Integral Time Absolute Error Research Articles

Gradient descent-particle swarm optimization based deep neural network predictive control of pressurized water reactor power

A pressurized water reactor (PWR) is an integrated system of various interdependent subsystems that show highly nonlinear behavior, and each component is prone to uncertainties and malfunctions that initiate potential accidents. In contrast, PWR needs to be continuously monitored for stable and safe operation over a service time. In this study, a gradient descent-particle swarm optimization hybrid algorithm-based deep neural network (GD-PSO-based DNN) approach is proposed to monitor the PWR core power and outlet temperature. The Gaussian noise is introduced to the input signal, and the PWR core stability conditions are examined by using Lyapunov analysis. The simulation results verified under different conditions, in which the proposed control approach tracks the reference inputs successfully and enhances the stability as compared with the sliding mode control, linear quadratic regulator, and proportional-integral-derivative methods. The controller is validated by using the data from RELAP5 system codes, and the performance is examined using the mean square error, integral square error, integral absolute error, integral time square error, and integral time absolute error criterion functions. This study gives the benefit to apply the GD-PSO-based DNN control method for other nuclear engineering fields for system identification, prediction, and control.

A new optimal model predictive control scheme for a wind energy conversion system

AbstractThe correct management of power exchange between the doubly‐Fed induction generator (DFIG) and the grid depends on the effective optimal operation of the DFIG based wind energy conversion system (WECS). A modified optimal model predictive controller (MPC) architecture for WECS is proposed in this paper. The proposed scheme is carried out in two stages, as follows: (a) Using the MPC model and the tracking factor, an optimal control law is created, and (b) the aforementioned optimized issue is addressed using the linear matrix inequality (LMI) approach. Some improvements were made to the conventional LMI‐based MPC technique to lower the high computational complexity. To perform active and reactive power control in DFIG, the proposed approach is applied on the rotor‐side converter (RSC) control. The control law is divided into two sections. The first section deals with rotor current, while the second section deals with the RSC switching states. The LMI is used in the second portion of the control law to find the best switching state solution. The proposed method was created using the MATLAB/SIMULINK environment and tested in a 1hP DFIG‐WECS setup. By comparing the obtained results to conventional LMI‐PI, MPC‐based WECS, the effectiveness of the obtained results is verified. Variable wind speed conditions are used to vary all the results. Integral absolute error, integral time absolute error, and Integral square error measurements are used to compare the tracking performance index of all methods.

Design of sliding mode control optimised by the Bees algorithm for LFC in the Great Britain power system

A design of Sliding Mode Control (SMC) is proposed in this work for Load Frequency Control (LFC) in the simplified Great Britain (GB) power system. The sliding surface of the proposed design has been identified to have five parameters. In order to guarantee the best usage of the proposed SMC design, the optimal gains of this controller are optimised by the Bees Algorithm (BA) and Particle Swarm Optimisation (PSO); the optimizations are conducted by employing the Integral Time Absolute Error (ITAE) objective function. A step load perturbation is applied to study the dynamic response of the system. The supremacy of the proposed approach is proved by comparing the results obtained with that from Proportional Integral Derivative (PID) controller tuned by BA. It is observed that the BA optimised SMC offers the best dynamic performance among the investigated techniques. Moreover, the results demonstrate the robustness of the proposed SMC based BA controller against system parametric uncertainties.

Stability Enhancement of PV Powered Microgrid using Levenberg-Marquardt Algorithm Based Intelligent Controller Under Grid-connected Mode

An effective and robust controller is designed using Levenberg-Marquardt(LM) algorithm-based Artificial Neural Network (ANN) for the solar Photo-Voltaic (PV) based distributed generation units for stabilizing the grid-connected microgrid (MG) under load changes and irradiance variations. Atest system comprising of two PV units and one diesel generator unit con-nected to the utility grid is modelled and considered for the controller designin MATLAB/Simulink environment. PV generated power is injected into thegrid through voltage source converter (VSC) regulated by using the proposedANN controller. Based on the grid voltage and available PV generation,the ANN controller regulates the inverter current by setting the referencevoltage vector to synthesize gating pulses for the inverter. The robustnessof the controller design is analysed and validated through time-domainsimulations by subjecting it to extreme operating conditions. The controllerperformance is evaluated by Integral Square Error (ISE) and Integral TimeAbsolute Error (ITAE) for the test system. The results are compared with conventional PI and PID controllers to prove the superior performing ANNcontroller.

AUTOMATIC GENERATION CONTROL OF A MULTI-AREA POWER SYSTEM BASED ON GREY WOLF OPTIMIZATION ALGORITHM

This paper presents an automatic generation control algorithm applicable for a multi-area power system. A more practical models is used to represent the main components of the power system. The frequency bias factor (B) is set optimally by using an artificial intelligence technique. The generation rate constraints (GRC) are taken into consideration with dead band characteristics of the governor. For the first time, a sequential optimization of the fractional order (PID) control parameters, the governor speed regulation (R) and the frequency bias factor (B) is proposed. The objective function to be minimized is the updated integral time absolute error (UITAE). The tuning of the control parameters is dependent on minimizing the objective function by using the Grey wolf optimization (GWO) algorithm. The proposed algorithm is tested on an interconnected three power pools different system (Reheat, Gas and Hydro) with varying degrees of load step change. The simulation results of the presented process are compared to those achieved by using the particle swarm optimization method. The results obtained reveal the robustness of the proposed algorithm in terms of settling time and peak overshoot.

Optimized Sliding Mode Control of Three-Phase Four-Switch Inverter BLDC Motor Drive Using LFD Algorithm

This paper presents a low-cost Brushless DC (BLDC) motor drive system with fewer switches. BLDC motors are widely utilized in variable speed drives and industrial applications due to their high efficiency, high power factor, high torque, low maintenance, and ease of control. The proposed control strategy for robust speed control is dependent on two feedback signals which are speed sensor loop which is regulated by Sliding Mode Controller (SMC) and current sensor loop which is regulated by Proportional-Integral (PI) for boosting the drive system adaptability. In this work, the BLDC motor is driven by a four-switch three-phase inverter emulating a three-phase six switch inverter, to reduce switching losses with a low complex control strategy. In order to reach a robust performance of the proposed control strategy, the Lévy Flight Distribution (LFD) technique is used to tune the gains of PI and SMC parameters. The Integral Time Absolute Error (ITAE) is used as a fitness function. The simulation results show the SMC with LFD technique has superiority over conventional SMC and optimization PI controller in terms of fast-tracking to the desired value, reduction speed error to the zero value, and low overshoot under sudden change conditions.

Design of fractional order PID controller for AVR system using whale optimization algorithm

In this paper a robust fractional order PID (FOPID) controller is proposed to control the automatic voltage regulator (AVR) system, the tuning of the controller gains are done using whale optimization algorithm (WOA) and integral time absolute error (ITAE) cost function is adopted to achieve an efficient performance. The transient analysis was done and compared with conventional PID in terms of overshoot, settling time, rise time, and peak time to explain the superiority of the proposed controller. Finally, a robustness analysis is done by adding external disturbances to the system and changing the system parameters by ±20% from its original value, the controller overcomes the disturbances signals with less than 0.25 s and faces the changes of the system values and returning the response within (0.7-1) sec and led the system to the desired response efficiently. The numerical simulations showed that the smart WOA offers satisfying results and faster response reflected clearly on the robust and stable performance of the proposed controller in improving the transient analysis of AVR system response.

Characteristic of Fuzzy, ANN, and ANFIS for Brushless DC Motor Controller: An Evaluation by Dynamic Test

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).

Improving Neural Network Based on Seagull Optimization Algorithm for Controlling DC Motor

This article presents a direct current (DC) motor control approach using a hybrid Seagull Optimization Algorithm (SOA) and Neural Network (NN) method. SOA method is a nature-inspired algorithm. DC motor speed control is very important to maintain the stability of motor operation. The SOA method is an algorithm that duplicates the life of the seagull in nature. Neural network algorithms will be improved using the SOA method. The neural network used in this study is a feed-forward neural network (FFNN). This research will focus on controlling DC motor speed. The efficacy of the proposed method is compared with the Proportional Integral Derivative (PID) method, the Feed Forward Neural Network (FFNN), and the Cascade Forward Backpropagation Neural Network (CFBNN). From the results of the study, the proposed control method has good capabilities compared to standard neural methods, namely FFNN and CFBNN. Integral Time Absolute Error and Square Error (ITAE and ITSE) values from the proposed method are on average of 0.96% and 0.2% better than the FFNN and CFBNN methods.

A Novel Sooty Terns Algorithm for Deregulated MPC-LFC Installed in Multi-Interconnected System with Renewable Energy Plants

This paper introduces a novel metaheuristic approach of sooty terns optimization algorithm (STOA) to determine the optimum parameters of model predictive control (MPC)-based deregulated load frequency control (LFC). The system structure consists of three interconnected plants with nonlinear multisources comprising wind turbine, photovoltaic model with maximum power point tracker, and superconducting magnetic energy storage under deregulated environment. The proposed objective function is the integral time absolute error (ITAE) of the deviations in frequencies and powers in tie-lines. The analysis aims at determining the optimum parameters of MPC via STOA such that ITAE is minimized. Moreover, the proposed STOA-MPC is examined under variation of the system parameters and random load disturbance. The time responses and performance specifications of the proposed STOA-MPC are compared to those obtained with MPC optimized via differential evolution, intelligent water drops algorithm, stain bower braid algorithm, and firefly algorithm. Furthermore, a practical case study of interconnected system comprising the Kuraymat solar thermal power station is analyzed based on actual recorded solar radiation. The obtained results via the proposed STOA-MPC-based deregulated LFC confirmed the competence and robustness of the designed controller compared to the other algorithms.

PID Controllers Design for a Quadrotor System Using Teaching Learning Based Optimization

Optimized Proportional Integral Derivative controllers are designed to control the translational and rotational motions of a quadrotor system with six degrees of freedom. The teaching learning based optimization algorithm is used to obtain the proportional, integral and derivative gains of six PID controllers so that the integral time absolute error criterion is minimized. The control objective, is to enforce the horizontal position, altitude and yaw angle of the quadrotor to track their desired reference trajectories while stabilizing its roll and pitch angles. The efficiency and the control performance of the proposed scheme are demonstrated through numerical simulation and compared with those of the PID controllers designed using genetic algorithm, the sliding mode control and other control techniques proposed in the literature. The simulation study shows the good performance of the proposed control scheme in terms of transient response characteristics, tracking accuracy and disturbance rejection.

A Hybrid Genetic-Fuzzy Controller for a 14-Inch Astronomical Telescope Tracking

The performance of on telescope depend strongly on its operating conditions. During pointing, the telescope can move at a relatively high velocity, and the system can tolerate trajectory position errors higher than during tracking. On the contrary, during tracking, Alt-Az telescopes generally move slower but still in a large dynamic range. In this case, the position errors must be as close to zero as possible. Tracking is one of the essential factors that affects the quality of astronomical observations. In this paper, a hybrid Genetic-Fuzzy approach to control the movement of a two-link direct-drive Celestron telescope is introduced. The proposed controller uses the Genetic algorithm (GA) for optimizing a fuzzy logic controller (FLC) to improve the tracking of the 14-inch Celestron telescope of the Kottamia Astronomical Observatory (KAO). The fuzzy logic input is a vector of the position error and its rate of change, and the output is a torque. The GA objective function used here is the Integral Time Absolute Error (ITAE). The proposed method is compared with a conventional Proportional-Differential (PD) controller, an optimized PD controller with a GA, and a Fuzzy controller. The results show the effectiveness of the proposed controller to improve the dynamic response of the overall system.

PSO and GA tuned conventional and fractional order PID controllers for quadrotor control

Purpose This study aims to compare the performance of the conventional and fractional order proportional-integral-derivative (PID and FOPID) controllers tuned with a particle swarm optimization (PSO) and genetic algorithm (GA) for quadrotor control. Design/methodology/approach In this study, the gains of the controllers were tuned using PSO and GA, which are included in the heuristic optimization methods. The tuning processes of the controller’s gains were formulated as optimization problems. While generating the objective functions (cost functions), four different decision criteria were considered separately: integrated summation error (ISE), integrated absolute error, integrated time absolute error and integrated time summation error (ITSE). Findings According to the simulation results and comparison tables that were created, FOPID controllers tuned with PSO performed better performances than PID controllers. In addition, the ITSE criterion returned better results in control of all axes except for altitude control when compared to the other cost functions. In the control of altitude with the PID controller, the ISE criterion showed better performance. Originality/value While a conventional PID controller has three parameters (Kp, Ki, Kd) that need to be tuned, FOPID controllers have two additional parameters (µ). The inclusion of these two extra parameters means more flexibility in the controller design but much more complexity for parameter tuning. This study reveals the potential and effectiveness of PSO and GA in tuning the controller despite the increased number of parameters and complexity.

Optimal design of Fractional order PID controller based Automatic voltage regulator system using gradient-based optimization algorithm

Considering the superior control characteristics and increased tuning flexibility of the Fractional-Order Proportional Integral Derivative (FOPID) controller than the conventional PID regulator, this article attempts to explore its application in the optimal design of the Automatic Voltage Regulator (AVR). Since FOPID has two additional tuning parameters (µ and ʎ) than its mentioned conventional counterpart, its tuning process is comparatively difficult. To overcome the stated issue, a self-regulated off-line optimal tuning method based on the Gradient-Based Optimization (GBO) algorithm is adopted in the current study. The optimal FOPID gains are obtained by minimizing the selected Fitness Function (FF) that is chosen as Integral Time Absolute Error (ITAE) in the current study. The simulations are performed using MATLAB/SIMULINK 2018a to test and compare the performance of the proposed GBO-based optimal AVR design based on the dynamic response, stability, and robustness evaluation metrics with some of the recently published metaheuristic optimization algorithm based optimal AVR designs in the literature. The results show that the proposed AVR design provides the most optimal dynamic response and enhanced stability among the considered AVR designs, thus proves its efficacy and essence.

Fractional order PI control combined with improved frequency droop method for power management in standalone LVDC microgrids

According to increasing growth of DC loads, DC microgrids (MGs) have an effective role in future power systems. Improvement of power management is one of the important issues in DC MGs. In this paper, in order to provide an accurate power management in standalone low-voltage DC (LVDC) MG, including photovoltaics (PVs) and battery energy storage systems (BESSs), an AC component is superimposed to the output voltage of DC-DC converters by inspecting the frequency droop control of the synchronous generators. In addition, two corrective terms based on the calculation of AC active and reactive powers are added to this AC component, which is named improved frequency droop method (IFDM). Different operating modes for PV system comprising maximum power point tracking (MPPT) and voltage control mode (VCM); and BESS consisting of charge, discharge, and idle are considered in the proposed power management scheme based on the state of charge (SoC) of local BESS. On the other hand, the conventional proportional-integral (PI) controllers in DC-DC converters' control structure present poor transient dynamic performance and low loading level. Hence, fractional order PI (FOPI) controllers are designed by optimization of integral time absolute error (ITAE) criteria. The effectiveness of the proposed FOPI controllers combined with IFDM scheme is evaluated by simulations conducted in MATLAB/SIMULINK software. The FOPI-IFDM approach provides accurate current sharing and better voltage regulation without dependence on communication link in comparison with PI-IFDM under load, line impedance, and solar irradiance variations.

Optimum PID controller for airplane wing tires based on gravitational search algorithm

In this paper, the gravitational search algorithm (GSA) is proposed as a method for controlling the opening and closing of airplane wing tires. The GSA is used to find the optimum proportional-integral-derivative (PID) controller, which controls the wing tires during take-off and landing. In addition, the GSA is suggested as an approach for overcoming the absence of the transfer function, which is usually required to design the optimum PID. The use of the GSA is expected to improve the system. Two of the most popular optimisation algorithms-the harmony search algorithm (HSA) and the particle swarm optimisation (PSO)-were used for the sake of comparison. Moreover, the GSA-, HSA- and PSO-based optimum PID controllers were compared with one of the most important PID tuning methods, the Ziegler-Nichols (ZN) method. In this study, the integral time absolute error (ITAE) was used as a fitness function. First, four transfer functions for different applications were used to compare the performance of the GSA-based PID (PID-GSA), HSA-based PID (PID-HSA), PSO-based PID (PID-PSO) and Ziegler-Nichols-based PID (PID-ZN). Next, the GSA was used to design the optimum PID controller for the opening and closing systems of the airplane wing tires. The results reveal that the GSA provides better outcomes in terms of ITAE when compared with the other adopted algorithms. Furthermore, the GSA demonstrates a fast and robust response to reference variation.

Design, implementation, control and optimization of single stage pilot scale reverse osmosis process.

In this paper, a single-stage pilot-scale reverse osmosis (RO) process is considered. The process is mainly used in various chemical industries such as dye, pharmaceutical, beverage, and so on. Initially, mathematical modeling of the process is to be done followed by linearization of the system. Here a dual loop construction with a master and a slave is used. The slave uses the conventional proportional integral derivative (PID) with a reference model of the RO process and the master uses the fractional order proportional integral derivative (FOPID) with a real time RO process. The slave's output is compared with output of the real time RO process to obtain the error which is in turn used to tune the master. The slave controller is tuned using Ziegler Nichols method and the error criterion such as integral absolute error (IAE), integral squared error (ISE), integral time squared error (ITSE), integral time absolute error (ITAE) are calculated and the minimum among them was chosen as the objective function for the master loop tuning. Hence the tuning of the controller becomes a whole. Therefore two optimization techniques such as particle swarm optimization (PSO) and bacterial foraging optimization algorithm (BFO) are used for the tuning of the master loop. From the calculations, the ITSE had the minimum value among the performance indices, hence it was used as the objective function for the BFO and PSO. The best-tuned values will be obtained with the use of these techniques and the best among all can be considered for various industrial applications. Finally, the performance of the process is compared with both techniques and BFO outperforms the PSO from the simulations.

Control of TITO processes using sliding mode controller tuned by ITAE minimizing criterion based Nelder-Mead algorithm

Abstract Control of multi input and multi output (MIMO) process with interaction is often encountered in process industry. Such MIMO processes are controlled using conventional sliding mode controller (SMC) and tuned by integral square error (ISE) minimizing criterion based Nelder-Mead algorithm. SMC tuned by integral time absolute error (ITAE) minimization criterion based Nelder-Mead algorithm is proposed in this work. Three categories of two inputs and two outputs (TITO) process models are represented in the matrix form, with each of the matrix element representing a first order plus dead time (FOPDT) process. These TITO models are categorized based on the ratio ε, between dead time and time constant of the FOPDT model which forms the matrix element of the TITO model. The performance of conventional SMC is evaluated for these three categories of TITO models, in which the TITO process models with the ratio ε greater than the one, exhibited by poor closed loop performance, whereas the proposed SMC when applied to the these process models delivered superior closed loop performance.

Design of centralized controller for multivariable process using MOPSO algorithm

Objective: To estimate centralized PID controller parameters for 4 outputs and 5 inputs crude distillation non-square system with RHP zeros process. Methods/Analysis: The Multi- Objective Particle Swam Optimization (MOPSO) algorithm is applied to determine the PID controller parameters for the considered distillation column process. Findings: The performance of the proposed controller is compared with two centralized controller schemes, Davison’s and Tanttu and Lieslehto methods. The Integral Square Error (ISE), Integral Absolute Error (IAE) and Integral of Time Absolute Error (ITAE) are chosen as performance indices. The simulation results prove that MOPSO tuned centralized controller gives the best performance when compared to other analytical techniques for both set point tracking and in disturbance rejection environment. Novelty: In practice, conventional PID controllers are tuned using classical methods, which require complex numerical calculations. In this paper, an attempt is made to fine tune the PID controller for a MIMO process using Multi Objective optimization technique and obtained challenging results as compared to conventional methods. Keywords: Nonsquare system; Centralized control; Multi Objective Particle Swam Optimization; PID controller

Genetic Algorithm–Based Robust Controller for an Inverted Pendulum Using Model Order Reduction

Abstract Robust stabilization is an important characterization to get improved in the control system to optimize the performance of the desired system. Most of the controllers available suffer from problems such as difficulty in the tuning process, sluggishness in response time, quick and global convergence, etc. This paper considered proportional-integral optimized with genetic algorithm (GA-PID)controller on inverted pendulum for the control of the angle position. A MATLAB script for a GA was developed to obtain optimum PID parameters that would keep the pendulum angle at equilibrium (i.e., returns the pendulum to the desired point as quickly as possible) by minimizing an objective function (integral time absolute error [ITAE]). Furthermore, obtained outcomes confirm the performance of holding on the upright position from the downward direction such that the angle of the pendulum is manipulated to control the inverted position in its erect position in a rapid manner. In the experimental analysis, the developed GA-based PID controller is compared with the conventional PID controller to evaluate the performance of the inverted pendulum. The obtained results show that the GA-based PID controller confirms the enhanced performance indexes by holding minimum settling time and peak overshoot on comparing with the conventional PID controller.