of the proportional–integral–derivative (PID) controller with the linear quadratic regulator (LQR) based on four fitness functions, the mean squared error (MSE), the integral squared error (ISE), the integral time squared error (ITSE) and the integral time absolute error (ITAE). Then, the response of the two controllers, PID and LQR, with the genetic algorithm was compared to the response performance of the fuzzy and fuzzy integral (Fuzzy-I) controllers. The MATLAB 2024a program simulation was employed to represent the system time response of each proposed controller. The output simulation of these controllers shows that the type of system stability response was related to the type of controller implemented. The results show that the Fuzzy-I controller outperforms the other proposed controllers according to the least Jmin function, which represents the minimum summation of the overshoot, settling time, and steady-state error of the cruise control system. This study demonstrates the effectiveness of driving accuracy, safety, and comfortability during acceleration and deceleration due to the smoothness and stability of the Fuzzy-I controller with a settling time of 5.232 s and when converging the steady-state error to zero.

Advanced control and energy management algorithm for a multi-source microgrid incorporating renewable energy and electric vehicle integration

This paper presents a comprehensive study on advanced control and energy management in a multi-source/multi-load microgrid. The microgrid integrates solar panels, a wind turbine system, a Li-ion battery-based storage system, an electric vehicle (EV), and a DC load, all inter-connected through power electronic converters to a DC bus and linked to the AC grid via a DC/AC inverter. The study outlines the primary control objectives: DC bus voltage regulation, optimization of photovoltaic and wind energy conversion, and maintaining high-quality energy injection into the grid. Given the intermittent nature of solar and wind energy and the varying energy demands that affect battery life and performance, a novel energy management algorithm is introduced. This algorithm addresses different operating modes, such as Constant Current (CC) and Constant Voltage (CV), to enhance network stability, energy quality, and optimize energy distribution between the various sources and the EV. The proposed fuzzy logic controllers, known for their robustness to uncertainties, flexibility, and ease of implementation, are employed to achieve these objectives. The Particle Swarm Optimization (PSO) is used to fine-tune the fuzzy logic control parameters, ensuring optimal performance. This optimization process included minimizing Integral Absolute Error (IAE), Integral Square Error (ISE), and Integral Time-weighted Square Error (ITSE) as objective functions. Extensive simulations under various operating scenarios demonstrated significant improvements in control accuracy, stability, and system performance.

Comparative performance analysis of robust and adaptive controller for three-link robotic manipulator system

Abstract Three-link robotic manipulator systems (TLRMS) often used in automation industries offer many capabilities, but become very complex in terms of their control and operations. In order to enhance trajectory tracking in the X and Y axes, this study investigates the application of a fractional-order nonlinear proportional, integral, and derivative (FONPID) controller for a three-link robotic manipulator system (TLRMS). Using a cost function that combines the integral of square error (ISE) and the integral of absolute change in controller output (IACCO), the cuckoo search algorithm (CSA) maximises the performance of the controller. The fractional-order term enhances the robustness and the nonlinear term supports the adaptiveness of the FONPID controller. The fractional-order proportional, integral, and derivative (FOPID) and classic PID controllers are contrasted with the FONPID controller's efficacy. The findings show that the CSA-tuned FONPID performs better than the other controllers, providing more robust and accurate tracking. By demonstrating fractional-order control's promise for intricate robotic systems, this study advances the discipline.

Optimization of dual-stage controllers in renewable energy sources-based interconnected power systems through refinement of the African Vultures Optimization Algorithm

With an emphasis on a three-region system, this paper explores automaticgeneration control within a conventional framework. Area 2 uses thermal-thermal sources, Area 3 uses gas-thermal sources, and Area 1 uses thermal-biodiesel sources. IPD(1 + I) is a unique cascade controller that combines integral-proportional-derivative (IPD) components with one-plus-integral (1 + I) components. To find the best gains and settings for the IPD(1 + I) controller, a meta-heuristic method called the African Vulture Optimization Algorithm (AVOA) is applied. Reducing the integral squared error (ISE), as determined by the performance index (Pi), is the main goal. The performance of the IPD(1 + I) controller is evaluated by contrasting it with a range of secondary controllers. Hybrid Peak Area-ISE (hPA-ISE), a novel performance metric, is also assessed in addition to the conventional ISE. The incorporation of renewable energy sources, such solar thermal energy and solid oxide fuel cells, significantly improves the system’s performance. Interestingly, under normal conditions, the IPD(1 + I) controller’s parameter settings continue to work for both sinusoidal and random load situations, obviating the need for additional tuning.

Enhancing DC Motor Speed Control Performance Using Heuristic Optimization and Comparative Analysis of Control Methods

Direct Current (DC) motors are an important component that converts electrical energy into mechanical energy, used in a wide range of applications from industrial applications to home appliances. DC motor speed control has an important role in industrial processes to increase efficiency, realize precise movements and optimize energy consumption. In this study, various control methods and parameter optimization techniques for speed control of DC motors, which have a wide range of applications, have been systematically analyzed. The aim of the study is to develop an effective control strategy to ensure that DC motors reach the determined target speed by monitoring them in real time at different speeds and to minimize fluctuations caused by variable loads or external factors. In our study, Proportional-Integral-Derivative (PID), Proportional-Integral (PI), and Proportional-Derivative (PD) control methods were used. The parameters of these controllers were tuned using Matlab Tuned, The Cheetah Optimizer (CO) Algorithm, a new generation heuristic optimization method, and Particle Swarm Optimization (PSO), a widely accepted optimization method. The performances of the controllers were determined using criteria such as Integral of Absolute Error (IAE), Integral Squared Error (ISE), and Integral of Time multiplied by Absolute Error (ITAE). According to the results obtained, it was found that the PID, PI and PD control parameters determined using the CO Algorithm performed better than the controllers created using Matlab Tuned and PSO methods. New optimization methods, such as the CO Algorithm, have been found to have significant potential to improve the performance of control systems. Thanks to this study, it offers a practical approach for optimizing DC motor speed control in industrial processes. As a result, it has been found that the control parameters determined by the CO Algorithm have significant potential in improving the performance of DC motor speed control and control systems compared to other optimization methods.

A Nonlinear Active Disturbance Rejection Feedback Control Method for Proton Exchange Membrane Fuel Cell Air Supply Subsystems

The control strategy of the gas supply subsystem is very important to ensure the performance and stability of the fuel cell system. However, due to the inherent nonlinear characteristics of the fuel cell gas supply subsystem, the traditional control strategy is mainly based on proportional integral (PI) control, which has the disadvantages of large limitation, large error, limited immunity, and inconsistent control performance, which seriously affects its effectiveness. In order to overcome these challenges, this paper proposes an optimal control method for air supply subsystems based on nonlinear active disturbance rejection control (ADRC). Firstly, a seven-order fuel cell system model is established, and then, the nonlinear ADRC and traditional PI control strategies are compared and analyzed. Finally, the two strategies are simulated and compared. The validation results indicate that the integral absolute error (IAE) measure of PI control is 0.502, the integral square error (ISE) measure is 0.1382, and the total variation (TV) measure is 399.1248. Compared with the PI control, the IAE and ISE indexes of ADRC were reduced by 61.31% and 58.03%, respectively. ADRC is superior to PI control strategy in all aspects and realizes the efficient adjustment of the system under different working conditions. ADRC is more suitable for the nonlinear characteristics of the gas supply system and is more suitable for the oxygen excess ratio (OER).

Optimization of the different controller parameters via OBL approaches based artificial ecosystem optimization involving fitness distance balance guiding mechanism for efficient motor speed regulation of DC motor

This study proposes a new optimization approach, which is called as artificial ecosystem optimization algorithm with fitness-distance balance guiding mechanism by using opposite based learning methods (FDBAEO_OBLs) for the speed regulation of direct current (DC) motor. The performance of the proposed FDBAEO_OBL algorithm is tested in two different experimental studies. In the first experimental study, the proposed approach is tested in the CEC2020 benchmark test functions and the FDBAEO algorithm, which included the best OBL approach, is determined using non-parametric Wilcoxon and Friedman statistical analysis methods. Second, the parameters of proportional integral derivative (PID), tilt integral derivative (TID), proportional integral derivative with filter (PIDF), tilt integral derivative with filter (TIDF), fractional-order proportional integral derivative (FOPID), fractional-order proportional integral derivative with filter (FOPIDF), proportional integral derivative with fractional-order filter (PIDFF) and fractional-order proportional integral derivative with fractional-order filter (FOPIDFF) controller structures to be used in DC motor closed loop speed control are determined with FDBAEO_OBL, and the performances of the controllers are investigated. Integral absolute error (IAE), integral time absolute error (ITAE), integral time squared error (ITSE) and integral squared error (ISE) performance indices are used as the objective function of the operation process in which the control parameters are determined. According to the comparative step response results of the controller structures, the four best controller structures for DC motor speed regulation are determined. The performances of these controllers are examined under different simulation conditions and according to the results obtained, it is seen that the best controller structure is FOPIDFF. The FDBAEO_OBL algorithm, which is used in both benchmark test functions and DC motor speed regulation, shows an effective, durable and superior performance in finding the optimal solution values during the optimization.

Performance Evaluation of Fractional Proportional–Integral–Derivative Controllers Tuned by Heuristic Algorithms for Nonlinear Interconnected Tanks

This article presents an in-depth analysis of three advanced strategies to tune fractional PID (FOPID) controllers for a nonlinear system of interconnected tanks, simulated using MATLAB. The study focuses on evaluating the performance characteristics of system responses controlled by FOPID controllers tuned through three heuristic algorithms: Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Flower Pollination Algorithm (FPA). Each algorithm aims to minimize its respective cost function using various performance metrics. The nonlinear model was linearized around an equilibrium point using Taylor Series expansion and Laplace transforms to facilitate control. The FPA algorithm performed better with the lowest Integral Square Error (ISE) criterion value (297.83) and faster convergence in constant values and fractional orders. This comprehensive evaluation underscores the importance of selecting the appropriate tuning strategy and performance index, demonstrating that the FPA provides the most efficient and robust tuning for FOPID controllers in nonlinear systems. The results highlight the efficacy of meta-heuristic algorithms in optimizing complex control systems, providing valuable insights for future research and practical applications, thereby contributing to the advancement of control systems engineering.