Integral Of Time Weighted Squared Error Research Articles

Comparative Analysis: Fractional PID vs. PID Controllers for Robotic Arm Using Genetic Algorithm Optimization

This paper presents a comparative analysis of a fractional-order proportional–integral–derivative (FO-PID) controller against the standard proportional–integral–derivative (PID) controller, applied to a nonlinear robotic arm manipulator systems. The genetic algorithm (GA) optimization method was implemented to tune the gain parameters of the FO-PID and PID controllers. The performance of the FO-PID and PID controllers were evaluated though different cost functions, including integral of squared error (ISE), integral of absolute error (IAE), integral of time-weighted absolute error (ITAE), and integral of time-weighted squared error (ITSE). The performance of these controllers was examined via extensive simulations by using MATLAB/SIMULINK for different operating scenarios of the robotic arm manipulator system. Based on the obtained results, a comparative performance matrix is proposed, wherein cost functions ISE, IAE, ITAE, and ITSE are represented as columns while characteristic parameters (overshoot, rising time, and settling time) are represented as rows. The proposed performance matrix facilitates the selection between the PID and FO-PID controllers.

Comparative Analysis of Intelligence Optimization Algorithms in the Thermo-Economic Performance of an Energy Recovery System Based on Organic Rankine Cycle

Abstract This paper compares the performance of a group of intelligent algorithms such as the genetic algorithm (GA), particle swarm optimization (PSO), and repulsive particle swarm optimization (RPSO) based on the optimization of thermo-economic indicators such as the payback period (PBP), the levelized energy cost (LEC), the specific investment cost (SIC), and also in the optimization of the thermodynamic process (net power output) of an energy recovery system in a 2 MW natural gas internal combustion engine based on an organic Rankine cycle. Four parameters were considered to analyze and compare the performance of these algorithms: integral of squared error (ISE), integral of absolute error (IAE), integral of time-weighted absolute error (ITAE), and the integral of time-weighted squared error (ITSE). Analyses of variances (ANOVA) were proposed for each of the parameters studied. The PSO and RPSO algorithms presented the best performance in terms of the mean and the standard deviation of the ISE, IAE, ITAE, and ITSE parameters. Significant differences were not found between the three algorithms in terms of the parameters considered. However, significant differences did exist when comparing groups (pairs) of algorithms considering a significance level of 5%. The ANOVA analysis showed that ITAE was the most affected parameter by population size, while the IAE and ITSE parameters were the less affected. In the optimization, the PSO algorithm obtained the best performance in terms of convergence with values of 0.1110 USD/kWh (LCOE), 4.6971 years (PBP), 1114 USD/kWh (SIC), and 173.64 kW (Wnet). PSO-based algorithms obtained better performance in computational terms compared with the genetic algorithms.

Effects of objective function in PID controller design for an AVR system

Regulation capability of an automatic voltage regulator (AVR) system still needs to be improved to keep the output voltage of the generator within the AVR system at the desired level. Researchers have been developing new control structures and designing controllers to improve the performance of the AVR system. Designing of PID controller, which is commonly preferred controller due to its simple structure and robustness against to system parameter changes, has an important place among these studies. Especially with the development of metaheuristic algorithms, more successful PID controller designs are emerging by using these algorithms than traditional design methods. Undoubtedly, the objective function utilized also has a significant effect on this success. Therefore, effects of the objective function in PID controller design process for an AVR system are examined in this study. Two different PID controllers are designed using two different metaheuristic algorithms, namely, crow search algorithm (CSA) and ant colony optimization (ACO) algorithm. The parameters of the PID controllers are optimally tuned by using five different objective functions in both algorithms. These objective functions are: Integral of absolute error (IAE), integral of squared error (ISE), integral of time-weighted absolute error (ITAE), integral of time-weighted squared error (ITSE), and a commonly used user-defined objective function. The performance of the designed PID controllers are compared in terms of transient response characteristics and performance metrics. In addition, in order to evaluate the stability of the AVR system with the designed controllers, bode analysis, pole-zero map analysis and robustness analysis are performed.

Application of grey wolf optimization algorithm for load frequency control in multi-source single area power system

In this paper, application of evolutionary intelligence-based Grey Wolf Optimizer (GWO) algorithm has been presented to estimate the optimal parameters of Proportional-Integral-Derivative (PID) controller for load frequency control (LFC) in multi-source single area power network. The multi-source single area power network which is considered here is comprised of reheat turbine thermal power plant, gas power plant and hydro power plant with the mechanical hydraulic governor. In this paper, the parameters of PID controller for LFC of under study system are optimized using GWO algorithm by considering four important performance indices (instead of considering one or two) namely Integral of Time-weighted Squared Error (ITSE), Integral of Time-weighted Absolute Error (ITAE), Integral of Squared Error (ISE) and Integral of Absolute Error (IAE). The implemented technique has been compared with Genetic Algorithm (GA) technique for 1%, 2% and 5% load disturbances to show the effectiveness and applicability for LFC in multi-source single area power network.

Voltage control of switched reluctance generator using grasshopper optimization algorithm

<p>This paper presents<strong> </strong>a terminal voltage control approach of a Switched Reluctance Generator (SRG) based wind turbine generating systems. The control process is employed using a closed loop stimulated by the error between the reference voltage and the generator output voltage due to load and wind speed variation. This error feeds the tuned Proportional Integral controller (PI).</p><p>Tuning of PI controller by conventional analysis methods is difficult by the existence of a significant non-linearity. A novel strategy method is presented here to determine optimum PI controller parameters of voltage control of SRG using Grasshopper Optimization Algorithm (GOA). This proposed approach is a simple and effective algorithm that is able to solve many optimization problems. The simplicity of algorithm provides high quality tuning of optimal PI controller parameters. The integral of time weighted squared error (ITSE) is used as the performance of the proposed GOA-PI controller. The effectiveness of the proposed strategy is tested with the three-phase 12/8 structure SRG. Outcomes indicate the supremacy of GOA over Whale Optimization Algorithm (WOA) and Particle Swarm Optimization (PSO) in terms of control performance measures.</p>

Parçacık Sürü Optimizasyonu Ayarlı Türev Etkisi Filtreli Bir PID Denetleyici için Hata Tabanlı ve Kullanıcı Tanımlı Amaç Fonksiyonlarının Performans Analizi

In this study, we investigate the performance analysis of transient and steady state characteristics of the commonly used error-based objective functions (EBOF) such as integral of squared error (ISE), integral of time weighted squared error (ITSE), integral of absolute error (IAE), and integral of time weighted absolute error (ITAE) and a user-defined objective function (UDOF). In optimization process, particle swarm optimization (PSO) algorithm tuned proportional-integral-derivative controller with derivative filter (PIDF) is employed for a second order plus dead time (SOPDT) test system. Simulation results shows the superiority of the UDOF in terms of settling time, overshoot, and settling minimum value compared to EBOFs.

Adaptive Fuzzy Control Method for a Single Tilt Tricopter

This article proposes an adaptive fuzzy gain scheduling (FSG) design of the traditional proportional integral derivative (PID) control method by using fuzzy logic rules to schedule controlled gains at different phases. Owing to minimization of the tracking error of the controller design using three parameters and the integral of time weighted-squared error (ITSE) minima criterion of the controller design process, the fuzzy rules of the triangular membership functions are exploited online to verify the PID controller gains in different operated scheduling modes. For that reason, the controller designs can be used to tune the system models during the whole operation time period to enable efficient error tracking. The continuous genetic algorithm (GA) is considered an innovation because in it, the decode chromosome step is totally neglected. Owing to this improvement, it is superior to the standard GA because it requires less storage and enables naturally faster convergence. In this research, the controlled parameters were optimized using the continuous GA to enhance the efficiency of the proposed method. Thereafter, it was implemented to a single tilt Tricopter model to test whether the control performance is better when compared with the conventional PID control method.

Comparative performance analysis of teaching learning based optimization for automatic load frequency control of multi-source power systems

• Application of teaching learning based optimization to AGC problems. • PID controller gains have been optimized by teaching learning based optimization. • Dynamic performance is analyzed for single area system and multi area with HVDC link. • Dynamic performances of TLBO based PID controller are better than DE-PID controller. • Sensitivity analysis is done to load changes and different cost functions. This paper presents a new population based parameter free optimization algorithm as teaching learning based optimization (TLBO) and its application to automatic load frequency control (ALFC) of multi-source power system having thermal, hydro and gas power plants. The proposed method is based on the effect of the influence of teacher on the output of learners and the learners can enhance their knowledge by interactions among themselves in a class. In this extensive study, the algorithm is applied in multi area and multi-source realistic power system without and with DC link between two areas in order to tune the PID controller which is used for automatic generation control (AGC). The potential and effectiveness of the proposed algorithm is compared with that of differential evolution algorithm (DE) and optimal output feedback controller tuning performance for the same power systems. The dynamic performance of proposed controller is investigated by different cost functions like integral of absolute error (IAE), integral of squared error (ISE), integral of time weighted squared error (ITSE) and integral of time multiplied absolute error (ITAE) and the robustness of the optimized controller is verified by its response toward changing in load and system parameters. It is found that the dynamic performance of the proposed controller is better than that of recently published DE optimized controller and optimal output feedback controller and also the proposed system is more robust and stable to wide changes in system loading, parameters, size and locations of step load perturbation and different cost functions.

Application of firefly algorithm with online wavelet filter in automatic generation control of an interconnected reheat thermal power system

This paper presents the implementation of the Firefly Algorithm (FA) with an online wavelet filter on the automatic generation control (AGC) model for a three unequal area interconnected reheat thermal power system. The model includes time delay, dead zone, boiler, Generation Rate Constraint (GRC), and high frequency noise components. A novel filtering technique based on wavelet transform is introduced for the purpose of removing noise(s) from the ACE signal. The performance of the filter is measured by formulating a signal integrity index. The simulation results show that the FA is able to outperform the Particle Swarm Optimization (PSO) in obtaining the minimum objective function based on Integral of Time Weighted Squared Error (ITSE). The results also shows that the proposed online wavelet filter performs with a higher degree of efficiency compared to the conventional low pass filter when the practical model of the AGC is analyzed. Further investigation by varying the GRC and time delay parameter confirms the robustness of the FA tuned controller with the online wavelet filter.

Multiobjective optimization using weighted sum Artificial Bee Colony algorithm for Load Frequency Control

This paper presents the implementation of multiobjective based optimization of Artificial Bee Colony (ABC) algorithm for Load Frequency Control (LFC) on a two area interconnected reheat thermal power system. The ABC algorithm is currently being applied in many research works due to the local and global search capability of the algorithm. This paper uses the weighted sum approach of the ABC to optimize the PID controller’s gains to provide a compromise between the frequency response’s settling time and maximum overshoot. The composite objective function comprising both objectives is characterized by the performance criterions – Integral of Time Multiplied Absolute Error (ITAE) and Integral of Time Weighted Squared Error (ITSE). Analysis is carried out to determine the best weightage set for this investigation. A performance index based on Least Average Error (LAE) is formulated to calculate the index of each weightage set. In order to ensure effective compensation in the system output, the PID controllers for both areas are tuned simultaneously. The tuning performance of the algorithm is evaluated by comparing the performance of the proposed controller with conventional PI and PID controller. The robustness of the proposed algorithm is further investigated by evaluating the response of the system under simultaneous step load perturbation (SLP), changing load demand and collectively varying system parameters in the range of ±50%. The simulation result shows the dynamic response of the controller emphasizes on the compromise between the settling time and maximum overshoot of the frequency response. Furthermore, the proposed algorithm is robust enough to operate under different operating conditions and system parameter variations.

Comparative performance analysis of Artificial Bee Colony algorithm in automatic generation control for interconnected reheat thermal power system

This study extensively presents the Automatic Generation Control (AGC) application of Artificial Bee Colony (ABC) algorithm. This algorithm is one of the new population based optimization algorithms which have been developed since 2005. In this study, the algorithm is applied to the interconnected reheat thermal power system in order to tune the parameters of PI and PID controllers which are used for AGC. The tuning performance of the algorithm is compared with that of Particle Swarm Optimization (PSO) algorithm through transient response analysis method. In addition to these, the robustness analysis is applied to the power system which is optimized by ABC algorithm so as to determine its response towards changing in the load and the system parameters, varied in the range of ±50%. The behavior of the system is also investigated with this analysis towards the different cost functions such as integral of absolute error (IAE), integral of squared error (ISE), integral of time weighted squared error (ITSE) and integral of time multiplied absolute error (ITAE). At the end of the study, it is seen that the ABC algorithm is successfully applied to the AGC in the application of interconnected reheat thermal power system, and it shows better tuning capability than the other similar population based optimization algorithm. Furthermore, it is also seen that the proposed system is robust and is not affected by changing in the load, the power system parameters and the cost functions.

I-PD Controller Tuning for Unstable System Using Bacterial Foraging Algorithm: A Study Based on Various Error Criterion

This paper proposes a novel method to tune the I-PD controller structure for the time-delayed unstable process (TDUP) using Bacterial Foraging Optimization (BFO) algorithm. The tuning process is focussed to search the optimal controller parameters (, , ) by minimising the multiple objective performance criterion. A comparative study on various cost functions like Integral of Squared Error (ISE), Integral of Absolute Error (IAE), Integral of Time-weighted Squared Error (ITSE), and Integral of Time weighted Absolute Error (ITAE) have been attempted for a class of TDUP. A simulation study for BFO-based I-PD tuning has been done to validate the performance of the proposed method. The results show that the tuning approach is a model independent approach and provides enhanced performance for the setpoint tracking with improved time domain specifications.

Bacterial Foraging Optimization Robust-RED for AQM/TCP Network

The congestion control problem of the intermediate nodes in the Internet has received extensively attention in control community. In this paper, a novel intelligent robust early detection controller based on a bacterial foraging optimization algorithm is presented to solve the problem of robust active queue management. However in This paper, design approach of robust BFO-RED active queue management with rejection disturbance in TCP network is proposed using bacterial foraging optimization based robust algorithm. To design disturbance traffic rejection tuning, disturbance rejection conditions based on ∞ H H / 2 are illustrated and the performance of response based on the bacterial foraging is computed for the designed RED as Integral of time weighted squared error (ITSE). Hence, parameters of classical RED are selected by bacterial foraging based robust ∞ H H / 2 algorithm to obtain the required response. We illustrate our results with NS2 simulations.

Automatic generation control application with craziness based particle swarm optimization in a thermal power system

In this study, a novel gain scheduling Proportional-plus-Integral (PI) control strategy is suggested for automatic generation control (AGC) of the two area thermal power system with governor dead-band nonlinearity. In this strategy, the control is evaluated as an optimization problem, and two different cost functions with tuned weight coefficients are derived in order to increase the performance of convergence to the global optima. One of the cost functions is derived through the frequency deviations of the control areas and tie-line power changes. On the other hand, the other one includes the rate of changes which can be variable depends on the time in these deviations. These weight coefficients of the cost functions are also optimized as the controller gains have been done. The craziness based particle swarm optimization (CRAZYPSO) algorithm is preferred to optimize the parameters, because of convergence superiority. At the end of the study, the performance of the control system is compared with the performance which is obtained with classical integral of the squared error (ISE) and the integral of time weighted squared error (ITSE) cost functions through transient response analysis method. The results show that the obtained optimal PI-controller improves the dynamic performance of the power system as expected as mentioned in literature.

Robust Tuning of PID Controller Using Bacterial-Foraging-Based Optimization

We propose a design approach to PID controllers with resistance to external disturbance in motor-controlled systems using a bacterial foraging-based optimal algorithm. PID controllers are used to operate AC motor drives because of their practical implementation and simple structure. Inexperienced personnel find it difficult, however, to achieve optimal PID gain because this is manually tuned by trial and error in industrial environments full of disturbances. To design disturbance-resistance tuning, we use disturbance-resistance conditions based on H∞ and calculcate response the performance based on bacterial foraging for the PID controller as an integral of time-weighted squared error. Hence, parameters for the PID controller are selected by our bacterial foraging-based optimal algorithm to obtain the required response.