Improved Adaptive PSO-based Gain Tuning for PID Controllers in Utility Boilers

In this paper, 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. The controller has been applied to a control study of Fluid Catalytic Cracking (FCC) unit riser temperature, and regenerator temperature respectively. Performance comparison 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.

This paper uses a particle swarm optimization (PSO) algorithm, an adaptive weighted PSO (AWPSO) algorithm, and a genetic algorithm (GA) to determine the optimal proportional-integral-derivative controller’s parameters of a hydraulic position control system. A typical hydraulic servo system has been selected as an application. The mathematical model of this hydraulic servo system which comprises the most relevant dynamics and nonlinear effects is considered. The model simulates the behavior of a REXROTH servo valve and includes the nonlinearities of friction forces, valve dynamics, oil compressibility, and load influence. The performance indices, which have been used in the optimization process, are integral absolute error, integral square error and integral time absolute error. The proposed controller is implemented on the simulation model to identify the best method for tuning the controller. Compared with GA and AWPSO results, the PSO method has been found to be more efficient and robust in improving the step response of a position control for hydraulic systems in terms of settling time, maximum overshoot and undershoot.

This paper proposes the particle swarm optimization (PSO) technique-based proportional integral derivative (PID) controller suggested for frequency regulation of a micro grid (MG) system. MG system integrates with thermal power generating units, renewable energy sources (RES) like photovoltaic (PV), wind energy generators (WTG), and Energy storage systems (ESS) such as fuel cell (FC) and battery energy storage system (BESS). Indentifying the supremacy of proposed technique-based controller and supremacy is examined with three objective functions (integral absolute error [IAE], integral time absolute error [ITAE], and integral squared error [ISE]). The results of the system are compared with conventional PID controller results. From the comparison, it is clearly evident that PSO-PID controller gives better performance over conventional methods in terms of various time domain specific parameters such as settling time, peak overshoot, and undershoot. In both methods, ITAE objective function used controller produce more effective response in MG under sudden load demand situation.

Aiming at the control variables of reactive power optimization are discrete, and some parameters in the standard particle swarm optimization (PSO) algorithm need to be predefined by test, so the algorithm's practicability is restricted. For these reasons, an adaptive particle swarm optimization (APSO) algorithm is proposed by the authors. APSO introduces the self-adaptive tuning strategy and boundary constraint conditions can find the global optimal solution and solve the discrete variables. The reactive power optimization results of the standard IEEE-30-bus power system show that APSO is efficient than standard PSO. The global convergence accuracy and convergence stability is obviously improved compared with that of PSO.

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.

Model reduction techniques are simplification methods based on mathematical approaches employed to realize reduced models for the original high order systems. Some existing classical model reduction techniques for multivariable system are considered and compared for their performances. Interlacing property and coefficients matching (IPCM) method gives overall minimum integral square error (ISE), integral absolute error (IAE) and integral time absolute error (ITAE) values compared to other methods. Though the IPCM method is efficient, it may not guarantee for minimization of all objective functions simultaneously. In this paper, model reduction approach based on objectives like ISE, IAE and ITAE using multi-objective differential evolution (MODE) method is proposed for reducing the numerator and the denominator is reduced by interlacing property. MODE method minimizes the small, normal and large errors persisting for long time between original and reduced models. This multi-objective approach is applied for model reduction of 10th order multivariable linear time invariant power system model. Simulation results are demonstrated for single and multi-objective model reduction and compared with multi-objective particle swarm optimization (MOPSO) method to prove the validity of proposed MODE technique.

This paper presents a new neural network based model reference adaptive system (MRAS) to solve low speed problems for estimating rotor resistance in vector control of induction motor (IM). The MRAS using rotor flux as the state variable with a two layer online trained neural network rotor flux estimator as the adaptive model (FLUX-MRAS) for rotor resistance estimation is popularly used in vector control. In this scheme, the reference model used is the flux estimator using voltage model equations. The voltage model encounters major drawbacks at low speeds, namely, integrator drift and stator resistance variation problems. These lead to a significant error in the estimation of rotor resistance at low speed. To address these problems, an offline trained NN with data incorporating stator resistance variation is proposed to estimate flux, and used instead of the voltage model. The offline trained NN, modeled using the cascade neural network, is used as a reference model instead of the voltage model to form a new scheme named as “NN-FLUXMRAS.” The NN-FLUX-MRAS uses two neural networks, namely, offline trained NN as the reference model and online trained NN as the adaptive model. The performance of the novel NN-FLUX-MRAS is compared with the FLUX-MRAS for low speed problems in terms of integral square error (ISE), integral time square error (ITSE), integral absolute error (IAE) and integral time absolute error (ITAE). The proposed NN-FLUX-MRAS is shown to overcome the low speed problems in Matlab simulation.

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.

Abstract: This study presents a comparative analysis of five metaheuristic algorithms for optimizing Proportional Integral Derivative (PID) controller parameters in a vehicle cruise control system. The selected algorithms include the Rain Optimization Algorithm (ROA), Student Psychology-Based Optimization (SPBO), Sine Cosine Algorithm (SCA), Gradient-Based Optimization (GBO), and Grey Wolf Optimization (GWO). The PID parameters are optimized using four common performance criteria: Integral Time Absolute Error (ITAE), Integral Absolute Error (IAE), Integral SquareError (ISE), and Integral Time Square Error (ITSE). Unlike conventional tuning methods, metaheuristic approaches provide more flexible and adaptive parameter selection, enhancing the control system's robustness. The study analyses the algorithms under several internal and external disturbances, including road incline, passenger mass, and measurement noise. The findings demonstrate that no singular algorithm is universally superior; instead, efficacy is contingent upon the particular system conditions and control objectives. The Sine Conine Algorithm (SCA) has superior overall performance under typical settings, while GWO attains the quickest response time for slope fluctuations. Conversely, ROA reduces overshoot, rendering it appropriate for applications that necessitate stability. Additionally, the proposed methods are compared with the classical Ziegler-Nichols tuning approach, demonstrating the advantages of metaheuristic algorithms in terms of reduced overshoot, faster settling time, and improved robustness. The findings indicate that the SCA with the ITAE criterion yields superior performance under varying disturbance conditions. However, the fastest system response under different slope conditions isachieved with the parameter values determined by the GWO employing the ITSE criterion. The system model is designed in a MATLAB environment and the detailed comparative results are provided in figures and tables.Cite this article as: F. Heybetli, Y. Danayiyen, A. Begüm Taşdemir and Ş. Şenyiğit, "Comparative analysis of metaheuristic algorithms in PID-based vehicle cruisecontrol systems," Electrica, 25, 0051, 2025. doi: 10.5152/electrica.2025.24051.

Aircraft are the most common kind of transportation utilized by the government, commercial, military, and so on. Controlling the motion of an aircraft is a highly nonlinear operation. However, regulating direction and motion is critical in the aviation industry to prevent accidents, injury, and other problems. It is vital to pay attention to factors like stability in an aircraft. For stabilization, 3 orientationswere used to determine the movements: yaw, pitch, and roll. The main purpose of this research is to create a controller that could be used to regulate the pitch of an aircraft. This part of control will assist the plane in dropping or rising. Pitch can be varied by altering the elevator, which is located on the plane's rear portion. The longitudinal mechanics of aircraft were used to create the aircraft pitch system mathematically. The advanced controller, neuro-fuzzy, is used to regulate the pitch automatically. The performance of the neuro-fuzzy controller is equated to the traditional Proportional Integral Derivative (PID) controller. Two parameters are used for comparison: time characteristics and assessment metrics. Integral square error (ISE), Integral Absolute Error (IAE), and Integral Time Absolute Error (ITAE) is the assessment measures used in this study. The simulation outcomedemonstrates that the neuro-fuzzy controller outperforms the PID controller.

The proportional integral derivative (PID) regulator is the most often utilized controller in the industry due to its benefits. It permits linear systems to operate well, but it causes non-linear behavior when the system is subjected to physical variable circumstances, such as temperature and saturation. A PID controller is insufficient in this case. The proportional integral (PI) controller inside the direct torque control (DTC) regulates the speed of the doubly fed induction motor (DFIM). However, the system consisting of DTC and a DFIM is non-linear due to its multivariable parameters, resulting in undesirable overshoots and torque ripples. As a result, several approaches are used to improve the DTC’s robustness. The integration of optimization methods was discovered. These algorithms are used to provide gains that are near-optimal, bringing the system closer to its ideal state in order to accomplish effective torque and speed control. This article focuses on a comparative study of the different objective functions, in order to have very effective DFIM behaviors, by using a genetic algorithm. Agenetic algorithm (GA) is presented in this study for adjusting the optimal PID parameters in DTC to control the DFIM, utilizing objective functions such as integral square error (ISE), integral time absolute error (ITAE), and integral absolute error (IAE), employed independently and in a weighted combination. This article offers a comparison of several objective functions inside the DTC and DFIM, which will be utilized in future research into another optimization technique for this control type. Matlab/Simulink was used to construct the novel hybrid structure based on the GA-DTC intelligent control. The simulation results demonstrated the efficiency of the GA-DTC intelligent control with a weighted combination, providing acceptable performance with respect to rapidity, precision, and stability, as well as an improvement of 14.53% in the rejection time reduction, fewer torque ripples and flux ripples on the stator and rotor by 27.88%, 15.13%, and 4.375%, respectively, and respective increases of 32.45% and 71% in the THDs of the stator and rotor currents, which are acceptable.

In the real world, the tracking controllers designed for ideal scenarios will be inaccurate due to presence of noise. This paper deals with trajectory tracking control of a two-link manipulator using three different tracking controllers namely, Proportional Integral Derivative (PID), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Back-stepping controller in a noisy environment. Here, the PID controller is designed using the singular perturbation technique, it helps in dealing with external noise. However, its performance is not good with variable noise. Thus, the ANFIS controller is developed in which the rules are based on data collected from previously designed PID controller. Lastly, the back-stepping controller based on the virtual control signal using Lyapunov for zero error tracking is developed. The three controllers for the manipulator have been tested with the introduction of variable random noise and a fixed noise quantity. Performance analysis of these controllers is based on ISE (Integral Square Error), IAE (Integral Absolute Error), ITSE (Integral Time Squared Error), and ITAE (Integral Time Absolute Error). The simulation results illustrate the accuracy of the ANFIS controller which has better tracking in comparison to the other two control schemes with comparable torque inputs.

In this article we describe a novel Adaptive particle swarm optimization (APSO) algorithm based on population diversity information. It is presented to solve the precocious convergence problem of particle swarm optimization algorithm. The APSO algorithm uses the information of the population diversity to adjust nonlinearly inertia weight. Velocity mutation factor and position interchange factor are both introduced and the global performance is clearly improved. The APSO algorithm is applied to optimization of parameters in the optimal model based on support vector machine (SVM). SVM is a popular classification method with many diverse applications. A novel Adaptive particle swarm optimization (APSO) based approach for parameter determination and feature selection of the SVM, termed APSO+SVM is developed. The illustrating example shows that the classification accuracy of APSO+SVM is higher than other traditional methods of classification, so using APSO+SVM method to classify is feasible and effective.

This paper presents a modern approach for speed control of an induction motor (IM) using the particle swarm optimization (PSO) method for determining the optimal parameters, Kp and Ki, of the integral proportional (IP) controller. The use of PSO as an optimization algorithm makes the drive robust, with faster dynamic response, higher accuracy and insensitive to load variation. Comparison between different controllers is achieved, using an IP controller which is tuned by two methods, firstly manually and secondly using the PSO technique. Integral time absolute error, integral absolute error and integral square error performance indices are considered to satisfy the required criteria in output speed of an IM. From the simulation results it is observed that the IP controller designed with PSO yields better results when compared to the traditional method in terms of performance index.

Brushless DC (BLDC) motors are the most popular motors used by the industry because they are easy to control. BLDC motors are generally controlled by artificial controls such as Fuzzy Logic Controller (FLC), Artificial Neural Network (ANN), and Adaptive Neuro-Fuzzy Inference System (ANFIS). However, the performance of the BLDC control system in previous studies was compared separately with their respective parameters, making it difficult to evaluate comprehensively. Therefore, in order to investigate the characteristic performance of Fuzzy, ANN, and ANFIS, this article provides a comparison of these artificial controls. Two scenarios of the dynamic tests are conducted to investigate control performance under constant torque-various speed and constant speed-various torque. By dynamic testing, characteristics of Fuzzy, ANN, and ANFIS can be observed as real applications. The testing parameters are: Settling Time, Overshoot and Overdamp (in the graph and average value), and then statistic performance are: Integral Square Error (ISE), Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE), and Mean Absolute Error (MAE). The test result in scenario 1 showed that the ANN has a better performance compared to other controllers with the MAE, IAE, ITAE, and ISE value of 31.3003; 105.6280; 208.0630; and 5,7289 e4, respectively. However, in scenario 2, ANN only has a better performance compared to other controllers on just a few parameters. In scenario 2, ANN is indeed able to maintain speed but it has a more ripple value than ANFIS. Even so, the ripple that occurs in ANN does not have too much value compared to the setpoint. Therefore, the MAE value of the ANN is smaller than the ANFIS (18.8937 of ANN and 28.4685 of ANFIS).