Integral Of Time Multiplied Absolute Error Research Articles

Controlling parameters proportional integral derivative of DC motor using a gradient-based optimizer

In this paper, a gradient-based optimizer (GBO) algorithm is presented to optimize the parameters of a proportional integral derivative (PID) controller in DC motor control. The GBO algorithm which mathematically models and mimics is inspired by the gradient-based Newton method. It was developed to address various optimization issues. To determine the performance of the proposed method, a comparison method with the ant colony optimization (ACO) method. It was compared using the integral of time multiplied absolute error (ITAE). They are most popularly used in the literature. From the test results, the proposed method is promising and has better effectiveness. The proposed method, namely GBO-PID, shows the best performance.

A hybrid optimization algorithm for improving load frequency control in interconnected power systems

The objective of this study is to develop an algorithm named Modified Artificial Bee Colony and Particle Swarm Optimization (MHABC-PSO) to address load frequency control (LFC) challenges in a two-area interconnected power system. The proposed MHABC-PSO algorithm is designed with two key modifications to enhance global exploration capability and improve convergence speed. Hence, a decision block is introduced in the employed bee (EB) phase incorporating a control parameter “limit” to allow each candidate solution (CS) to explore itself up to the “limit” value and boost local exploration. In addition, an introduction of a novel selection mechanism utilizing heuristic information (η) in EBs phase guides the onlooker bee (OB) phase to select better solutions based on success and failure history, thus promoting exploitation and reducing biased exploration. To address the efficacy of the proposed algorithm at the system level, three different two-area power systems are studied, incorporating various complexities, linearity, and non-linearity such as thermal-hydro, reheat thermal, and thermal-hydro-gas turbine configurations with HVDC link, SSSC, and CES. The algorithm is applied to optimize four objective functions (i.e. ITAE, IAE, ISAE, and ITE). The fitness function maximizes controller gains by utilizing the integral time multiplied absolute error (ITAE). Other objective functions like IAE, ISAE, and ITE are employed for a comprehensive analysis. Evaluation of MHABC-PSO effectiveness is conducted through ITAE values, peak deviations, and settling times of frequency and power deviations in different two-area systems. Results demonstrate that MHABC-PSO settles the system more quickly with zero steady-state error under step load perturbations (SLPs) of 1% and 2%. Comparative analysis with ABC, PSO, SFLA-TLBO, and OHABC-PSO using ITAE index and controller settling times shows the superiority of MHABC-PSO for LFC analysis. In conclusion, the proposed MHABC-PSO algorithm proves to be an efficient and effective solution for LFC, outperforming other algorithms in terms of the specified objective functions and exhibiting rapid convergence and optimal gains for controllers, effectively addressing LFC issues by combining exploration and exploitation techniques.

Optimal control of DC motor using leader-based Harris Hawks optimization algorithm

Direct Current (DC) motor is considered a very critical component of various industrial drive equipment. This is due to their unique advantages including reasonable cost, speed-torque characteristics, ease of control, etc. While most DC motor drive applications often employ PID controllers to regulate the speed of the machine, selecting the optimal design parameters for the controllers used in these applications often posed a serious challenge. Moreover, as the complexity of the industrial process increases, the need for precise speed and position tracking becomes necessary. This current study proposes a novel Leader-based Harris Hawks Optimization (LHHO) algorithm for the design of Proportional-Integral-Derivative (PID) and Fractional Order Proportional-Integral-Derivative (FOPID) controllers to achieve optimal speed regulation of DC motors. The LHHO algorithm is an innovative meta-heuristic algorithm that draw inspiration from the cooperative hunting behavior and leadership prowess of the Harris Hawks called the “seven pounds”. While several error functions were tested in this study, the integral of time multiplied absolute error (ITAE) has been adopted as the error function for obtaining the parameters of PID and FOPID controllers using the LHHO algorithm. Through quantitative evaluations and comparisons with existing techniques, the proposed controllers (LHHO-PID and LHHO-FOPID) have revealed significant improvements in key performance metrics, including rise time, settling time, and maximum overshoot during transient periods when ITAE is used as the error function. Furthermore, the stability response and robustness analyses were carried out by varying the parameters of the DC motor under eight scenarios, which confirmed competitive performance in system response and transient behavior.

Optimization of Load Frequency Control Gain Parameters for Stochastic Microgrid Power System

Interconnected multi-area microgrids are vital for the future of sustainable and reliable power systems. Effective load frequency control (LFC) is indispensable for ensuring their stable operation. This paper introduces a PID-based LFC system tailored for a stochastic microgrid with diverse power sources, including solar, wind, diesel engine generators, and electrical batteries. The gain parameters of the proposed microgrid PID LFC controller are optimized using genetic algorithms (GA), teaching learning-based optimization (TLBO), and cohort intelligence algorithms. Integral time-multiplied absolute error (ITAE) and integral time-squared error (ITSE) serve as the cost functions for all optimization algorithms. The study evaluated the performance of these optimized microgrid PID LFC configurations under random step load disruptions. Our primary findings reveal that the cohort intelligence-optimized PID LFC controller excels in minimizing computation time (upto 76% and 94% lesser than GA and TLBO respectively) and exhibits superior robust response characteristics. Moreover, the cohort intelligence algorithm requires fewer iterations (upto 66% and 90% lesser than GA and TLBO respectively) and enhances power supply quality within the multi-power microgrid electrical framework, specifically in terms of effective load frequency control.

A Novel Black Widow Optimized Controller Approach for Automatic Generation Control in Modern Hybrid Power Systems

This research paper demonstrates an application of the Black Widow Optimization (BWO) approach to address the issue of load-frequency control (LFC) in networked power systems. BWO is an innovative metaheuristic method that quickly suggests technique is initially evaluated on a non-reheat thermal-thermal (NRTT) power system spanning two areas of interconnection, and then it is applied to two different actual power systems: (a) a two-area thermal-thermal considering Generation Rate Constraint (GRC); and (b) a two-area having thermal, hydro, wind, solar, and gas systems. The BWO method uses two fitness functions based on integral time multiplied absolute error (ITAE) and integral square error (ISE) to optimize controller gains. The suggested BWO algorithm's performance has been compared to that of existing meta-heuristic optimization methods, such as grey wolf optimization (GWO), comprehensive learning particle swarm optimization (CLPSO), and an ensemble of parameters in differential evolution (EPSDE). The simulation results show that BWO's tuning skills are better than other population-based planning methods like CLPSO, EPSDE, and GWO. The ITAE value is enhanced by 33.28% (GWO), 40.28% (EPSDE), and 43.27% (CLPSO) when the BWO algorithm is used in conjunction with the PID Controller for thermal system.

Optimal PID Controller Design for Liquid Level Tank via Modified Artificial Hummingbird Algorithm

To enhance controller performance, the optimization of control parameters has emerged as a critical research area. Among the array of optimization algorithms, the modified elite opposition-based artificial hummingbird algorithm (m-AHA) stands out for its ability to emulate behavioral strategies of hummingbirds and elite opposition-based technique. This paper, therefore, proposes m-AHA optimizer as a novel approach to optimize control parameters in a three-tanks liquid level system. By fine-tuning the parameters of proportional-integral-derivative (PID) controller, superior performance is achieved. Comparative evaluations with competitive algorithms, including the arithmetic optimization algorithm with Harris hawks optimization and covariance matrix adaptation evolution strategy, assess the m-AHA optimizer-based approach for three-tank liquid level system control. The ITAE (integral of time multiplied absolute error) performance index analyzes time domain and frequency metrics, revealing the outstanding performance of the m-AHA optimizer-based approach.

Frequency Support Studies of a Diesel–Wind Generation System Using Snake Optimizer-Oriented PID with UC and RFB

The present paper discusses the modeling and analysis of a diesel–wind generating system capable enough to cater to the electrical power requirements of a small consumer group or society. Due to high variations of the load demand or due to changes in the wind speed, the frequency of the diesel–wind system will be highly disturbed, and hence to regulate the frequency and power deviations of the wind turbine system, an effective controller design is a necessary requirement, and therefore this paper proposes a novel controller design based on PID scheme. The parameters of this controller is effectively optimized through a new snake optimizer (SO) in an offline manner to minimize frequency and power deviations of an isolated diesel–wind system. The performance of SO-PID for the diesel–wind system is evaluated by considering the integral of time multiplied absolute error (ITAE), integral absolute error (IAE), and integral of time multiplied square error (ITSE). The results were calculated for a step change in load, step change in wind speed, load change at different instants of time with diverse magnitude, and for random load patterns, and they were compared with some of the recently published results under similar working conditions. In addition, the effect of an ultracapacitor (UC) and redox flow battery (RFB) on SO-PID was investigated for the considered system, and the application results demonstrated the advantages of our proposal over other studied designs.

Development of Slime Mold Optimizer with Application for Tuning Cascaded PD-PI Controller to Enhance Frequency Stability in Power Systems

Multi-area power systems (MAPSs) are highly complex non-linear systems facing a fundamental issue in real-world engineering problems called frequency stability problems (FSP). This paper develops an enhanced slime mold optimization algorithm (ESMOA) to optimize the tuning parameters for a cascaded proportional derivative-proportional integral (PD-PI) controller. The novel ESMOA proposal includes a new system that combines basic SMO, chaotic dynamics, and an elite group. The motion update incorporates the chaotic technique, and the exploitation procedure is enhanced by searching for a select group rather than merely the best solution overall. The proposed cascaded PD-PI controller based on the ESMOA is employed for solving the FSP in MAPSs with two area non-reheat thermal systems to keep the balance between the electrical power load and the generation and provide power system security, reliability, and quality. The proposed cascaded PD-PI controller based on the ESMOA is evaluated using time domain simulation to minimize the integral time-multiplied absolute error (ITAE). It is evaluated in four different test situations with various sets of perturbations. For tuning the cascaded PD-PI controller, the proposed ESMOA is compared to the golden search optimizer (GSO) and circle optimizer (CO), where the proposed ESMOA provides the best performance. Furthermore, the findings of the proposed cascaded PD-PI controller based on the ESMOA outperform previous published PID and PI controllers adjusted using numerous contemporary techniques.

Vertical channel stabilization of barometer‐aided inertial navigation systems by optimal control

AbstractThis study investigates the problem of inertial navigation system's (INS's) vertical channel instability, which primarily results from the positive gravity feedback that takes place in the numerical integration step of the accelerometer measurements. Traditional solutions to the problem include using information from auxiliary sensors, typically barometers and global navigation satellite systems (GNSSs), integrated into INSs through feedback control loops (referred to as mechanizations) and/or Kalman filters (KFs). Most studies on this subject lack clarity regarding the methodology used for the mechanization tuning (by showing excessive empiricism) and/or disregard the benefits of using optimal control techniques for the purpose of the latter. This study, therefore, reviews the main mechanization used for vertical channel stabilization of baro‐inertial integrations and presents, as its main contribution, the performance analysis of new tuning techniques based on optimal control theory, namely, by linear quadratic regulator (LQR) and by minimization of performance indices such as the integral absolute error (IAE), integral squared error (ISE), integral of time multiplied absolute error (ITAE), and integral of time multiplied squared error (ITSE). To validate the proposed tunings, the integrated altitude and vertical velocity mean errors (MEs) and standard deviations (SDs) are used as metrics, which are compared with the corresponding MEs/SDs of the empirical tuning with highest performance/acceptance in the literature. We also evaluate the ability of the mechanizations to fulfill their ultimate goal, namely, to track the reference barometer input, by also attenuating its noise. Based on simulated and experimental results, the present study demonstrates and validates the effectiveness/robustness of the proposed optimal tunings, particularly those based on LQR and ITAE minimization.

Weighted mean of vectors optimization algorithm and its application in designing the power system stabilizer

Accurate design of the power system stabilizer (PSS) models is a crucial issue due to their significant impact on the stability of power system operation. However, identifying the parameters of a PSS model is a challenging task owing to its nonlinearity and multi-modality characteristics. Due to such characteristics, handling algorithms may be prone to stagnation in local optima. Therefore, this paper proposes a potent integrated optimization algorithm by comprising the weIghted meaN oF vectOrs (INFO) optimizer with chaotic-orthogonal based learning (COBL) and Gaussian bare-bones (GBB) strategies, named INFO-GBB, for achieving the optimal parameters of a PSS model used in a single-machine infinite-bus (SMIB) system. In the INFO-GBB, the COBL aims to enhance the searching capability to explore new regions using the orthogonal design aspect and thus improving the diversity of solutions. Also, the GBB is adopted to assist the algorithm to perform an immediate vicinity of the best solution and thus enhances the exploitation capabilities. The effectiveness and efficacy of the INFO-GBB algorithm is validated on CEC 2020 benchmark suits and the designing task of the PSS model. The achieved results by the INFO-GBB are compared with eighteen well-known algorithms. The statistical verifications along with the Friedman test have ascertained that the INFO-GBB is capable of achieving promising performances compared to the other counterparts. The results obtained based on the Friedman test illustrate that the INFO-GBB offers superior performance over the state-of-the-art algorithms as it outperforms fifteen out of eighteen algorithms by an average rank greater than 61% for benchmark problems while outperforming O-LSHADE, LSHADE, and TSA algorithms by 25%,33%, and 58%, respectively. Furthermore, the applicability of the INFO-GBB is realized through designing the PSS model used in a SMIB system. The obtained results indicate that the INFO-GBB algorithm exhibits accurate and superior performance compared to other peers as it provides the lowest value for the integral of time multiplied absolute error (ITAE) performance index which is used as an objective function. For example, the achieved results of the mean ITAE found by INFO-GBB is 1.36E−03 with improvement percentages of 24.93%, 19.78%, 13.04%, 26.64%, and 24.86%, over the LSHADE, GWO, EO, RSA, and original INFO algorithms, respectively. Therefore, the INFO-GBB can efficiently affirm its superiority and stability to deal with the function optimization task and parameters’ estimation of the PSS model.

Proportional-Integral-Derivative Controller Based-Artificial Rabbits Algorithm for Load Frequency Control in Multi-Area Power Systems

A major problem in power systems is achieving a match between the load demand and generation demand, where security, dependability, and quality are critical factors that need to be provided to power producers. This paper proposes a proportional–integral–derivative (PID) controller that is optimally designed using a novel artificial rabbits algorithm (ARA) for load frequency control (LFC) in multi-area power systems (MAPSs) of two-area non-reheat thermal systems. The PID controller incorporates a filter with such a derivative coefficient to reduce the effects of the accompanied noise. In this regard, single objective function is assessed based on time-domain simulation to minimize the integral time-multiplied absolute error (ITAE). The proposed ARA adjusts the PID settings to their best potential considering three dissimilar test cases with different sets of disturbances, and the results from the designed PID controller based on the ARA are compared with various published techniques, including particle swarm optimization (PSO), differential evolution (DE), JAYA optimizer, and self-adaptive multi-population elitist (SAMPE) JAYA. The comparisons show that the PID controller’s design, which is based on the ARA, handles the load frequency regulation in MAPSs for the ITAE minimizations with significant effectiveness and success where the statistical analysis confirms its superiority. Considering the load change in area 1, the proposed ARA can acquire significant percentage improvements in the ITAE values of 1.949%, 3.455%, 2.077% and 1.949%, respectively, with regard to PSO, DE, JAYA and SAMPE-JAYA. Considering the load change in area 2, the proposed ARA can acquire significant percentage improvements in the ITAE values of 7.587%, 8.038%, 3.322% and 2.066%, respectively, with regard to PSO, DE, JAYA and SAMPE-JAYA. Considering simultaneous load changes in areas 1 and 2, the proposed ARA can acquire significant improvements in the ITAE values of 60.89%, 38.13%, 55.29% and 17.97%, respectively, with regard to PSO, DE, JAYA and SAMPE-JAYA.

Metaheuristic Optimization Techniques Used in Controlling of an Active Magnetic Bearing System for High-Speed Machining Application

Smart control tactics, wider stability region, rapid reaction time, and high-speed performance are essential requirements for any controller to provide a smooth, vibrationless, and efficient performance of an in-house fabricated active magnetic bearing (AMB) system. In this manuscript, three pre-eminent population-based metaheuristic optimization techniques: Genetic algorithm (GA), Particle swarm optimization (PSO), and Cuckoo search algorithm (CSA) are implemented one by one, to calculate optimized gain parameters of PID controller for the proposed closed-loop active magnetic bearing (AMB) system. Performance indices or, objective functions on which these optimization techniques are executed are integral absolute error (IAE), integral square error (ISE), integral time multiplied absolute error (ITAE), and integral time multiplied square error (ITSE). The significance of an optimization technique and objective function can obtain only by implementing it. As a result, several comparisons are made based on statistical performance, time domain, frequency response behavior, and algorithm execution time. Finally, the applicability of optimization strategies in addition to the performance indices is determined with the aid of the comparative analysis. That could assist in choosing a suitable optimization technique along with a performance index for a high-speed application of an active magnetic bearing system.

DE-Algorithm-Optimized Fuzzy-PID Controller for AGC of Integrated Multi Area Power System with HVDC Link

A power system’s nonlinearity and complexity increase from time to time due to increases of power demand. Therefore, properly designed power system controlsare required. Without these, system instability will cause equipment failures, and possibly even cascading events and blackouts. To cope with this, intelligent controllers using soft computing are necessary for real time operation. In this paper, the reheat type three-area thermal power system is considered, and the output scaling factors, gain parameters of fuzzy membership functions, and parameters of fuzzy-proportional integral derivative (FPID) controllers are optimized using a differential evolution (DE) optimization techniqueand integral time multiplied absolute error (ITAE) as objective functions. To improve the limitations of the controller and to enhance stability of the system, high voltage direct current (HVDC) technology is advantageous due to its quickresponse capabilities. In this paper, a HVDC is connected in parallel to the system, revealing that a FPID controller with a HVDC provides better and more accurate resultscompared to a system without a controller. The test results presented in this paper show the proposed controller’s suitability for managing random load changes.

Optimal PID Controller Tuning for DC Motor Speed Control Using Smell Agent Optimization Algorithm

This paper presents an optimal PID controller for speed control of DC motor using Smell Agent Optimization (SAO) Algorithm. DC Motor is an energy converter which transforms electrical energy into mechanical energy used in several industrial applications. A SAO based PID is proposed for optimal tuning of the parameters of the controller to improve speed control of the motor. The SAO uses the phenomenon of smell perception and the intuitive trailing behavior of an agent to identify the source of smell. The integral of time multiplied absolute error (ITAE) is taken as the objective function for obtaining the parameters of the PID controller. It has been observed SAO-PID controller outperforms the GA based PID controller with less settling time, rise time and overshoot. Keywords— DC motor, PID controller, rising time, settling time, smell agent optimization algorithm

Simultaneous controllers for stabilizing the frequency changes in deregulated power system using moth flame optimization

This paper introduces a stochastic idea for two-area automatic generation control (AGC) of the restructured system for enhancing the system dynamic performance. In this work, a new 2-degree of freedom of proportional-integral derivative-fractional order proportional derivative with filter (2DOF PID-FOPDN) approach is proposed for the AGC two area system. To ensure realization of optimal gains of the controller, a novel nature-inspired moth-flame optimization (MFO) is suggested using integral of time multiplied absolute error (ITAE) model. The performance of MFO-based 2DOF PID-FOPDN is evaluated against Cuckoo search (CS), Bat algorithm (BA), and Teaching learning-based optimization (TLBO) approaches in different contract scenarios of deregulated system. Further work to reduce the changes in tie-line has been applied through different FACTS controllers, such as Distributed power flow controller (DPFC), Thyristor-controlled series capacitor (TCSC), Unified power flow controller (UPFC), and Static synchronous series compensator (SSSC); integrated into the AGC system with the co-ordination of Ultra-capacitor (UC). The results indicate that the MFO-based 2DOF PID-FOPDN shows superior performance with DPFC-UC over other approaches in all contract scenarios of liberalized system. A sensitivity analysis is examined to recognize the robustness of the suggested approach under ± 25% deviation in loading and system parameters.

Improved fractional [formula omitted] controller for AVR system using Chaotic Black Widow algorithm

Optimal tuning of fractional order proportional integral derivative (FOPID) controller parameters for automatic voltage regulator (AVR) system is a complex problem which requires the solution of real order integral and differential equations. Therefore, a novel optimization technique called Chaotic Black Widow Optimization (ChBWO) algorithm is proposed to tune the parameters of the FOPID controller. A new cost function is defined with a combination of Zwe-Lee Gaing’s (ZLG) and integral of time multiplied absolute error (ITAE) objectives. The proposed controller performance (rise time, settling time, and overshoot) is compared with the existing state-of-the-art techniques. To verify the robustness of the proposed controller the plant parameters are deviated from -50% to 50%. The simulation results show that the proposed controller is robust to variations in plant parameters. Moreover, disturbance analysis is also carried out by incorporating sudden changes in the reference signal. The results demonstrate that the controller is stable, robust, and sustains the sudden disturbances.

An optimal second‐order sliding mode based inter‐area oscillation suppressor using chaotic whale optimization algorithm for doubly fed induction generator

AbstractThis paper suggests an inter‐area oscillation suppressor based on second‐order sliding mode controller (SOSMC) for doubly fed induction generator (DFIG) to suppress the inter‐area power system oscillations. SOSMC‐based suppressor targets at improving the reactive power control capability of DFIG to retrieve the stability of affected power system caused by fault occurrence into the stable condition. This controller has been initially designed for two‐area power system, after that it has been extended for multi‐area power systems. SOSMC‐based suppressor has no sensitivity to the uncertainty and variation of the parameter in all system operation conditions as compared with the conventional suppressors. Due to exploration and exploitation capability of chaotic whale optimization algorithm (CWOA), it is applied as main optimizer to optimally tune the suppressor's parameters and merge with the dynamic stability scheme. This optimization algorithm is beneficial for complex dynamic stability problem, because during the iterative procedure, it can enhance the exploration capability to find the best solution. The optimization scheme based on CWOA has been compared with the conventional whale optimization algorithm (WOA) and particle swarm optimization (PSO). The suppressor damping capability has been evaluated with consideration of some possible disturbance scenarios. Furthermore, the objective function has been carried out based on the prominent dynamic performance criteria such as integral of time multiplied absolute error (ITAE), integral of absolute error (IAE), integral of squared error (ISE), and integral of time multiplied squared error (ITSE). Considering the various operating points, the SOSMC‐based suppressor ameliorates the system robustness as compared to the conventional suppressor. At last, the simulation results extracted from both interconnected power systems confirm the enhancement of power system operability and performance in suppression of the inter‐area oscillations, and also validate the robustness of the suggested control strategy against the model uncertainties and unmodeled dynamics.

FUTBOL LİGİ MÜSABAKASI ALGORİTMASININ DOĞRUSAL OLMAYAN VE BİRBİRİNE BAĞLI GÜÇ SİSTEMLERİNDE YÜK FREKANS KONTROLÜ İÇİN ANALİZİ

Load Frequency Control (LFC) is a significant tool that provides an equilibrium between generating and consuming real power for efficient operation of power system. In this paper, design and performance analysis of Soccer League Competition (SLC) algorithm is provided for optimal solution of LFC in nonlinear interconnected power systems. SLC algorithm has ability of escaping from local minimums while increasing searching capability accuracy with their operators. PID controller parameters are optimized in order to minimize Integral of Time multiplied Absolute Error (ITAE) as objective function. In order to demonstrate efficiency of SLC, two different nonlinear test systems are employed as case studies. At the first instant of study, two area nonlinear thermal power plants with proper value of Generation Rate Constraints (GRC) is considered as test system. Then, the simulations are employed for three-area unequal power system consist of important system limitations such as GRC, Time Delay (TD) and Governor Dead Band (GDB). Simulation results reveal that better dynamic performance of different test systems is obtained using SLC among the considered algorithms.

OPTIMAL DESIGN OF FRACTION-ORDER PROPORTIONAL-DERIVATIVE PROPORTIONAL-INTEGRAL CONTROLLER FOR LFC OF THERMAL-THERMAL-WIND TURBINES CONSIDERING NONLINEARITIES

The power system must be kept safe during load disturbances in order to control frequency instability during load disturbances change. Cascade Controller (CC) is employed to boost the performance of the power system mainly in the presence of nonlinear aspects. As a result, in this study, A proposed cascade fractional order proportional-derivative proportional integral (FOPDPI) controller is used to fine-tune the load frequency control (LFC) subjects of a three-area power system (thermal-thermal-wind) in the interconnected power system (IPS). As a third area in the studied model, renewable energy is used, such as high penetrating power wind turbines. The FOPDPI controller gains are adjusted using a recently published optimization scheme, such as the Harris hawk optimizer (HHO). To thoroughly test the efficiency and fitness of the proposed controller, the HHO-based FOPDPI and conventional PID controllers are applied to a three-area model with/without nonlinearities such as generation rate constraint (GRC), governor dead band (GDB), and boiler dynamics (BD) under different step load perturbation (SLP). The HHO algorithm's cost function is the Integral time multiply absolute error (ITAE) criterion. The investigation reveals that the proposed scheme HHO: FOPDPI provides greater stability than HHO: PID in both linearities by 58% and nonlinearity aspects by 62%.

A novel design of optimal intelligent fuzzy TID controller employing GA for nonlinear level control problem subject to actuator and system component fault

PurposeThe purpose of this article is about the design of controllers for conical two-tank noninteracting level (CTTNL) system in simulation. Local linearization around the equilibrium point has been done for the nonlinear CTTNL system to obtain a linearized model transfer function.Design/methodology/approachThis article deals with the design of novel optimal fractional-order tilt-integral-derivative (TID) controller using type-1 fuzzy set for the CTTNL prototype system. In this study, type-1 fuzzy TID controller parameters have been optimized through genetic algorithm (GA) and those set of values have been employed for the design of proportional-integral-derivative (PID) controller.FindingsA performance comparison between FTID and PID controller is then investigated. The analysis shows the superiority of FTID controller over PID controller in terms of integral absolute error (IAE), integral square error (ISE), integral of time multiplied absolute error (ITAE) and integral of time multiplied squared error (ITSE) integral errors. The transient and steady state performance of the FTID controller are superior as compared to conventional PID controller. In future, the FTID controller fault-tolerance capability tested on CTTNL system subject to actuator and system component (leak) faults. The detailed study of robustness in presence of model uncertainties will be incorporated as a scope of further research.Originality/valueA performance comparison between FTID and PID controller is then investigated. The analysis shows the superiority of FTID controller over PID controller in terms of IAE, ISE, ITAE and ITSE integral errors. Additionally, fault-tolerant performance of the proposed controller evaluated with fault-recovery time (Frt) parameter. The transient and steady state performance of the FTID controller are superior as compared to conventional PID controller.