Comparative Study between Cost Functions of Genetic Algorithm Used in Direct Torque Control of a Doubly Fed Induction Motor

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.

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.

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.

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

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.

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.

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.

The internal model control (IMC) proportional integral derivative (PID) controller tuning rules provide an excellent tracking of set-point, but sluggish disturbance rejection, as the conventional IMC filter introduces slow process pole. Disturbance rejection is significant than set-point tracking in many industrial applications. This paper proposes the design of IMC-PID controller, cascaded with lead–lag filter, with an improved IMC filter to provide effective disturbance rejection and robust operation of the first-order processes (FOPs). The simulation study was conducted to show the effectiveness of the proposed method on various structures of the FOPs, calculating the controller parameters, maintaining similar robustness in terms of maximum sensitivity MS. Perturbations were incorporated in the parameters of the plant model simultaneously, for the robustness analysis of the controller. The closed-loop performance was evaluated with the integral error criteria, namely, integral absolute error, integral square error, and integral time absolute error. The proposed IMC filter provided good disturbance rejection. The results of recently published design methods were compared with that obtained from the proposed method, validating the usefulness of the proposed method.

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 takes up the challenge of modelling a complex nonlinear distillation column type-A and designs four optimal controllers for the same. The nonlinear plant is first linearized into a linear higher-order model. Thereafter, it is reduced into a lower-order model. Subsequently, the controllers are designed for the lower-order linear model. The controllers are designed by reducing the error cost functions, namely Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral Time Absolute Error (ITAE). The process of optimization is done heuristically using the Genetic Algorithm method of tuning. The four controllers designed are Proportional Integral Derivative, Fractional-order Proportional Integral Derivative, Tilt Integral Derivative and Fractional-order Internal Model Control. A thorough comparison is made between the three designed controllers, first on the Single Input Single Output (SISO), then to the reduced-order linear model and finally to the main plant. The FO-IMC controller is shown as an exhibition controller designed using GA to demonstrate the novelty of its kind. It has also been compared, but the results show poor performances as it has not been tuned with the same parameters as the rest.

Reactive Power Control of Isolated Wind-diesel Hybrid Power System Using Grey Wolf Optimization Technique

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).

Desalination plants have an important concern regarding controlling the permeate flow rate and pH during operability. This paper proposes the proportional integral derivative (PID) control design using modified Particle Swarm Optimization (PSO) techniques called autonomous groups PSO (AGPSO) in the two-input two-output (TITO) RO desalination plant to control the permeate flow rate and pH. Here, three different versions (AGPSO1, AGPSO2, and AGPSO3) of the AGPSO algorithm are utilized to design PID control for the same TITO plant. In addition, an integral time absolute error (<inline-formula> <tex-math notation="LaTeX">$J_{\mathrm {ITAE}}$ </tex-math></inline-formula>) based objective function is utilized to design a PID controller. The simulation results suggest that the proposed controller designs are flexible, self-tuning, and have stable characteristics, while the AGPSO3-PID control design attained a robust design for optimum tuning compared to existing improved grey wolf optimization PID (IGWO-PID) and other versions of AGPSO based PIDs (AGPSO1-PID, AGPSO2-PID). The design of AGPSO-PID achieved a minimum objective function than existing IGWO-PID and other versions of AGPSO based PIDs &#x007B;AGPSO1-PID, AGPSO2-PID&#x007D;. Finally, the proposed controller designs outperform the existing IGWO-PID design in literature in terms of control performance, demonstrating a precise control for and the improvement of plant performance.

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.