Modified whale optimization algorithm for fractional‐order multi‐input SSSC‐based controller design

In this paper, the design of a fractional‐order (FO) multi‐input–single‐output (MISO)–type static synchronous series compensator (SSSC) is proposed with a goal to improve the power system stability using modified whale optimization algorithm (MWOA). The proposed MWOA achieves an appropriate balance between exploitation and exploration stages of the original whale optimization algorithm. The performance of MWOA is validated by employing the benchmark test functions and further contrasted with whale optimization algorithm and other heuristic algorithms like gravitational search algorithm, particle swarm optimization, differential evolution, and fast evolutionary programming algorithms to demonstrate its strength. The proposed FO MISO SSSC controller is optimized by the MWOA technique and tested under single‐machine infinite bus system and further extended to a multi‐machine framework. To demonstrate the superiority of MISO‐type SSSC controller, the results obtained from it are compared with particle swarm optimization and differential evolution–based conventional single‐input–single‐output structured SSSC controllers. The comparison of results of MWOA with that of other methods validates its superiority in the present context.     

Comparison of PID and FOPID controllers tuned by PSO and ABC algorithms for unstable and integrating systems with time delay

This paper deals with optimization and design of an integer order–based and fractional order–based proportional integral derivative (PID) controller tuned by particle swarm optimization (PSO) and artificial bee colony (ABC) algorithms. These algorithms were used to find the best parameters for the best controller performance. A comparative study has been made to highlight the advantage of using ABC‐based controller over a PSO‐based controller. The validity of the controller tuning algorithms was tested in 2 different systems with time delay and a nonminimum phase zero used commonly in process control. The optimal tuning process of the PID and fractional order PID controllers has also been performed with 3 different cost functions. From the perspectives of time‐domain performance criteria, such as settling time, rise time, overshoot, and steady‐state error, the controller tuned by ABC gives better dynamic performances than controllers tuned by the PSO. Moreover, the results obtained from robustness analysis showed that the parameters of controller tuned by ABC are quite robust under internal and external disturbances.     

Design and performance analysis of elephant herding optimization based controller for load frequency control in thermal interconnected power system

In this present contribution, an attempt has been taken to design and analyze the performance of elephant herding optimization (EHO) based controller for load frequency control (LFC) applications of interconnected power system. The studied system is a two‐area nonreheat thermal interconnected system which is widely used in literature. A proportional‐integral‐differential controller is utilized for LFC of the studied system. EHO technique is applied to obtain the tuned set of controller parameters. The objectives considered for design of the controller are the minimization of settling times and integral‐time‐multiplied‐absolute‐error of frequency deviations (FDs) and tie‐line power deviation (TPD). The design objectives are integrated together to form a function with single objective by assigning equal weights after normalization. Several test cases of diverse set of disturbances are taken into account to test the performance of the proposed controller and the obtained results are compared with other controllers designed with differential evolution, gray wolf optimization, particle swarm optimization, teacher‐learner‐based optimization, and whale optimization algorithm. Furthermore, the time‐domain simulations of FDs and TPD are illustrated to support the tabulated results. In addition, comparative statistical analysis is presented to validate the robust behavior of the proposed controller.     

Globalized and bounded Nelder‐Mead algorithm with deterministic restarts for tuning controller parameters: Method and application

This paper develops and examines an optimization algorithm for simulation‐based tuning of controller parameters. The proposed algorithm globalizes the Guin augmented variant of Nelder–Mead's nonlinear downhill simplex by deterministic restarts, linearly growing memory vector, and moving initial simplex. First, the effectiveness of the algorithm is tested using 10 complex and multimodal optimization benchmarks. The algorithm achieves global minima of all benchmarks and compares favorably against the evolutionary, swarm, and other globalized local‐search multimodal optimization algorithms in probability of finding global minimum and numerical cost. Next, the proposed algorithm is applied for tuning sliding mode controller parameters for a servo pneumatic position control application. The experimental results reveal that the system with sliding mode controller parameters tuned using the proposed algorithm targeting smooth position control with maximum possible accuracy, performs as desired and eliminates the need of manual online tuning for desired performance. The results are also compared with the performance of the same servo pneumatic system with parameters tuned using manual online tuning in an earlier published work. The system with controller parameters tuned using the proposed algorithm shows improvement in accuracy by 28.9% in sinusoidal and 42.2% in multiple step polynomials tracking.     

An optimized fuzzy continuous sliding mode controller combined with an adaptive proportional-integral-derivative control for uncertain systems

This article discusses the design of a hybrid fuzzy variable structure control algorithm combined with genetic algorithm (GA) optimization technique to improve the adaptive proportional-integral-derivative (PID) continuous second-order sliding mode control approach (APID2SMC), recently published in our previous article in the literature. In this article, first, as an improved extension to APID2SMC published recently in the literature, an adaptive proportional-integral-derivative fuzzy sliding mode scheme (APIDFSMC) is presented in which a fuzzy logic controller is added. Second, a GA-based adaptive PID fuzzy sliding mode control approach (APIDFSMC-GA) is introduced to obtain the optimal control parameters of the fuzzy controller in APIDFSMC. The proposed control algorithms are derived based on Lyapunov stability criterion. Simulations results show that the proposed approaches provide robustness for trajectory tracking performance under the occurrence of uncertainties. These simulation results, compared with the results of conventional sliding mode controller, APID2SMC, and standalone classical PID controller, indicate that the proposed control methods yield superior and favorable tracking control performance over the other conventional controllers.     

Comparative performance analysis of 2DOF state feedback controller for automatic generation control using whale optimization algorithm

This paper presents the design of two‐degree‐of‐freedom state feedback controller (2DOFSFC) for automatic generation control problem. A recently developed new metaheuristic algorithm called whale optimization algorithm is employed to optimize the parameters of 2DOFSFC. The proposed 2DOFSFC is analyzed for a two‐area interconnected thermal power system including governor dead band nonlinearity and further extended to multiunit hydrothermal power system. The supremacy of the 2DOFSFC is established comparing with proportional‐integral, proportional‐integral‐derivative (PID), and 2DOFPID controllers optimized with different competitive algorithms for the concerned system. The sensitivity analysis of the optimal 2DOFSFC is performed with uncertainty condition made by varying bias coefficient B and regulation R parameters. Furthermore, the proposed controller is also verified against random load variations and step load perturbation at different locations of the system.     

How to optimize the TS‐fuzzy knowledge base to achieve desired performances: Accuracy and robustness

Designing an effective criterion/learning to find the best rule and optimal structure is a major problem in the design process of fuzzy neural controller. In this paper, we introduce a new robust model of Takagi Sugeno fuzzy logic controller. A hybrid learning algorithm, called hybrid approach to fuzzy supervised learning (HAFSL), which combines the genetic algorithm (GA) and gradient descent technique (GD) is proposed for constructing an efficient and robust fuzzy neural network controller (FNNC). Two phases of design and learning process are presented in this work. A GA is used for finding near optimal structure/parameters of the FNNC that minimizes the number of rules (initialization procedure). The second stage of learning algorithm uses the backpropagation algorithm based on GD method to fine tune the consequent parameters of the controller. The genes of chromosome are arranged into two parts, the first part contains the control genes (the certainty factors) and the second part contains the parameters genes that representing the fuzzy knowledge base. The effectiveness of this chromosome formulation enables the fuzzy sets and rules to be optimally reduced. The performances of the HAFSL are compared to these found by the traditional PI with genetic optimization (GA‐PI). Simulations demonstrate that the proposed HAFSL and GA‐PI algorithms have good generalization capabilities and robustness on the water bath temperature control system. Copyright © 2007 John Wiley & Sons, Ltd.     

Model‐free online tuning of controller parameters using a globalized local search algorithm

In an earlier work, the authors proposed a globalized bounded Nelder‐Mead algorithm with deterministic restarts and a linearly growing memory vector. It was shown that the algorithm was a favorable option for solving multimodal optimization problems like controller tuning because of the greater probability of finding the global minimum and lesser numerical cost. Therefore, the algorithm was successfully used for model‐based offline tuning of sliding mode controller parameters for a servo‐pneumatic position control application. However, such offline tuning requires a sufficiently adequate system model, which, in some applications, is difficult to attain. Moreover, it is not generally appreciated as an essential requirement for controller tuning by the end user like the industry. An improvement in performance of optimization algorithm for tuning is expected if it relies on measurements coming directly from an actual physical system and not just its mathematical model. Therefore, in this paper, we apply the aforementioned algorithm for model‐free online optimization of controller parameters. The application involves the programmatic control of a real‐time interface of a physical system by the algorithm for data flow and logical decisions for optimization. For comparison with the results of the model‐based offline tuning suggested in earlier work, the sliding mode controller parameters are tuned online for the same position control application. The experimental results reveal that the system performance with controller parameters tuned online using the algorithm compares favorably to the one with model‐based offline tuning especially at higher priority level for accuracy. The improvement in system performance amounts to 21%.     

Multiobjective fault‐tolerant fixed‐order/PID control of multivariable discrete‐time linear systems with unmeasured disturbances

In this paper, a multiobjective fault‐tolerant fixed‐order output feedback controller design technique is proposed for multivariable discrete‐time linear systems with unmeasured disturbances. Initially, a multiobjective fixed‐order controller is designed for the system by transforming the problem of tuning the parameters of the controller into a static output feedback problem and solving a mixed H₂/H_∞ optimization problem with bilinear matrix inequalities. Subsequently, the fixed‐order controller is used to construct the closed‐loop system and an active fault‐tolerant control scheme is applied using the input/output data collected from the controlled system. Motivated by its popularity in industry, the proposed method is also used to tune the parameters of proportional‐integral‐derivative controllers as a special case of structured controllers with the fixed order. Two numerical simulations are provided to demonstrate the design procedure and the flexibility of the proposed technique.     

A multiobjective optimization approach for linear quadratic Gaussian/loop transfer recovery design

This article bestows the linear quadratic Gaussian (LQG)/Loop Transfer Recovery (LTR) optimal controller design for a perturbed linear system having insufficient information about systems states through a multiobjective optimization approach. A Kalman filter observer is required to estimate the unknown states at the output from the noisy data. However, the main downside of the LQG controller's is that its robustness cannot be guaranteed because it consists of linear quadratic regulator (LQR) and Kalman observer, and due to observer incorporation within the LQR framework results in loss of robustness which is undesirable. Therefore, it is necessary to recover the robustness by tuning the controller which further plays havoc with system performance and control effort for certain plants. The present work addresses the investigation of the trade-off between multiobjective indexes (formulated on the basis of robustness, optimal control, and performances) through three multiobjective optimization algorithms as NSGA-II, multiobjective simulated annealing and multiobjective particle swarm optimization. The tuned parameters meet the competitive multiobjective performance indexes that are verified through simulation results. The Pareto front with multiple solutions helps to design a robust controller depending on the weightage given to the respective performance indexes. Simulation results reveal that the proposed multiobjective control strategy helps in recovering the characteristics of LQG/LTR.     

Optimization of buffer allocation in unreliable production lines based on availability evaluation

The buffer allocation problem is an important issue in production lines design. In this paper, we present new evaluation and optimization methods to optimally allocate buffers in unreliable production lines. Through analyzing different states of the machines and buffers by Markov process and incorporating the aggregation method, we make an evaluation on the system availability, instead of the throughput rate of the line. The optimization method is proposed by combining particle swarm optimization and estimation of distribution algorithm to maximize the system availability. It generates the new populations by estimation of distribution algorithm and particle swarm optimization to take their respective advantages in global and local optimization. Numerical tests and simulations are performed to validate the performance of the evaluation and optimization methods. The results indicate the effectiveness and efficiency of the proposed methods.     

Improving the grid frequency by optimal design of model predictive control with energy storage devices

This paper proposes the optimal design of model predictive control (MPC) with energy storage devices by the bat‐inspired algorithm (BIA) as a new artificial intelligence technique. Bat‐inspired algorithm‐based coordinated design of MPCs with superconducting magnetic energy storage (SMES) and capacitive energy storage (CES) is proposed for load frequency control. Three‐area hydrothermal interconnected power system installed with MPC and SMES is considered to carry out this study. The proposed design procedure can account for generation rate constraints and governor dead bands. Transport time delays imposed by governors, thermodynamic processes, and communication telemetry can be captured as well. In recent papers, the parameters of MPC with SMES and CES units are typically set by trial and error or by the designer's expertise. This problem is solved here by applying BIA to tune the parameters of MPC with SMES and CES units simultaneously to minimize the deviations of frequency and tie line powers against load perturbations. Simulation results are carried out to emphasize the superiority of the proposed coordinated design as compared with conventional proportional‐integral controller and with BIA‐based MPC without SMES and CES units.     

Analysis of moth flame optimization optimized cascade proportional-integral-proportional-derivative controller with filter for automatic generation control system incorporating solar thermal power plant

In the fast developing electric power system network, ancillary services like automatic generation control (AGC) plays a vital and significant role to ensure good quality of power supply in the system. To distribute good quality of power, a hybrid AGC system along with an efficient and intelligent controller is compelled. So, in this article, a cascaded proportional-integral (PI)-proportional-derivative (PD) controller with filter (PI-PDF) is proposed as secondary controller for AGC system. A nature inspired optimization algorithm named as moth flame optimization (MFO) algorithm is employed for simultaneous optimization of controller gains. Initially, a two-area interconnected nonreheat thermal power system is investigated. Analysis revealed that MFO-tuned PI controller performs better than the different optimization techniques tuned PI controller for the same system and PI-PDF controller performs better than PI controller does. Then, the study is extended to a three-area interconnected hybrid system with proper generation rate constraint. Area-1 consists of solar thermal-thermal unit; area-2 consists of thermal-hydro unit and area-3 thermal-gas unit as generating sources. Performance of PI-PDF controller is compared with classical controllers such as PI, PID, PIDF, and PI-PD controller without filter. Result analysis divulges that MFO-tuned PI-PDF controller performs better than all other controllers considered in this article. Robustness of the PI-PDF controller is evaluated using parameter variations and random load variation.     

Experimental investigation of Harris Hawk optimization-based maximum power point tracking algorithm for photovoltaic system under partial shading conditions

An integrated quasi Z-source DC–DC converter (qZSC) along with Harris Hawk Optimization (HHO)-based maximum power point tracking (MPPT) algorithm is proposed in this paper to increase the efficiency of photovoltaic (PV) system. The qZSC-based PV system experiences more voltage and current stress during partial shading conditions (PSCs), which causes overheat on qZSC components hence, degrade the efficiency and reliability of the system. Conventional swarm intelligence-based MPPT algorithms track the G_MPP during PSC, but these take longer convergence time and fail to settle at G_MPP. This uncertainty of finding the G_MPP leads to fluctuations at output of qZSC, hence more stress on the converter components. HHO in tracking the G_mpp eliminates premature local MPPs, enhances convergence speed by expanding the search space for finding the G_MPP. The proposed system is developed in MATLAB/Simulink environment and verified the results by developing prototype model in the laboratory by using C2000™ Piccolo™ Launch Pad™, LAUNCHXL-F28027 controller. The tracking performance of the proposed HHO-based MPPT algorithm is tested under fast changing and PSCs in comparison with perturb & observe (P&O), particle swarm optimization (PSO), and artificial bee colony (ABC)-based MPPT algorithms. The simulation and experimental results show that the proposed HHO-based MPPT algorithm is robust, tracks maximum power point in minimum convergence time in comparison with P&O, PSO and ABC-based MPPT algorithms. Hence, voltage and current fluctuations at the output of qZSC are reduced. Therefore, voltages and current stress on qZSC components are reduced and the efficiency of the system is improved.     

Hybrid BOA-GWO-PSO algorithm for mitigation of congestion by optimal reactive power management

The generation of power with load optimization, particularly in the current deregulated electricity market conditions, is a very important process for improved planning and operation of the grid. In addition, it is very important for the system not to experience problems due to congestion, have tensile stability, and protection to increase the share of electricity from renewable sources with the current supply system. This article presents load balancing with the butterfly optimization algorithm (BOA) in a hybridized form to minimize and maximize loads when used in pool and hybrid markets. The methods have been designed to prevent the drawbacks of BOA and generate a better trade-off between exploration and exploitation abilities by hybridizing it with particle swarm optimization (PSO) and gray wolf optimizer (GWO). Empirical research on other algorithms shows that proposed hybrid BOA-GWO-PSO algorithm performs better and shows potential in diverse problems. These studies give it a significant advantage over BOA in general, and when it is employed to solve complex optimization problems validated on benchmark IEEE 30 bus system. A comparative analysis has been conducted to validate the potency of the hybrid BOA-GWO-PSO approach with some conventional meta-heuristic algorithms. Analysis of results by mathematical validation on 23 benchmark functions and application in congestion management by optimal reactive power management (RPM) reveal that the proposed technique has the potent to solve real world optimization problems and is competitive with recent methods reported in state-of- art literature.     

Quadratic boundedness of LPV systems via saturated dynamic output feedback controller

For the linear parameter varying systems with bounded disturbance, a saturated dynamic output feedback controller is designed by specifically considering input saturation, to stabilize the closed‐loop system. The controller parameters and the corresponding region of attraction are calculated by solving an off‐line optimization problem with respect to input saturation, state constraints, and robust stability. In the off‐line optimization problem, both the unknown and available scheduling parameters are considered for the linear parameter varying systems. When the unknown scheduling parameters are considered, the off‐line optimization problem is nonconvex and can be solved by the cone complementary linearization method. When the available scheduling parameters are considered, the off‐line optimization problem can be reformulated as convex optimization due to the parameter dependent form of controller parameters. In the both cases, input saturation is specifically handled by introducing a set of linear matrix inequalities into the off‐line optimization problem, which can reduce the conservatism of the controller design and fully exploit the controller capability. Based on the real‐time estimated state, system output, and scheduling parameters, the actual input can be obtained by saturating the dynamic output feedback controller, and steer the augmented state quickly converge to the neighborhood of the origin. Two numerical examples are provided to illustrate the proposed approaches.     

Meta-heuristics algorithms for optimization of gains for dynamic voltage restorers to improve power quality and dynamics

This article discusses metaheuristic algorithms for optimizing controller gains for dynamic voltage restorers (DVRs) that use an impedance control strategy to compensate for unbalance in source voltages, voltage harmonics, and sag/swell in source voltages. The gains of the proportional-integral (PI) controllers become critical for proper DVR load voltage extraction. Various techniques for optimization, such as whale optimization technique, gray wolf optimization technique, particle swarm optimization technique, and ant lion optimization technique, are used to obtain DC and AC PI controller gains for DVR. The impedance control strategy employs simple calculations to determine the resistance and reactance of a polluted source voltage, without the use of frame conversions as in synchronous reference theory, instantaneous reference power theory, and so on. The quick calculations of the impedance control scheme improve the power quality and dynamics. The Metaheuristic algorithms are used to calculate the number of iterations required to achieve the best possible controller gains, which further helps to improve power quality and dynamics. Among these optimization techniques, the antlion optimization technique provides fast convergence and the best possible controller gain values to improve the dynamics of the dc-link voltage of voltage source converter and terminal voltage, thereby improving power quality. The proposed antlion optimization technique-based DVR model is simulated in MATLAB R2019, and the results are validated with RT-LAB.     

Distributed controller design and performance optimization for discrete‐time linear systems

This article addresses the problem of distributed controller design for linear discrete‐time systems. The problem is posed using the classical framework of state feedback gain optimization over an infinite‐horizon quadratic cost, with an additional sparsity constraint on the gain matrix to model the distributed nature of the controller. An equivalent formulation is derived that consists in the optimization of the steady‐state solution of a matrix difference equation, and two algorithms for distributed gain computation are proposed based on it. The first method consists in a step‐by‐step optimization of said difference matrix equation, and allows for fast computation of stabilizing state feedback gains. The second algorithm optimizes the same matrix equation over a finite time window to approximate asymptotic behavior and thus minimize the infinite‐horizon quadratic cost. To assess the performance of the proposed solutions, simulation results are presented for the problem of distributed control of a quadruple‐tank process, as well as a version of that problem scaled up to 40 interconnected tanks.     

PI control based on parameter space approach supported metaheuristic optimization algorithms and ANFIS in a natural gas combined cycle power plant

In this article, proportional-integral (PI) control to ensure stable operation of a steam turbine in a natural gas combined cycle power plant is investigated, since active power control is very important due to the constantly changing power flow differences between supply and demand in power systems. For this purpose, an approach combining stability and optimization in PI control of a steam turbine in a natural gas combined cycle power plant is proposed. First, the regions of the PI controller, which will stabilize this power plant system in closed loop, are obtained by parameter space approach method. In the next step of this article, it is aimed to find the best parameter values of the PI controller, which stabilizes the system in the parameter space, with artificial intelligence-based control and metaheuristic optimization. Through parameter space approach, the proposed optimization algorithms limit the search space to a stable region. The controller parameters are examined with Particle Swarm Optimization based PI, artificial bee colony based PI, genetic algorithm based PI, gray wolf optimization based PI, equilibrium optimization based PI, atom search optimization based PI, coronavirus herd immunity optimization based PI, and adaptive neuro-fuzzy inference system based PI (ANFIS-PI) algorithms. The optimized PI controller parameters are applied to the system model, and the transient responses performances of the system output signals are compared. Comparison results of all these methods based on parameter space approach that guarantee stability for this power plant system are presented. According to the results, ANFIS- PI controller is better than other methods.     

Optimal design of trajectory parameters and position tracking with balance for riderless bicycle

Riderless bicycles are typically nonholonomic, underactuated, and nonminimum‐phase systems. The instability and complex dynamic coupling make the trajectory generation and tracking of the bicycles more challenging. In this paper, we consider both the trajectory generation and position tracking of a riderless bicycle. To achieve smooth motion performances, the desired planar trajectory of the contact point of the bicycle's rear wheel is constructed using a parameterized polynomial curve that can connect two given endpoints with associated tangent angles. The optimal parameters of the polynomial curve are obtained by minimizing the maximum of the roll angle's quasistatic trajectory of the bicycle, and this problem is solved by the particle swarm optimization algorithm. Then, position tracking of the desired planar trajectory with balance is converted into an optimization problem subject to the dynamic constraints. The cost function is designed as the combination of the position errors and the roll acceleration of the bicycle, in order to achieve an accurate tracking performance and to prevent the bicycle from falling down. This optimization problem is solved by the Gauss pseudospectral method. Simulation results are presented to demonstrate the effectiveness of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.