Integral Square Error Research Articles

Model based control strategies to control voltage of Proton Exchange Membrane Fuel Cell

Abstract The present work deals with the evaluation of model based control strategies for a PEM fuel cell to control voltage. PEM fuel cell is an electrochemical device that converts the chemical energy to electrical energy. Stack voltage is affected by many factors like stack temperature, moisture content of the membrane, partial pressure of hydrogen and air, inlet rate of hydrogen and air and also fuel starvation affects the rate of reaction and hence the voltage produced. In this work, two single input single output models are taken with stack voltage as controlled variable and hydrogen and air flow rate as manipulated variables respectively. The simulation study on two different control structures i.e., feedback and feedback plus feed forward control structures evaluates the effectiveness of proposed controllers concerning set-point tracking and disturbance rejection. Comparative study is carried out by simulations by implementing various model based control strategies, PI, IMC-PID and MPC. The results shows that MPC gives best results in terms of Integral Square error (ISE), Integral Absolute error (IAE) and controller effort (TV). In addition, robust stability analysis is carried out for uncertainty in the process parameters. Also, the controller fragility is studied for uncertainty in the controller parameters.

Lower Order Approximation of Bounded-Parameter Uncertain Systems using Amplitude Matching and Whale Optimization Algorithm with Constriction Factor

Lower order modelling of uncertain bounded systems is presented in this paper using amplitude matching and Whale Optimization Algorithm (WOA) with Constriction Factor (CF). The amplitude matching technique ensures to retain the stability and dynamics of the original higher-order systems. The proposed optimization algorithm for minimum Integral Square Error (ISE) approximates the model so that the responses match closely. The results are validated by comparing the ISE values of existing models. The presented technique is applicable for both Linear Time Invariant Continuous Systems (LTICS) and Linear Time Invariant Discrete Systems (LTIDS) without any need for tedious calculation of domain transformation.

Optimization of Proportional Integral Derivative Parameters of Brushless Direct Current Motor Using Genetic Algorithm

Optimal performance of the Brushless Direct Current (BLDC) motor is to be realized using an efficient Proportional Integral Derivative (PID) controller. However, conventional tuning technique fails to perform satisfactorily under parameter variations, nonlinear conditions and time delay. Also using conventional technique to tune the parameters gain of the PID controller is a difficult task. To overcome these difficulties, modern heuristic optimization technique are required to optimally tune the Proportional, Integral, Derivative of the controller for optimal speed control of three phase BLDC motor. Thus, genetic algorithm (GA) based PID controller was used to achieve a high dynamic control performance. The Brushless DC Motor mathematical equation which describes the voltage and corresponding rotational angular speed and torque of the brushless DC motor was employed using electrical DC Machines theorem. The Genetic algorithm was further analyzed by adopting the three common performance indices i.e. Integral Time Absolute Error (ITAE), Integral Square Error (ISE) and Integral Absolute Error (IAE) in order to capture and compare the most suitable BLDC Motor speed and torque control characteristics. All simulations were done using MATLAB (R2018a). The simulation result showed that the system with GA-PID controller had the better system response when compared with the existing technique of ZN-PID controller.

Robust analytical proportional‐integral‐derivative tuning rules for regulation of air pressure in supply manifold of proton exchange membrane fuel cell

AbstractThe core aim of this manuscript is to recommend analytical tuning rules to regulate and control the air supply pressure moving from the supply manifold (SM) to the electrode (cathode) of proton exchange membrane fuel cell (PEMFC). This is done to have an optimal oxygen excess ratio in the fuel cell for enhanced energy generation. The higher order dynamics of PEMFC is approximated to be non‐integer first‐order stable plus time delay model. A simple proportional ‐integral/proportional‐integral‐derivative (PI/PID) control scheme is designed for a specific maximum sensitivity (Ms) using analytical tuning rules. This, in turn, enhances its dynamic performance by regulating the SM pressure. The proposed integer order PI/PID control technique is compared with the other fractional order IMC‐PI control techniques that are recently published. The simulation results obtained prove that the proposed tuning rules provide a good response compared with fractional order controllers and thereby maintaining the SM pressure. The robustness of the novel controller is analyzed by introducing perturbations and noise to the dynamic model. The tuning rules proposed are applicable for two maximum sensitivity values of 1.4 and 2 as a measure of robustness. To measure system performance, few time domain metrics and integral absolute error (IAE), integral square error (ISE), and TV metrics are used. For both the Ms values, the proposed techniques provide stable and improved responses.

Centralized Airflow Control to Reduce Output Power Variation in a Complex OWC Ocean Energy Network

A centralized airflow control scheme for a complex ocean energy network (OEN) is proposed in this paper to reduce the output power variation (OPV). The OEN is an integrated network of multiple oscillating water columns (OWCs) that are located at different geographical sites connected to a common electrical grid. The complexity of the OWC-OEN increases manifolds due to the integration of several OWCs and design of controllers become very challenging task. So, the centralized airflow control scheme is designed in two stages. In control stage-1, a proportional-integral- (PI-) type controller is designed to provide a common reference command to control stage-2. In control stage-2, the antiwindup PID controllers are implemented for the airflow control of all the OWCs simultaneously. In order to tune the large number of control parameters of this complex system, a fitness function based on integral squared error (ISE) is minimized using the widely adopted particle swarm optimization (PSO) technique. Next, the simulation results were obtained with random wave profiles created using the Joint North Sea Wave Project (JONSWAP) irregular wave model. The OPV of the proposed OWC-OEN was reduced significantly as compared to the individual OWC. It was further observed that the OPV of the proposed scheme was lower than that achieved with uncontrolled and MPPT controlled OWC-OEN. The effect of communication delay on the OPV of the proposed OWC-OEN scheme was also investigated with the proposed controller, which was found to be robust for a delay up to 100 ms.

Hybrid fuzzy-PID like optimal control to reduce energy consumption

The electric motor is one of the appliances that consume considerable energy. Therefore, the control method which can reduce energy consumption with better performance is needed. The purpose of this research is to minimize the energy consumption of the DC motor with maintaining the performance using Hybrid Fuzzy-PID. The input of the Fuzzy system is the error and power of the system. Where error is correlated with matric Q and power is correlated with matric R. Therefore, adjusting the fuzzy rule on error and power is like adjust matrices Q and R in LQR method. The proposed algorithm can reduce energy consumption. However, system response is slightly decrease shown from ISE (Integral Square Error). The energy reduction average is up to 5.58% while the average of ISE increment is up to 1.89%. The more speed variation in the system, the more energy can be saved by the proposed algorithm. While in terms of settling time, the proposed algorithm has the longest time due to higher computation time in the fuzzy system. This performance can be increased by tuning fuzzy rules. This algorithm offers a solution for a complex system which difficult to be modeled.

Optimal and Analytical Tuning of I-PD Controllers for Controlling Stable Processes with Inverse Response

A positive zero in the transfer function of a process causes an initial response in opposite to the final steady-state. This characteristic is known as inverse response and makes the control more challenging. In the literature, usually, well known tree term controllers, that is, Proportional-Integral-Derivative (PID) controllers, are used to control such processes. In this paper, simple analytical expressions have been derived to find optimum tuning parameters of I-PD controllers to control open loop stable processes with time delay and a positive zero. Time weighted versions of Integral of Squared Error (ISE) criterion, namely ISTE, IST2E and IST3E criteria, which have been proved to be resulting in quite satisfactory closed loop responses, have been used to derive optimum tuning rules. Effectiveness of obtained tuning rules has been shown by simulation examples.

Performance analysis of distributed power flow controller with ultra-capacitor for regulating the frequency deviations in restructured power system

Abstract This paper presents a novel approach for automatic generation control (AGC) of two-area deregulated system with unequal sources for sustaining the frequency and tie-line power at perturbations. The combination of ultra-capacitor (UC) and various FACTS controllers such as Thyristor-controlled series capacitor (TCSC), Static synchronous series compensator (SSSC), Unified power flow controller (UPFC), and Distributed power flow controller (DPFC) have been investigated in AGC of interconnected system with thermal-wind and hydro-diesel generating units. An innovative metaheuristic method called bat algorithm (BA) is used to ascertain the optimal gain parameters of the two degree of freedom (2DOF) controllers using an integral squared error (ISE) criteria. Furthermore, the productive assessment of the bat tuned 2DOF controllers are also compared with teaching learning-based optimization (TLBO) and cuckoo search (CS) methods optimized 2DOF in distinct contract scenarios of the suggested restructured system. The effect of the coordinated performance of UC and DPFC has been mitigated the oscillatory response of the AGC system at various operating circumstances. The investigations disclose that the bat optimized 2DOF-PID yield the productive outcomes with coordination of DPFC and UC in all contract transactions of the restructured system.

Denoising Autoencoders and LSTM-Based Artificial Neural Networks Data Processing for Its Application to Internal Model Control in Industrial Environments-The Wastewater Treatment Plant Control Case.

The evolution of industry towards the Industry 4.0 paradigm has become a reality where different data-driven methods are adopted to support industrial processes. One of them corresponds to Artificial Neural Networks (ANNs), which are able to model highly complex and non-linear processes. This motivates their adoption as part of new data-driven based control strategies. The ANN-based Internal Model Controller (ANN-based IMC) is an example which takes advantage of the ANNs characteristics by modelling the direct and inverse relationships of the process under control with them. This approach has been implemented in Wastewater Treatment Plants (WWTP), where results show a significant improvement on control performance metrics with respect to (w.r.t.) the WWTP default control strategy. However, this structure is very sensible to non-desired effects in the measurements—when a real scenario showing noise-corrupted data is considered, the control performance drops. To solve this, a new ANN-based IMC approach is designed with a two-fold objective, improve the control performance and denoise the noise-corrupted measurements to reduce the performance degradation. Results show that the proposed structure improves the control metrics, (the Integrated Absolute Error (IAE) and the Integrated Squared Error (ISE)), around a 21.25% and a 54.64%, respectively.

An Adaptive Decoupling Control Design for Flotation Column: A Comparative Study Against Model Predictive Control

Multivariable nature of the flotation process compels advanced control strategies, including Model Predictive Controllers (MPC), leading to robust and effective compensation of disturbances. However, the complexity of calculations and implementation has limited their application in the industry. On the other hand, decoupling methods promise drastic reduction in computation time and complexity, while considering the multivariable relations between the inputs and outputs indirectly. Therefore, in this paper, an Adaptive Decoupling Controller (ADC) was designed and implemented on a pilot flotation column and its control performance was compared to MPC and SISO PID. Results showed that the weak coupling of variables in the studied case (and also reported by other researchers) causes a satisfactory control of the column by ADC, even better than the MPC in terms of Integral Squared Error index (ISE), Mean Squared Error index (MSE) and total energy consumption, with lower costs of computation and implementation.

Optimal IMC-PID controller design for large-scale power systems via EDE algorithm-based model approximation method

In this paper, the authors propose an optimal IMC-PID controller design for the Load Frequency Control (LFC) of large-scale power system via model approximation method. The model approximation method uses the Enhanced Differential Evolution (EDE) algorithm to determine an optimal Reduced Order Model (ROM) for the considered large-scale power system by minimizing the performance measure called Integral Square Error (ISE) between their step responses. Later, the LFC design is carried out using an optimal ROM instead of processing with the large-scale power system model. Thus, this simplifies the design, reduces the computational efforts and also helps in determining the lower order controller. An optimal IMC design methodology is proposed by minimizing ISE between the actual output and the reference input responses of the large-scale power system using EDE algorithm. Further, PID controller gains are acquired by least square model matching with the optimal IMC transfer function. The proposed IMC-PID controller design allows a satisfied reference input tracking performance, robustness in disturbance rejection and improves the dynamic stability of the power system. The proposed method is validated by applying it to a single area power system of third-order SISO model and also extended to a centralized two-area thermal–thermal non-reheated power system of a seventh-order MIMO model. The simulation results and the comparison of error performance indices show the efficacy of the proposed method over the significant methods available in the literature.

Nonlinear H∞ Measurement Feedback Control Algorithm for Quadrotor Position Tracking

This paper presents a new framework to solve the position tracking problem of a quadrotor helicopter. This algorithm consists of a cascade architecture which employs a measurement feedback nonlinear H∞ algorithm in the outer-loop to track the reference trajectory via noisy measurements, and a state-feedback nonlinear H∞ in the inner-loop to stabilize the attitude dynamics. The obtained structure for the outer-loop includes a robust controller-estimator combination which satisfies the stability and convergence of both parts. Analytical results show the asymptotic stability and output boundedness for both inner and outer loops and consequently the cascade system. The Monte-Carlo simulations are performed to numerically examine the robust performance and the region of attraction of the overall system. Different environmental disturbances and modeling uncertainties are considered in 1000 simulations to verify the robust performance and boundedness of all states. Moreover, to quantify the performance of the algorithm, two numerical indexes; Integrated Square error (ISE), and Integral of the Absolute value of the control Derivative (IADU) are suggested and utilized for statistical analysis of the state tracking performance and control effort, respectively. Finally, a Software-in-the-Loop (SIL) test is performed using PX4-FMU open source autopilot and Raspberry-Pi 3 as an auxiliary processor to show the capability of the algorithm for hardware implementation.

Time delay handling in dominant pole placement with PID controllers to obtain stability regions using random sampling

This paper proposes a new formulation of proportional–integral–derivative (PID) controller design using the dominant pole placement method for handling second-order-plus-time-delay (SOPTD) systems. It transforms the transcendental exponential delay term of the plant into finite number of discrete-time poles by a suitable choice of the sampling time. The PID controller has been discretised using Tustin’s method and the controller gains are obtained using the dominant pole placement criterion where the plant is discretized using the pole-zero matching method. Random search and optimisation have been used to obtain the stability region in the desired closed loop parameters space by minimising the integral squared error (ISE) criterion by randomly sampling from the stabilizable region. Then these closed loop parameters are mapped on to the PID controller gains. Effectiveness of the proposed methodology is shown for nine test-bench plants with different lag to delay ratios, open loop damping, and sampling times.

Learning Stable Robust Adaptive NARMA Controller for UAV and Its Application to Twin Rotor MIMO Systems

This study presents a nonlinear auto-regressive moving average (NARMA) based online learning controller algorithm providing adaptability, robustness and the closed loop system stability. Both the controller and the plant are identified by the proposed NARMA based input–output models of Wiener and Hammerstein types, respectively. In order to design the NARMA controller, not only the plant but also the closed loop system identification data are obtained from the controlled plant during the online supervised learning mode. The overall closed loop model parameters are determined in suitable parameter regions to provide Schur stability. The identification and controller parameters are calculated by minimizing the $$\varepsilon $$ -insensitive error functions. The proposed controller performances are not only tested on two simulated models such as the quadrotor and twin rotor MIMO system (TRMS) models but also applied to the real TRMS with having severe cross-coupling effect between pitch and yaw. The tracking error performances of the proposed controller are observed better compared to the conventional adaptive and proportional–integral–derivative controllers in terms of the mean squared error, integral squared error and integral absolute error. The most noticeable superiority of the developed NARMA controller over its linear counterpart, namely the adaptive auto-regressive moving average (ARMA) controller, is observed on the TRMS such that the NARMA controller shows a good tracking performance not only for the simulated TRMS model but also the real TRMS. On the other hand, it is seen that the adaptive ARMA is incapable of producing feasible control inputs for the real TRMS whereas it works well for the simulated TRMS model.

Real Time Implementation and Analysis of Enhanced Artificial Bee Colony Algorithm Optimized PI Control algorithm for Single Phase Shunt Active Power Filter

This paper proposes a new hybrid novel optimization approach, called Enhanced Artificial Bee Colony Algorithm (EABC) for designing an optimal PI controller for single-phase Shunt Active Power Filter (SAPF). The proposed EABC algorithm optimizes the gain values of the PI controller to improve the dynamic performance of SAPF. In this EABC, the adaptive real coded genetic algorithm (ARGA) is integrated with the Artificial Bee Colony (ABC) algorithm and this integration improves the exploration and exploitation ABC and speed up the convergence rate. The minimization of integral square error (ISE) is considered as an objective function to manipulate the gain values of the PI controller. The system tested with MATLAB simulation results are implemented in the hardware circuit with the same set of parameters. The proposed hardware system is designed with the Cyclone-IV EP4CE30F484 FPGA controller and the gain value for this proposed controller is fed from the simulation results tested with ABC and EABC algorithm. The results obtained from the hardware setup is compared with simulation results. The experimental result enhanced the performance of THD of source current, settling time and percentage peak overshoot of DC Link voltage.

Comparison of Particle Swarm Optimization and Ziegler Nichols Techniques

Two tuning techniques namely: Particle Swarm Optimization (PSO) and Ziegler Nichols (ZN) technique are compared. PSO is an optimization technique based on the movement and intelligence of swarms. PSO applies the concept of social interaction to problem solving. It is a computational method that optimizes a problem by iteratively trying to improve a candidate solution about a given measure of quality. Ziegler Nichols tuning method is a heuristic method of tuning a PID controller. The ZN close loop tuning is performed by setting the I (integral) and D (derivative) gains to zero and increasing proportional gain to obtain sustained oscillations. The DC Motor is represented by second order transfer function is used as a plant, which is controlled using PID controller. The PID controller parameters are chosen by tuning the controller using PSO algorithm and ZN method. The response of the system to unit step input is plotted and performance measures are evaluated for comparing PSO algorithm and ZN technique. Here we have compared the two tuning methods based upon the settling time (Ts), peak overshoot (Mp) and the two performance indices namely Integral square error (ISE) and Integral Absolute error (IAE).

Optimization of Threshing Quality Control Strategy Based on Type-2 Fuzzy Logic Controller

At present, loss rate and grain damage are the most complicated problems for combine harvester. Besides, existing controllers that control threshing quality do not take into account environmental noise, data fluctuations, and other detection factors. In this paper, considering the interference of uncertain factors, a control strategy with low crashed rate and reduced loss rate using type-2 Fuzzy Logic Controller (FLC) is proposed. This control strategy takes threshing separation component as a research object and adopts combination of theory with experimental analysis. Firstly, basic data acquisition experiment of threshing system is designed. Secondly, a control strategy is established by adequately previous filled test data. In the process of control strategy design, Fuzzy Logic Toolbox evaluates the performance of type-2 FLC. Integral of Square Error (ISE) and Integral of the Absolute value of the Error (IAE) show a better performance of type-2 FLC than of type-1 FLC. At last, field experiments are designed to verify the effectiveness of type-2 control strategy. The field test shows that the maximum reduction of grain damage rate and loss rate can reach to 44.08 % and 29.6 %. Experiment results show that the type-2 FLC can significantly reduce loss rate, crashed rate, and improve threshing quality.

AUTOMATIC GENERATION CONTROL OF A THERMAL POWER PLANT WITH REHEAT TURBINE USING PSO OPTIMIZED INTEGRAL CONTROLLER

In this paper an approach has been presented for load frequency control of a single area thermal power plant with reheat turbine. Integral controller has been preferred for control of manipulated variable of the control system representing a single-area thermal power system, since the basic intention of load frequency control execution is to annihilate the frequency deviation resulting from step load disturbance acting on a power system. The gain of the integral controller is optimized with the help of Particle Swarm Optimization (PSO) technique. Various objective functions such as IAE (Integral Absolute Error), ITAE (Integral Time Absolute Error), ITSE (Integral Time Square Error) and ISE (Integral Square Error) are used as benchmark criteria for optimizing the gain of the controller. The controller performance exhibits divergence based upon objective functions. In the second part of the research, we have tested the system for robustness by administrating the system performance for parameter variations. The simulation results have affirmed the robust performance of the system.

SIMULATION AND PERFORMANCE OF LIQUID LEVEL CONTROLLERS FOR LINEAR TANK

Level control of liquid in a tank or any similar container is widely used in applications such as chemical and oil industrial processes. Control the level at desired value is very important. This paper studies the performance of P, PI, and PID controllers in controlling the level of a liquid. Mass balance is used to find mathematical model of water tank level. Ziegler-Nichol (Z-N) and Cohen-Coon (C-C) tuning methods are used to evaluate parameters of the controllers. The error indices such as Integral Absolute Error (IAE) and Integral Squared Error (ISE) are used to compare between performances of the controllers. MATLAB is used to test the control system performance and compare the results with real values. Both simulation and experimental results show that liquid level system can be controlled effectively by using Z-N tuning method. The result shows that the PI controller gives better performance in comparison with P and PID controller.

Heuristic Algorithm Assisted Controller Design for Nonlinear Type Liquid Level Process

In process control industries, controlling the liquid inside the non-linear tanks such as a conical tank, hopper tank and spherical tank is a highly challenging task due to the change in the cross section area of the tank. The aim of this project is to design a suitable controller to control the level of the hopper type tank by using conventional controllers like Ziegler-Nichols tuning method (ZN) and computational controllers using metaheuristic algorithms such as Bacteria Foraging Optimization (BFO) algorithm, Particle Swarm Optimization (PSO) algorithm and Firefly Algorithm (FA). This controller can be used for the industries that deal with this nonlinear type of process. The mathematical model for the conical tank was done to identify the transfer function of the system. The conventional and computational controllers were designed and implemented using MATLAB/Simulink to choose the best controller for the conical/hopper type tank liquid level process based on the time domain specifications such as rise time, settling time and peak overshoot percentage. Moreover, the performance of the system was analyzed based on the error indices such as Integral Square Error (ISE), Integral Absolute Error (IAE), Integral Time Square Error (ITSE) and Integral Time Absolute Error (ITAE). Also, servo and regulatory operations were tested for the chosen best controller.