Integral Time Absolute Error Research Articles

Control of CSTR using firefly and hybrid firefly-biogeography based optimization (BBFFO) algorithm

Continuous Stirred Tank Reactor (CSTR) is the core of numerous procedures due to its simple structure, low cost, stable and productive activity. This paper presents PID controller tuning by using firefly and hybrid Firefly with biogeography based optimization (BBFFO) algorithms for continuously stirred tank reactor (CSTR). In this paper, BBO-FF is iterated to come to the ideal or the close to the ideal of PID controller parameters. Principle accentuate is given to improve the progression reaction and cost proficiency attributes. The CSTR framework is simulated with the proposed hybrid controller which improves the robustness as well as the behavior of the framework. Simulation results demonstrate the adequacy and the effectiveness of the hybridization also present significant upgrade of the time reaction parameters, for example settling time, rise time, overshoot, and integral time absolute error. Studies appeared that the proposed versatile techniques with metaheuristic calculations are quick and efficient in the reduction of error. Both Firefly and Biogeography based optimization is Metaheuristic methodology. The proposed approach BBFFO-PID is compared with the PSO-PID controller in terms of performance indices. Hybridization of the Firefly algorithm with BBO Algorithm for PID controller tuning of CSTR is simulated on MATLAB 2014Ra.

Development of buck power converter circuit with ANN RL algorithm intended for power industry

PurposeThis paper aims to deal with application of artificial intelligence for solving real time control complication adhered with the controlled operation of a buck power converter. This type of converter finds application for power conversion at various levels for the direct current-direct current power industry to step down the input voltage.Design/methodology/approachUse of ANN-RL (Artificial Neural Networks- Reinforcement Learning)-based control algorithm to control buck power converter shows robustness against parameter and load variation. Because of non-linearity instigated by element used for switching, control of this converter becomes an arduous control predicament. All the classical control techniques are based on an approximate linear model of the step down converter and these techniques fail to handle actual non-linearity.FindingsIn this paper, a reinforcement learning-based algorithm has been used to handle and control buck power converter output voltage, without approximating the model of converter. The non-linearity instigated in converter is subjected to state of switch. Model of buck power converter is defined as a multi-step decision problem so that it can be solved using mathematical model of Markov decision process (MDP) and, in turn, reinforcement learning can be implemented. As MDP model is available for a discrete state system so model of converter has to be discretized and then value iteration is applied and output is analyzed. Load regulation and integral time absolute error analysis is done to show efficacy of this technique.Originality/valueTo mitigate the effect of discretization function approximation using neural network is applied. MATrix LABoratory has been used for implementation and result indicates an improvement in the overall response.

Design of new fractional order PI–fractional order PD cascade controller through dragonfly search algorithm for advanced load frequency control of power systems

Owing to integrating the dense range of distinct electric power sources, high volume of power generation units, abrupt and continuous changes in load demand, and rising utilization of power electronics, the electric power system (EPS) is striving for high-performance control schemes to counterwork the concerns depicted above. Additionally, it is highly creditable to have the controller structure as simple as possible from a viewpoint of practical implementation. Thus, this paper describes a virgin application of fractional order proportional integral–fractional order proportional derivative (FOPI–FOPD) cascade controller for load frequency control (LFC) of electric power generating systems. The proposed controller includes fractional order PI and fractional order PD controllers connected in cascade wherein orders of integrator ( $$\lambda$$ ) and differentiator ( $$\mu$$ ) may be fractional. The gains and fractional order parameters of the controller are concurrently tuned using recently proposed dragonfly search algorithm (DSA) by minimizing the integral time absolute error (ITAE) of frequency and tie-line power deviations. DSA is the mathematical model and computer simulation of static and dynamic swarming behaviors of dragonflies in nature, and its implementation in LFC studies is very rare, unveiling additional research gap to be bridged. Performance of the advocated approach is first explored on popular two-area thermal PS with/without governor dead band (GDB) nonlinearity and then on three-area hydrothermal PS with suitable generation rate constraints. To highlight the prominence and universality of our proposal, the work is extended to single-/multi-area multi-source EPSs. Several comparisons with DSA optimized FOPID controller and the relevant recent works for each test system indicate the contribution of proposed DSA optimized FOPI–FOPD cascade controller in alleviating settling time/undershoot/overshoot of frequency and tie-line power oscillations.

Fault-tolerant control based on adaptive super-twisting nonsingular integral-type terminal sliding mode for a delta parallel robot

External disturbances, internal uncertainties and actuator faults with an unknown range have detrimental effects on controller performance of industrial robots. In this paper, to deal with such challenges, a new fault-tolerant control (FTC) strategy using a combination of nonsingular integral-type terminal sliding mode (NITSM) and adaptive high-order super-twisting (AST) control is proposed for a delta-type parallel robot. To eliminate the chattering of sliding mode controller as a key ingredient of excessive energy consumption and convergence rate reduction, high-order algorithm is applied. Stability analysis of the closed-loop system is performed using Lyapunov theory. Moreover, to achieve optimal performance, controller parameters are obtained using harmony search algorithm (HSA) by minimizing an objective function consisting of integral time absolute error (ITAE) and control signal rate. The proposed controller performance is compared with conventional sliding mode and feedback linearization control methods. The obtained results reveal the superiority of the proposed AST-NITSM.

Derivative Proportional – Integral Controller Using Nelder-Mead Optimization for Glycerine Purification Heating Process

It is important to purify the crude glycerine before to convert them into value-added products. Such dark colored crude have high free fatty acid content that can be removed via heating process. This paper focuses mainly on the heating control system, which has contributed to the improvement of the glycerine purification process system. The design of Derivative Proportional – Integral controller for the glycerine temperature control loop system could demonstrate some improvement of the glycerine heating process control response in term of process settling time and percent overshoot. Derivative Proportional – Integral is a proposed controller where Proportional and Derivative control actions operate on process variables rather than error signals. Meanwhile, the integral mode is connected to the forward path where the error signal is used as an input to the control mode. The output of the two control modes is then subtracted to drive the process. The Derivative Proportional – Integral controller was designed using the Nelder-Mead optimization algorithm with objective function of the Integral Time Absolute Error criteria calculated using Simpson's one-third rule. The control performance of the proposed controller was analyzed by comparing the rise time, percent overshoot and settling time of the response with that of the conventional PID controller. The simulation results show that the Nelder-Mead optimization algorithm can be used and can produce a good control system with zero percent overshoot and shorter heating time compared to the achievements of the PID control system. In addition, the robustness test of the controller has shown that the proposed control system can effectively detect changes in the operating temperature. The control performance shown by the proposed controller is excellent. The Derivative Proportional – Integral control system designed based on optimization algorithm techniques can improve the performance of the glycerine purification process heating system to meet the purified glycerine requirements.

Multiobjective Optimal Control of FOPID Controller for Hydraulic Turbine Governing Systems Based on Reinforced Multiobjective Harris Hawks Optimization Coupling with Hybrid Strategies

The controlling parameter tuning of the hydraulic turbine governing system (HTGS) is always deduced under single operating condition and is not suitable for the changeable operating conditions of the hydraulic turbine. For this purpose, multiobjective optimization problem of fractional order PID (FOPID) controller for HTGS is constructed through the consideration of no-load disturbance and on-load disturbance operation conditions, where the performance indicators of integral time absolute error (ITAE) under both operation conditions are employed as the objective functions. To achieve the optimum, the multiobjective version of newly proposed Harris hawks optimization (MOHHO) is established to solve the optimization issue. Additionally, hybrid strategies which include Latin hypercube sampling initialization, modified differential evolution operator, and mutation operator are coupled into MOHHO (HMOHHO) to promote the global searching capability. Simultaneously, the linear model of rabbit energy within MOHHO is replaced with a nonlinear one to further enhance the searching capacity. Subsequently, the effectiveness and superiority of the proposed HMOHHO are verified by several multiobjective UF and ZDT test problems. Finally, the practical application and contrastive analysis ascertain that the constructed multiobjective problem of FOPID controller is suitable for HTGS under changeable operating conditions, and the proposed HMOHHO is effective in solving the issue.

Robust controller design for systems with probabilistic uncertain parameters using multi-objective genetic programming

Optimal design of controllers without considering uncertainty in the plant dynamics can induce feedback instabilities and lead to obtaining infeasible controllers in practice. This paper presents a multi-objective evolutionary algorithm integrated with Monte Carlo simulations (MCS) to perform the optimal stochastic design of robust controllers for uncertain time-delay systems. Each potential optimal solution represents a controller in the form of a transfer function with the optimal numerator and denominator polynomials. The proposed methodology uses genetic programming to evolve robust controllers. Using GP enables the algorithm to optimize the structure of the controller and tune the parameters in a holistic approach. The proposed methodology employs MCS to apply robust optimization and uses a new adaptive operator to balance exploration and exploitation in the search space. The performance of controllers is assessed in the closed-loop system with respect to three objective functions as (1) minimization of mean integral time absolute error (ITAE), (2) minimization of the standard deviation of ITAE and (3) minimization of maximum control effort. The new methodology is applied to the first-order and second-order systems with dead time. We evaluate the performance of obtained robust controllers with respect to the upper and lower bounds of step responses and control variables. We also perform a post-processing analysis considering load disturbance and external noise; we illustrate the robustness of the designed controllers by cumulative distribution functions of objective functions for different uncertainty levels. We show how the proposed methodology outperforms the state-of-the-art methods in the literature.

Anti-Windup PID Controller by ITAE Tuning Rule for Steam Distillation System

In control engineering system, the PID controller is more prefer compared to the other controller. It very simple and easy to develop. Unfortunately, PID controller exhibit a weakness once spike at wind-up region. The wind-up problem is always happen due to inability of compensator to control the phenomenon. The main cause is created in controller design phase; neglect a nonlinearities dynamic. The issue can be solved by implementation of additional integral feedback compensation in order to minimize the effect of windup situation. The wind-up phenomenon can cause high overshoot, long settling time and loss productivity yield. This objective of this research to improve windup situation using backcomputation method tuning by Integral Time Absolute Error (ITAE) tuning rule. The propose ITAEProportional-Integral-Derivative integrated AntiWindup (ITAE-PID-AW) controllers revealed better performances compared to the ITAE-ProportionalIntegral-Derivative (ITAE-PID) controller.

Novel Active Disturbance Rejection Control Based on Nested Linear Extended State Observers

In this paper, a Novel Active Disturbance Rejection Control (N-ADRC) strategy is proposed that replaces the Linear Extended State Observer (LESO) used in Conventional ADRC (C-ADRC) with a nested LESO. In the nested LESO, the inner-loop LESO actively estimates and eliminates the generalized disturbance. Increasing the bandwidth improves the estimation accuracy which may tolerate noise and conflict with H/W limitations and the sampling frequency of the system. Therefore, an alternative scenario is offered without increasing the bandwidth of the inner-loop LESO provided that the rate of change of the generalized disturbance estimation error is upper bounded. This was achieved by the placing of an outer-loop LESO in parallel with the inner one that estimates and eliminates the remaining generalized disturbance originating from the inner-loop LESO due to bandwidth limitations. The stability of LESO and nested LESO was investigated using Lyapunov stability analysis. Simulations on uncertain nonlinear single-input-single-output (SISO) system with time-varying exogenous disturbance revealed that the proposed nested LESO could successfully deal with a generalized disturbance in both noisy and noise-free environments, where the Integral Time Absolute Error (ITAE) of the tracking error for the nested LESO was reduced by 69.87% from that of the LESO.

Fuzzy gain scheduling control apply to an RC Hovercraft

The Fuzzy Gain Scheduling (FGS) methodology for tuning the Proportional – Integral – Derivative (PID) traditional controller parameters by scheduling controlled gains in different phases, is a simple and effective application both in industries and real-time complex models while assuring the high achievements over pass decades, is proposed in this article. The Fuzzy logic rules of the triangular membership functions are exploited on-line to verify the Gain Scheduling of the Proportional – Integral – Derivative controller gains in different stages because it can minimize the tracking control error and utilize the Integral of Time Absolute Error (ITAE) minima criterion of the controller design process. For that reason, the controller design could tune the system model in the whole operation time to display the efficiency in tracking error. It is then implemented in a novel Remote Controlled (RC) Hovercraft motion models to demonstrate better control performance in comparison with the PID conventional controller.

Design of PID Intelligent Controller Combining Immune Genetic Algorithm

At present, there are many studies on "computer immunology" in the world, and there are many applications of immune genetic algorithm in engineering.The article discusses the immune genetic algorithm in the design of PID intelligent controller.Most objects in the practical industrial process fall in the distributed parameter system (DPS), where the proportional-integral-derivative (PID) control method is used to control the field. In this paper, the PID controller optimization method based on the immune genetic algorithm (IGA) (referred to as the PODM method) is applied to a class of distributed parameter objects to design the optimal controller, which is compared with several controllers based on the conventional tuning formulas. The simulation results suggest that the PID controller designed based on the PODM method can obtain relatively superior control effects in overshoot, tuning time, time integrated time absolute error (ITAE), and other indexes with relatively less control energy. The application of the PODM method to DPS can improve the control level of the PID controller in the industry at present.

A new method for optimal parameters identification of a PEMFC using an improved version of Monarch Butterfly Optimization Algorithm

In this paper, a circuit-based model of proton exchange membrane fuel cell (PEMFC) is developed for optimal selection of the model parameters. The optimization is based on using an improved version of Monarch Butterfly Optimization (IMBO) algorithm for minimizing the Integral Time Absolute Error between the measured output voltage and the output voltage of the achieved model. For validation of the proposed method, two different case studies including 6 kW NedSstack PS6 and 2 kW Nexa FC PEMFC stacks have been employed and the results have been compared with the experimental data and some well-known metaheuristics including Chaotic Grasshopper Optimization Algorithm (CGOA), Grass Fibrous Root Optimization Algorithm (GRA), and basic Monarch Butterfly Optimization (MBO) to indicate the superiority of the proposed method against the compared methods. Final results show a satisfying agreement between the proposed IMBO and the experimental data.

An Integral Tilt Derivative Control Strategy for Frequency Control in Multimicrogrid System

The multimicrogrid system is a complicated nonlinear system, which brings performance degradation due to deficient damping under the unexpected fluctuation in power generation due to the presence of renewable sources, dynamically changing loading conditions, and parameter variations. Owing to this, to provide consistent electric power with superlative attribute, sturdy and intelligent control techniques are amazingly imperative in the automatic generation control of microgrid (MG). The application of imperialist competitive algorithm (ICA)-based fractional-order integral proportional derivative with filter (IPDF), i.e., integral tilt derivative with filter controller (ITDF) controller in frequency control in two areas interconnected MG (isolation mode) with renewable penetration, is a novel work. A maiden attempt of the ICA is proposed to optimize the gains of the ITDF controller utilizing the integral time absolute error criterion. To demonstrate the supremacy of ICA, its outcomes are contrasted with two existing optimization strategies, namely the genetic algorithm and the particle swarm optimization. The effectiveness of the proposed controller is revealed by contrasting the dynamic responses of multi microgrid (MMG) with proportional integral derivative with filter (PIDF) and tilt integral derivative with filter (TIDF) controllers. At last, a sensitivity investigation is performed to exhibit the power of the studied strategy to wide variations in the MG parameters, magnitude as well as the location of step/random load disturbance. The proposed MMG is simulated in MATLAB/Simulink environment.

Recent methodology based Harris Hawks optimizer for designing load frequency control incorporated in multi-interconnected renewable energy plants

Abstract This paper proposes a reliable approach-based Harris Hawks Optimizer (HHO) to evaluate the optimal parameters of the Proportional-Integral (PI) controller simulating load frequency control (LFC) incorporated in a multi-interconnected system with renewable energy sources (RESs). During the optimization process, the integral time absolute error (ITAE) of the frequency and tie-line power is handled as the objective function. The HHO is selected due to its ease and requirement of less controlling parameters. Two different interconnected power systems are investigated as test systems to demonstrate the robustness of the proposed controller based HHO by comparing to other optimizers and traditional controller. The considered two systems include, one comprises two interconnected area of thermal and photovoltaic (PV) plants while the other system has four plants of PV, wind turbine (WT), and two thermal plants considering governor dead-band (GDB) and generation rate constraint (GRC). Different cases of load disturbance are studied, and the obtained results via the HHO are compared to Sine Cosine Algorithm (SCA), Multi-verse optimizer (MVO), Antlion Optimizer (ALO), and Grey wolf optimizer (GWO) as well as traditional controller. Moreover, sensitivity analysis is performed by changing the system parameters in a range of ± 10% and the performance of the proposed HHO-LFC is evaluated. The obtained results confirmed the reliability and superiority of the proposed approach based HHO in designing LFC for the considered systems.

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.

Optimal tuning linear quadratic regulator for gas turbine by genetic algorithm using integral time absolute error

For multiple input-multiple output (MIMO) systems, the most common control strategy is the linear quadratic regulator (LQR) which relies on state vector feedback. Despite this strategy gives very good result, it still has trial and error procedure to select the values of its weight matrices which plays a important role in reaching to the desiered system performance. In order to overcome this problem, the Genetic algorithm is used. The design of genetic algorithm based linear quadratic regulator (GA-LQR) utilized Integral time absolute error (ITAE) as a cost function for optimization. The propsed procedure is implemented on a linear model of gas turbine to control the generator spool’s speed and the output power.

Error Measurement of LCC Resonant Converter for X-Ray

X-rays are devices immensely used for diagnosis and treatment in medicinal field. X-rays are very popular as they are used in non-destructive testing. An X-ray device uses a high voltage power supply which can be produced by DC-DC converters. Resonant converters are prominent among the dc-dc converters for X-ray application as the switching is done at zero current and zero voltage. This paper presents a LCC resonant converter based PID controller tuned with optimization algorithms for non-linear system. Differential evolution optimization (DEO), grey wolf optimization (GWO) and grasshopper optimization algorithms (GOA) are used to identify the local minima in time domain system. The objective functions considered are minimization of integral absolute error (IAE), integral square error (ISE) and integral time absolute error (ITAE). The convergence curve is also plotted for the different optimization algorithms using MATLAB Simulink to study the convergence time.

Automatic generation control for single area power system using GNA tuned PID controller

This work investigates Automatic Generation Control in the one area thermal power system and optimization of gain parameters of conventional controller for non-reheat and reheat thermal power systems. Proportional – integral – derivative (PID) controller and PI controller is used for the comparison. The tuning of controller gain parameters is obtained by Integral Time Absolute Error (ITAE) approach for optimization. The proposed work utilizes new meta-heuristic algorithm for tuning of controller gain parameters. The GNA algorithm proved to be effective and robust for tuning a controller in the presence and absence of appropriate Generation Rate Constraint (GRC). The performance comparison and verification of simulation results is shown in time domain using Matlab. Finally, simulation result reveals that new GNA tuned PID controller provides more superior response in comparison to PI controller with and without including the effect of GRC.

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.

Optimal Control of Carbon Dioxide Exchange Process in a Membrane Oxygenator Using Particle Swarm Optimization Approach

The aim of this study is to evaluate the performance of Zeigler-Nichols continuous cycling and particle swarm optimization (PSO) method in tuning the optimal gains for Proportional-Integral-Derivative (PID). PID controller is implemented to control the rate of CO2 elimination from a membrane oxygenator during extracorporeal blood purification process. The sweep gas flow rate is chosen as the manipulated variable to control arterial CO2 partial pressure (pCO2) in blood. The Zeigler-Nichols continuous cycling tuning method is employed for tuning purpose and the performance of each controller (P-only, PI and PID) are evaluated based on three performance indices, namely integral absolute error (IAE), integral squared error (ISE) and integral time absolute error (ITAE). Next, the optimization algorithm known as PSO is used to calculate the gain parameter that can produce the best control action. The robustness of these tuning methods is assessed for set point tracking and load disturbance rejection tests. Results indicated that the PID is seen as the best controller compared to the classical controllers such as P and PI when Zeigler-Nichols continuous cycling as the tuning method is implemented. However, further tests highlighted the PSO-PID strategy (PID parameters that are optimized by PSO) showed even better control responses compared to PID alone. Thus, it can be concluded that optimization strategy by PSO method is the best tuning method to be used in determining the controller parameters for the automation of extracorporeal circulation control for both set point tracking and load disturbance rejection tests.