Integral Time Absolute Error Research Articles

Region of convergence by parameter sensitivity constrained genetic algorithm-based optimization for coordinated load frequency control in multi-source distributed hybrid power system

The imbalances created by generation and load can indeed result in frequency variations demanding a load frequency control (LFC). The LFC becomes even more complicated with the multi-source distributed hybrid power system (HPS), where designing optimal controller parameters by identifying the region of convergence (RoC) is critical as it guarantees the HPS's stability. Hence, this paper aims to address the frequency regulation (FR) issue in a state-of-the-art modeled multi-source distributed HPS with a coordinated control approach. The modeled HPS includes a reheat thermal power system (RTPS), wind turbine generator (WTG), fuel cell (FC) stack, battery energy storage system (BESS), diesel engine generator (DEG), and various controllers.A novel method called parameter sensitivity algorithm (PSA) is proposed to obtain the RoC of the controller gains and is further optimized using a constrained genetic algorithm (GA). To demonstrate coordinated control effectiveness, a hybrid objective function for optimization is formulated as constrained GA's fitness function using the integral time absolute error (ITAE) and integral absolute error (IAE). Furthermore, a comparative assessment for PI, PID with filter (PIDN), cascaded PI-PD with filter (PIPDN) controller topologies is carried out using error index-based performance metrics to ascertain the preeminence of the hybrid objective function over existing objective functions. The investigation results validate that the suggested optimized controllers provide enhanced FR and are robust to uncertainties. The practical feasibility of the proposed methodology is reinforced using dSPACE hardware in loop testing.

A New Fractional-Order Load Frequency Control for Multi-Renewable Energy Interconnected Plants Using Skill Optimization Algorithm

Connection between electric power networks is essential to cover any deficit in the generation of power from any of them. The exchange powers of the plants during load disturbance should not be violated beyond their specified values. This can be achieved by installing load frequency control (LFC); therefore, this paper proposes a new metaheuristic-based approach using a skill optimization algorithm (SOA) to design a fractional-order proportional integral derivative (FOPID)-LFC approach with multi-interconnected systems. The target is minimizing the integral time absolute error (ITAE) of frequency and exchange power violations. Two power systems are investigated. The first one has two connected plants of photovoltaic (PV) and thermal units. The second system contains four plants, namely, PV, wind turbine, and two thermal plants, with governor dead-band (GDB) and generation rate constraints (GRC). Different load disturbances are analyzed in both considered systems. Extensive comparisons to the use of chef-based optimization algorithm (CBOA), jumping spider optimization algorithm (JSOA), Bonobo optimization (BO), Tasmanian devil optimization (TDO), and Atomic orbital search (AOS) are conducted. Moreover, statistical tests of Friedman ANOVA table, Wilcoxon rank test, Friedman rank test, and Kruskal Wallis test are implemented. Regarding the two interconnected areas, the proposed SOA achieved the minimum fitness value of 1.8779 pu during 10% disturbance on thermal plant. In addition, it outperformed all other approaches in the case of 1% disturbance on the first area as it achieved ITAE of 0.0327 pu. The obtained results proved the competence and reliability of the proposed SOA in designing an efficient FOPID-LFC in multi-interconnected power systems with multiple sources.

Experimental Modeling of a New Multi-Degree-of-Freedom Fuzzy Controller Based Maximum Power Point Tracking from a Photovoltaic System

Conventional control methods, which follow the maximum power point (MPP), suffer from being slow or inaccurate during sudden changes in irradiance and temperature. These problems can be solved using artificial intelligence algorithms. The current study proposes a new multi-degree-of-freedom (MDOF) fuzzy logic controller (FLC) for maximizing the overall output performance of a photovoltaic system. The MDOF-FLC was compared to the simplified universal intelligent PID controller (SUI-PID) using the MDOF concept and the normal FLC. Simulation and experimental results show that the proposed MDOF-FLC controller has a 37.8% and 58.1% faster response with a better rise time compared to the SUIPID controller and the normal FLC, respectively. At the same time, the error, measured by the integral time absolute error (ITAE), was 29.4% and 62.5% lower, respectively.

Optimal online battery power control of grid-connected energy-stored quasi-impedance source inverter with PV system

This study presents an optimal online control that implements a biogeography-based optimization (BBO) algorithm on a battery energy system (BES) integrated into an energy-stored quasi-impedance source inverter (qZSI) that connects a photovoltaic (PV) power plant to the grid. The BBO algorithm was used to tune the PI regulator in the BES current control loop by minimizing the integral time absolute error (ITAE). Two different options for the BBO are compared in this application:1) a PI controller with online self-tuning based on BBO, and 2) a PI controller with offline tuning using BBO. Moreover, the BBO-based PI controllers were compared with a third controller tuned online using the particle swarm optimization (PSO) algorithm. To evaluate and compare the controllers, a PV power plant with a battery energy-stored qZSI was simulated under different operating conditions, such as step changes in the BES current reference, different sun irradiance, and a grid voltage sag. The results demonstrate better control of the BES current with the online tuning techniques (BBO and PSO) than with the offline tuning procedure, and similar results between the two online tuning algorithms. Nevertheless, throughout the simulation, the time of use of the BBO algorithm was almost 2.5 times smaller than the PSO algorithm. Therefore, the online BBO-based PI controller is considered the most suitable option.

Stability analysis of the pitch angle control of large wind turbines using different controller strategies

Reducing the environmental impact necessitates a boost in renewable energy conversion systems. Wind energy is regarded as one of the most essential energy sources. For this purpose, the high wind variations in the energy conversion chain require robust and reliable control. This research aims to implement a regulation based on artificial intelligence toward a blade orientation mechanism to improve the stability of energy conversion. On the other hand, an energy maximization technique called Maximum Power Point Tracking (MPPT) is integrated into the control system. A developed program in MATLAB estimates the turbine performance with two different strategies, namely the MPPT technique and the Pitch control mechanism. For the best control and more stability of energy conversion, three artificial intelligence controllers, which are Neuronal Network (PI-ANN), Fuzzy Logic (PI-FLC), and Neuro-Fuzzy (PI-NFLC), were employed. They are compared with the conventional controller (PI-C). This comparison is made to distinguish the most robust regulator against wind speed variations. The different performance indices showed that the controller PI-NFLC has an excellent response, with an Integral Time Absolute Error (ITAE) of 375.28, whereas the Integral Absolute Error (IAE) and Integral Time Square Error (ITSE) equal 13.87 and 406.59, respectively.

System Identification and Control of Automatic Car Pedal Pressing System

This paper mainly explores the system identification and control of an automatic car pedal pressing system. Specifically, the system identification was achieved using an artificial neural network, with the help of MATLAB’s System Identification Toolbox. The proportional-integral-derivative (PID) controller and fuzzy logic controller were designed, and normalized with membership functions. These functions were scaled with a gain as a scaling factor. The controller gains were tuned by a metaheuristic algorithm named particle swarm optimization (PSO). On this basis, the two controllers were compared with a number of performance indices, including integral squared error (ISE), integral absolute error (IAE), integral time absolute error (ITAE), and mean squared error (MSE). The car pedal pressing performance was measured at different speed levels for each controller.

A maiden robust FPIDD2 regulator for frequency-voltage enhancement in a hybrid interconnected power system using Gradient-Based Optimizer

This paper proposes a maiden intelligent controller design that consists of a fuzzy proportional-integral-derivative-double derivative (FPIDD) controller whose parameters are fine-tuned using the Gradient-Based Optimization algorithm (GBO). The proposed FPIDD2 regulator is employed as a secondary regulator for stabilizing the combined voltage and frequency loops in a two-area interconnected power system. The proposed FPIDD2 controller is tested in a two-area hybrid system, with each area comprising a mix of traditional (thermal, gas, and hydraulic power plants) and renewable generation units (wind and solar power). Additionally, the proposed controller takes into account system nonlinearities (such as generation rate limitations and governor deadband), system uncertainties, and load/renewables changes. The dynamic responses of the system demonstrate that FPIDD2 has superior ability to attenuate the deviations in voltage and frequency in both areas of the system. In the investigated hybrid system, the suggested FPIDD2 is compared to a GBO-tuned integral derivative tilted (ID-T) controller and FPID controller. As a fitness function for the GBO, the criteria of minimizing the integral time absolute error (ITAE) are applied. The results are presented in the form of MATLAB/SIMULINK time-domain simulations. The simulation outcomes prove that the presented controller has an outstanding performance compared with the other control strategies in the dynamic response of the system in terms of rising and settling times, maximum overshoot, undershoot values and ITAE. The ITAE value of the FPIDD2 regulator tuned by the GBO technique was enhanced by 90.9% with the GBO-based ID-T and 55.4% with GBO-based FPID controllers.

A Robust Artificial Bee Colony-Based Load Frequency Control for Hydro-Thermal Interconnected Power System

The presented work examines load frequency control (LFC) to develop the dynamic behavior of the power system under different load disturbances that have occurred in multi-interconnected power systems. An artificial bee colony (ABC) algorithm is proposed to design an optimal proportional integral derivative (PID) controller simulating the LFC installed in a hybrid hydro-thermal interconnected power system. The proposed approach incorporating ABC is employed to determine the optimal parameters of the controller during load disturbance applied on one area. The integral time absolute error (ITAE) of the frequency and exchange power violations is considered as the target to be minimized. Moreover, integral absolute error (IAE) and sum squared error (SSE) are calculated. To prove how the proposed model controller is effective, two-interconnected power systems are presented during a wide range of operating cases, and then the behavior of the proposed controller is compared to that of the designed via a chef-based optimization algorithm (CBOA), seagull optimization approach (SOA), and sine cosine approach. Regarding the 5% disturbance on the thermal plant, the ABC outperformed the other approaches hence achieving the best fitness value of 1.80936, IAE of 3.147938, and SSE of 0.1787486. On the other hand, during a 5% disturbance on the hydro plant, the ABC succeeded in getting ITAE, IAE, and SSE with values of 3.43291, 3.630509, and 0.5233815, respectively. The efficiency and prevalence of the proposed LFC-PID is confirmed by the achieved results.

Systematically derived weights based order diminution of continuous systems using GWO algorithm

In this research article, approximation of higher order systems (HOSs) is proposed by minimizing the errors between time moments (TMs) and Markov parameters (MPs) of HOS and desired reduced order model (ROM) using grey wolf meta-heuristic optimization algorithm by utilizing systematic procedure of finding weights. The TMs and MPs of HOS and ROM are utilized to frame the objective function. The weights associated with the objective function are determined by systematic procedure namely analytic hierarchy process (AHP). The multi-objective problem is converted into single-objective problem by utilizing these weights. In objective function, normalized errors are minimized using grey wolf optimization (GWO) algorithm to derive the desired ROM. To ensure the steady state matching between HOS and its ROM, first TMs of HOS and desired ROM are matched. The Hurwitz stability criterion is utilized to retain the stability of HOS. The determination of efficacy of proposed method is attained by considering two test systems. The comparative analysis is also done by considering time domain specifications (TDSs) and error indices (EIs) for these test systems. The TDSs considered for comparative analysis are rise time, peak time, settling time and peak. The errors such as integral-absolute-error (IAE), integral-square-error (ISE), integral-time-absolute-error (ITAE), integral-time-square-error (ITSE), integral-time-square-absolute-error (IT2AE) and integral-time-squared-square-error (IT2SE) between HOS and those of the ROMs are tabulated as EIs. The comparative analysis demonstrates the productiveness and efficacy of the proposed method. The utility of proposed method is ensured by providing the step response, impulse response, Bode plot and Nyquist plot.

Optimizing BLDC motor drive performance using particle swarm algorithm-tuned fuzzy logic controller

A brushless DC (BLDC) motor is synchronous motor with trapezoidal/square wave counter-electromotive force, which is a typical example of highly coupled nonlinear systems. In industrial control, BLDC motor drive usually uses proportional–integral (PI) controller to control the speed, but it is very difficult to adjust the scale factors. In this study, we present a particle swarm algorithm-tuned fuzzy logic-PI (PF-PI) controller applied to the speed control system. The objective of this paper is to optimally tune the PI controller parameters to obtain the best drive response. The scale factors are optimized using particle swarm optimized-PI (P-PI) controller and PF-PI controller. The three performance indicators integral time absolute error (ITAE), integral time square error (ITSE) and integral square error (ISE) are used to measure the effectiveness of PF-PI controller optimization. The results show that the optimal torque ripple and speed response curves are obtained by using ITAE as the performance indicator. The conclusions demonstrate that the proposed method provides superior dynamic performance for BLDC motor.HighlightsIn terms of research content, we propose a new PF-PI controller driven control system based on the traditional BLDC speed control system, and the applicability of three performance indicators on the controller is discussed.In terms of research method, we compare the no-load start, variable speed and sudden addition disturbance load start capabilities of P-PI controller and PF-PI controller, and verify the fast and robustness of PF-PI controller.In the research significance, the PI controller structure is improved and the dynamic performance of BLDC speed control system is enhanced.

Optimal backstepping controller for controlling DC motor speed

In this paper, squirrel search algorithm (SSA) is adapted to tune the optimal parameters of a backstepping controller for controlling speed in DC motor; Lyapunov stability theorem is applied to derive the control low to achieve system stability analysis. M-file and Simulink platform is used to simulate the response of the system, a comparison with conventional controllers is utilized, all gains are tuned using SSA method and integral time absolute error (ITAE) fitness function to test the efficient performance of the proposed controller also a comparison with other tuned different controllers is done. Transient response analysis is used to validating the proposed controller performance. The simulation results showed a stable response and efficint performance for the proposed controller when compared with the two conventional controllers used by 41.6% for PID controller and by 32% for PI controller in rise time while in settling time is superior by 36.97% for PID controller and by 41.82% for PI controlle these values led for achieving the desired speed in fast and stable response.

Studying the Applicability of Swarm Intelligence in Designing Optimized PI Controller for DC-DC Zeta Converter: A MATLAB-Based Approach

Studying the stability of power converters and improving the performance is a major concern for researchers in the domain of power electronics. In this context, the DC-DC Zeta converter is studied in this paper and the closed-loop operation is comprehensively investigated by employing swarm intelligence (SI) algorithms with a view to design an optimized proportional-integral (PI) controller. These algorithms have been increasingly used to develop and optimize power converters in recent years. The state-space averaging technique was used to design the converter’s closed-loop transfer function. Hence, the traditional and SI algorithm-based PI controllers are inspected, and comparative analysis is presented. Four objective functions termed as integral absolute error, integral time absolute error, integral square error, integral time squared error, gain values, and different performance parameters such as percentage of overshoot, rise time, settling time, and peak amplitude are tabulated to examine the stability of the system. Furthermore, eigenvalues have been analyzed for determining the stability of the system extensively. Finally, a detailed comparative study is shown to provide a detailed evaluation of the performances where ant colony optimization for continuous domains (ACOR)-based PI controller has shown promising results than other SI-based controllers in terms of percentage of overshoot (2.27%), rise time (1.54 μs), and settling time (0.103 μs). All the simulation results and analysis are obtained using the MATLAB-Simulink.

An Improvement of Model Predictive for Aircraft Longitudinal Flight Control Based on Intelligent Technique

This paper introduces a new intelligent tuning for the model predictive control (MPC) based on an effective intelligent algorithm named the bat-inspired algorithm (BIA) for the aircraft longitudinal flight. The tuning of MPC horizon parameters represents the main challenge to adjust the system performance. So, the BIA algorithm is intended to overcome the tuning issue of MPC parameters due to conventional methods, such as trial and error or designer experience. The BIA is adopted to explore the best parameters of MPC based on the minimization of various time domain objective functions. The suggested aircraft model takes into account the aircraft dynamics and constraints. The nonlinear dynamics of aircraft, gust disturbance, parameters uncertainty and environment variations are considered the main issues against the control of aircraft to provide a good flight performance. The nonlinear autoregressive moving average (NARMA-L2) controller and proportional integral (PI) controller are suggested for aircraft control in order to evaluate the effectiveness of the proposed MPC based on BIA. The proposed MPC based on BIA and suggested controllers are evaluated against various criteria and functions to prove the effectiveness of MPC based on BIA. The results confirm that the accomplishment of the suggested BIA-based MPC is outstanding to the NARMA-L2 and traditional PI controllers according to the cross-correlation criteria, integral time absolute error (ITAE), system overshoot, response settling time, and system robustness.

Neural network based adaptive sliding mode tracking control of autonomous surface vehicles with input quantization and saturation

The autonomous surface vehicle (ASV) is supposed to be able to adapt unknown environments without human interference. This paper investigates the problem of trajectory tracking control for ASVs in the present of parameter uncertainties, disturbances, input quantization and actuator saturation. The neural network (NN) approximation and an adaptive sliding mode control (SMC) strategy are combined for the ASVs with a priori unknown upper bound of parameter uncertainties, external disturbances and saturation errors. The NN is adopted to approximate the unknown continuous uncertainties and disturbances in the system. The adaptive law for the SMC parameter can guarantee no overestimation of the robust control parameter with respect to unknown upper bounds of the NN approximation errors and the saturation error. By adding the NN approximation into the adaptive SMC laws, the robust control parameter and the chattering can be reduced. Uniformly ultimately bounded (UUB) for sliding variables and tracking errors can be guaranteed by Lyapunov proof. Simulation examples are given to illustrate the improved performance with the proposed approach. The comparisons on the proposed control method with other algorithms are given by using the integrated absolute error (IAE) and integrated time absolute error (ITAE).

Impact of fractional filter in PI control loop applied to induction motor speed drive

Introduction. One of the main problems of electrical machine control systems is to obtain a satisfactory performance in the rejection of load disturbances, as well as in the set-point tracking tasks. Generally, the development of control algorithms does not take into account the presence of noise. Appropriate filtering is, therefore, essential to reduce the impact of noise on the output of the controller, in addition to the machine output. Recently, there has been a great tendency toward using fractional calculus to solve engineering problems. The filtering is one of the fields in which fractional calculus has received great attention. The importance of filters in signal processing and other engineering areas is unquestionable Novelty. The proposed work is intended to be a contribution in the recent works conducted on the influence of the fractional filtering on the control robustness of induction machines control. Purpose. The main contribution of this research is the application of fractional filtering to the standard PI control loop for an induction motor speed drive. Methods. In order to assess its impact and benefit, different structures for introducing the filters are investigated, A first order filter is considered in different positions, whether before or after the controller or even in both positions at the same time, with a noise source. A review of the index performance evolution (the Integral Square Error, Integral Absolute Error and Integral Time Absolute Error) has allowed a configuration design of the filter. Results. Intensive simulations were performed with a control setup using integer and fractional order filters, which permitted to conclude that the fractional filters give better performance indices compared to the integer one and thus improve the dynamic characteristics of the system.

Optimized speed control with torque ripple reductions of BLDC motor based on SMC approach using LFD algorithm

Brushless DC motors (BLDCM) are utilized in various applications, including electric cars, medical and industrial equipment, where highefficiency speed control is necessary to meet load and tracking reference fluctuations. In this study, the optimal parameters of proportional-integral (PI) and sliding mode controller (SMC) for BLDC motor speed control are determined using Lévy flight distribution (LFD) technique. The integral time absolute error (ITAE) is used as a fitness function with the LFD algorithm for tuning the PI and SMC parameters. The optimization algorithms' performance is presented statistically and graphically. The simulation results show the SMC based on the LFD technique has superiority over SMC without optimization and PI controller in fast-tracking to the desired value with zero overshoot with rising time (6 ms) and low-speed ripple up to (± 9 RPM) under non-uniform conditions.

Advanced optimal GWO-PID controller for DC motor

<p><span>The current work aims to use traditional control algorithms and advanced optimization algorithms that was chosen for its ease of control and the possibility of using it in many industrial applications. By setting the appropriate specifications for the simulation model and after conducting the planned tests that simulate different applications of the motor’s work within electrical systems, the results proved to obtain good performance of the motor’s work, better response, high accuracy, in addition to the speed. The goal is to design and tune a <a name="_Hlk112847502"></a>proportional–integral–derivative (PID) controller by <a name="_Hlk112847139"></a>grey wolf optimization (GWO) using T.F for a direct current (DC) motor. To adjust the parameters of the traditional controllers using the optimum advanced, an appropriate mechanism and technology from the advanced optimization techniques were chosen, as the gray wolf technology algorithm was chosen as an optimization technique and integral time absolute error (ITAE) to adjust the parameters of the traditional PID controller.</span></p>

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

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.

Optimized Luenberger Observer-Based PMSM Sensorless Control by PSO

In the real applications, we found that it is difficult to achieve good control performance through manually tuning proportional–integral (PI) parameters of phase locked loop (PLL) and speed-loop of Luenberger observer (LO) for the PMSM sensorless control system. Therefore, this paper is to use the particle swarm optimization (PSO) algorithm to optimize the PI parameters of PLL and speed-loop of Luenberger observer of the system. Firstly, the ranges of PLL parameters are obtained by analyzing the PLL subsystem stability. Then, the ranges of PI parameters of PLL and speed-loop are set based on theoretical estimation and empirical values. The control system model is realized in MATLAB/Simulink that considers the constraints such as the saturation. The integral time absolute error is the objective function, and the PSO with different topologies is used to optimize the PI parameters. The simulation and experimental results show that the proposed method is feasible, and the optimized parameters can effectively improve the precision of position estimation and speed estimation. Moreover, the simulations and experiments are carried out to verify the robustness of the proposed method, and the results show that the optimized system can achieve good performance when there are uncertainties or disturbances.

The effect of an evolutionary algorithm's rapid convergence on improving DC motor response using a PID controller

Mobile robots experience a lot of challenges with path tracking because of the significant problem with DC motor speed control. The particle swarm optimization (PSO) tuned proportional integral derivative (PID) controller is commonly used to control DC motor speed. However, it fails to reach the optimal solution quickly. Therefore, this paper demonstrates the application of the artificial bee colony (ABC) algorithm to tune a PID controller for speed regulation of a DC motor. The proposed approach was used to obtain the optimal PID controller gains (proportional, integral, and derivative) by minimizing the integral of time absolute error (ITAE) as the objective function. The analysis of statistical tests, transients, and frequency responses was conducted to test the rapid convergence of the proposed approach. Also, the performance of the proposed ABC-tuned PID controller has been compared with three variants of the PSO-tuned PID controller. The conducted simulation results and comparison with the proposed ABC controller and variant PSO controllers have shown that the proposed ABC-PID controller is more effective and robust than the variant PSO-PID controllers for the speed control of a DC motor.