A new decentralized robust controller design for multi-area load–frequency control via incomplete state feedback

This paper deals with load–frequency control of a multi-area power installation. The robust control theory is utilized to decouple the areas for a decentralized robust load–frequency controller. The proposed controller ensures that the overall multi-area power system is asymptotically stable. A new technique is included to exclude feedback from any immeasurable state. The product comprises a set of local load–frequency controllers, one for each area. The design and operation of each local controller requires solely the corresponding area's parameters and state measurements. Measurements of the immeasurable states are unnecessary. System parameter uncertainties and generation rate constraints are included in the simulation study of a three-area power system. Good results are reported. Copyright © 1998 John Wiley & Sons, Ltd.     

Optimal control strategy–based AGC of electrical power systems: A comparative performance analysis

This study extensively addresses the application of optimal control approach to the automatic generation control (AGC) of electrical power systems. Proportional‐integral structured optimal controllers are designed using full‐state feedback control strategy employing performance index minimization criterion. Some traditional single/multiarea and restructured multiarea power system models from the literature are explored deliberately in the present study. The dynamic performance of optimal controllers is observed superior in comparison to integral/proportional‐integral controllers tuned using some recently published modern heuristic optimization techniques. It is observed that optimal controllers show better system results in terms of minimum value of settling time, peak overshoot/undershoot, various performance indices, and oscillations corresponding to change in area frequencies and tie‐line powers along with maximum value of minimum damping ratio in comparison to other controllers. The results are displayed in the form of tables for ease of comparison. Sensitivity analysis affirms the robustness of the optimal feedback controller gains to wide variations in some system parameters from their nominal values.     

Decentralized control for multimachine power systems

A new approach to solve the problem of designing decentralized optimal controllers for large-scale power systems is proposed. The control law that results from the design is a decentralized one; accordingly, each subsystem is controlled only by its own variables. In using the proposed scheme, the cost functional for each subsystem is minimized, and the interacting effects between the subsystems are not ignored in deriving the control strategy. As a result, the application of the control scheme proposed by this paper provides optimality even if the subsystems are very strongly coupled. Results of investigation into the decentralized optimal control of a 10-machine system are satisfactory.     

Model predictive and linear quadratic Gaussian control of a wind turbine

Model Predictive and linear quadratic Gaussian controllers are designed for a 5MW variable‐speed pitch‐regulated wind turbine for three operating points – below rated wind speed, just above rated wind speed, and above rated wind speed. The controllers are designed based on two different linear dynamic models (at each operating point) of the same wind turbine to study the effect of utilising different control design models (i.e. the model used for designing a model‐based controller) on the control performance. The performance of the LQG controller is enhanced by improving the robustness, achieved by replacing the Kalman filter with a modified Luenberger observer, whose gain is obtained to minimise the effect of uncertainty and disturbance. Copyright © 2016 John Wiley & Sons, Ltd.     

Disturbance observer–based dynamic optimal setting control scheme for processes with nonlinear loops

This paper is concerned with optimal operational control problems that exist in industries. The performance index is optimized by set points reselection on the operational control layer together with controllers design on the loop control layer. Firstly, the operational indices need to be obtained through some optimization algorithms. Secondly, the widely used PID controllers are adopted to achieve performance optimization in the ideal situation. To minimize performance deterioration caused by harmonic disturbances, the disturbance observer–based optimal setting control is proposed for those industrial processes with nonlinear loops. In the proposed method, the controller structure or parameter is never changed, which is accordant with actual industrial conditions. Finally, numerical simulations are given to demonstrate the effectiveness and convenience of the results.     

Adaptive fuzzy finite-time optimal control for switched nonlinear systems

This article addresses the adaptive fuzzy finite-time control problem for a class of switched nonlinear systems whose powers are positive odd rational numbers and vary with the switching signal. The fuzzy logic systems (FLSs) are used to approximate the unknown nonlinearities of the controlled systems, and then by combining backstepping control algorithm with adding a power integrator technique, an adaptive finite-time controller is designed. By modifying and optimizing the relevant design parameters of the proposed adaptive finite-time controller, a novel adaptive finite-time optimal control approach is developed. The proposed two adaptive finite-time optimal control schemes can guarantee semi-globally practically finite-time stability of the closed-loop system. Moreover, the adaptive finite-time optimal controller can also achieve optimized performance in relation to the cost functional. Finally, a simulation example is given to illustrate the effectiveness of the proposed two adaptive finite-time control strategies.     

Design and assessment of variable‐structure LQG PID multivariable controllers

Control Performance Assessment (CPA) and tuning of PID controllers are studied in this paper. We propose a framework for systematic analysis of the tradeoff between the structural complexity of the controller and its performance. As the measure of the controller performance, an LQG based index is used. The problem is augmented with an additional term which forces sparsity on the complexity of a decentralized PID controller. The desired complexity is controlled via a weighting parameter which determines the cost of each additional element (i.e., P, I, and D terms). The result is a decentralized multivariable PID controller in which the complexity of each loop controller is optimized such that the desired LQG Performance Index is achieved with the lowest controller complexity. For larger multivariable systems, this will translate into a substantially reduced set of controller parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Stable ℋ︁2‐optimal controller synthesis

This paper considers fixed‐structure stable ℋ︁₂‐optimal controller synthesis using a multiobjective optimization technique which provides a trade‐off between closed‐loop performance and the degree of controller stability. The problem is presented in a decentralized static output feedback framework developed for fixed‐structure dynamic controller synthesis. A quasi‐Newton/continuation algorithm is used to compute solutions to the necessary conditions. To demonstrate the approach, two numerical examples are considered. The first example is a second‐order spring–mass–damper system and the second example is a fourth‐order two‐mass system, both of which are considered in the stable stabilization literature. The results are then compared with other methods of stable compensator synthesis. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal trajectory generation and robust flatness–based tracking control of quadrotors

This work proposes an optimal trajectory generation and a robust flatness–based tracking controller design to create a new performance guidance module for the quadrotor in dense indoor environments. The properties of the differential flatness, the B‐spline, and the direct collocation method are exploited to convert the constrained optimization problem into a nonlinear programming one, which can be easily resolved by a classic solver. After that, the obtained optimal reference trajectory is applied to the dynamic quadrotor model and two different flatness‐based controllers, namely, one based on feedback linearization and one based on feedforward linearization, are developed and compared to ensure the trajectory tracking despite the existence of disturbances and parametric uncertainties. Numerical simulation is executed to evaluate the proposed optimal trajectory generation approach and the robust tracking strategies. It turns out that the controller based on feedforward linearization outperforms the feedback linearization one in robustness and permits obtaining a performance guidance law for an uncertain quadrotor system.     

Reactive power management by using a modified differential evolution algorithm

In this article, a modified differential evolution (MDE) algorithm is proposed and applied to provide the solution for reactive power management by incorporating the flexible alternating current transmission systems (FACTS) controllers. The proper siting of FACTS controller has been achieved with an objective to minimize the losses and to improve the loading capability. The power flow analysis is performed to determine the optimal position for FACTS controllers. These controllers are incorporated in the most heavily loaded lines and hence controls the power flow in that particular line and allow more power to be transmitted in the remaining lines. The proposed MDE algorithm uses a novel DE/best3/1/bin mutation operator to produce three temporary mutant vectors which are averaged to obtain the mutant vector. Hence, the decision vectors of a generation simultaneously move toward the three best decision vectors of the population thereby maintains a better trade between exploration and exploitation. The proposed MDE algorithm is applied on different standard test bus (i.e., IEEE30, IEEE57, and IEEE118) systems with varying active and reactive loading (i.e., 100%, 110%, and 120%). The proposed method's performance is compared to those obtained from some well-known meta-heuristic algorithms. The proposed MDE algorithm optimized FACTS controllers reduce transmission loss by 60.90% in IEEE30 bus, 49.72% in IEEE57 bus and 8.37% in IEEE118 bus test system under base loading. The statistical analysis of the obtained results is carried out using the Wilcoxon signed rank test and the Friedman and Nemenyi hypothesis test, which ensures the reliability and robustness of the proposed method.     

High‐order observers‐based LQ control scheme for wind speed and uncertainties estimation in WECSs

Tip speed ratio control is a popular method in wind energy conversion systems in order to capture the maximum power. This method, however, requires wind speed information, which is difficult in practice to accurately measure it. Therefore, estimation methods are usually applied, where a high‐precision estimate leads to a high‐efficient system. Based on the fact that the wind speed varies in a random way, this paper proposes a generalized high‐order observer to estimate the aerodynamic torque and the wind speed accordingly. This observer algorithm releases the assumption that the wind speed should be slowly varying, which is required in previous observer designs. Moreover, two other generalized high‐order observers are also applied to estimate the uncertainties, which depend on state variables and cannot be considered as slow‐varying disturbances. Using the outputs of these observers, a robust high‐performance optimal control system is developed for the rotor speed to keep the optimal tip speed ratio. The stability analysis of the designed control system is fully presented. The effectiveness of the proposed technique is validated via simulation studies.     

Comparison of two methods for the design of active suspension systems

The design of controllers for active suspension systems can be formulated as an optimal control problem. The main objective of the controller is to isolate parts of the system from vibrations in other parts. Additional constraints are limited suspension travel, limited actuator force and good track-holding capability. The objective and the constraints can be used in the formulation of an optimality criterion. Two criteria are examined, with the corresponding LQ and H_∞ control design methods. The methods are compared with respect to their ability to generate a controller that achieves the best performance. For the LQ method three controllers with different structures were generated. To illustrate the use of the design methods, controllers have been designed for a simple but typical suspension system. For this system the controllers based on a quadratic norm perform comparably but the controllers based on output feedback are less robust. The H_∞ controller did not perform well for this problem when the same weighting functions were used to generate the controller as for the LQ method. Use of the H_∞ design method therefore requires careful tuning of the weighting functions. Use of the standard functions is inappropriate.     

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.     

Digital redesign of analog controllers based on minimizing integral of squared errors

Digital redesign is to replace an existing well‐designed analog feedback controller by a digital one along with a sampler and a hold. In this paper, we present a digital redesign technique which takes into account both closed‐loop and intersample behaviour. More precisely, we give a numerical procedure to optimally discretize an analog controller such that the integral of the squared error between the closed‐loop step responses of the analog and digital controlled systems is minimized. A parametric expression is derived for evaluating the integral performance index. With this expression, the optimal digital redesign problem becomes an optimal parameter selection problem which can be solved using existing optimal parameter search algorithms. Moreover, it allows one to obtain optimal reduced‐order digital controllers for sampled‐data control systems over a range of sampling periods. Copyright © 2003 John Wiley & Sons, Ltd.     

Hybridized gravitational search algorithm tuned sliding mode controller design for load frequency control system with doubly fed induction generator wind turbine

In this paper, the load frequency regulation problem of 2‐area interconnected power system is resolved using the sliding mode control (SMC) methodology. Interconnected 2‐area power systems with and without doubly fed induction generator wind turbines are considered for implementing the proposed optimal control methodology. Here, a heuristic gravitational search algorithm (GSA) and its variants such as opposition learning–based GSA (OGSA), disruption‐based GSA (DGSA), and disruption based oppositional GSA (DOGSA) are employed to optimize the switching vector and feedback gains of SMC. In order to overcome the inherent chattering problem in SMC, the control signals are considered in the objective function. The robustness of optimized SMC is analyzed by the inclusion of nonlinearities such as generation rate constraint (GRC), governor deadband, and time delay during the signal processing between the control areas, which are present in the real‐time power system. The insensitiveness of the optimal controller is shown by variation in system parameters like loading condition, speed governor constant, turbine constant, and tie‐line power coefficient. Further, the optimal SMC has been studied with significant load variations and wind power penetration levels in the control areas. The potential of proposed SMC design with chattering reduction feature is shown and validated by comparing the results obtained with the other reported methods in the literature.     

Finite-dimensional approximation for optimal fixed-order compensation of distributed parameter systems

In controlling distributed parameter systems it is often desirable to obtain low-order, finite-dimensional controllers in order to minimize real-time computational requirements. Standard approaches to this problem employ model/controller reduction techniques in conjunction with LQG theory. In this paper we consider the finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory. Our approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. We illustrate the technique by computing a sequence of first-order controllers for one-dimensional, single-input/single-output parabolic (heat/diffusion) and hereditary systems using a spline-based, Ritz-Galerkin, finite element approximation. Our numerical studies indicate convergence of the feedback gains with less than 2% performance degradation over full-order LQG controllers for the parabolic system and 10% degradation for the hereditary system.     

Renewable energy management of an hybrid water pumping system (photovoltaic/wind/battery) based on Takagi–Sugeno fuzzy model

This research work presents an optimal energy management for a hybrid water pumping system driven by a photovoltaic generator (PVG) and a wind turbine. These two renewable energies are used as power generation sources, whereas a battery is added as an energy-storing system, for the purpose of controlling the power flow and providing a constant load supply. The proposed management system, serve to guarantee the pumping system autonomy in a rural region where's no access to the electrical network. As a result, a maximum power point tracking (MPPT) controller is created based on the fuzzy Takagi–Sugeno (TS) model, ensuring maximum power transfer to the moto-pump in spite of wind speed and insolation changes. The synthesis of MPPT control law involves TS fuzzy reference models which generate the desired trajectories to track. A supervisor has been developed for energy management and its major purpose is to effectively use the battery to satisfy the power load requirements, and that is by maintaining the state of charge (SOC) to extend the battery's life. Finally, simulation results have been done based on Matlab/Simulink with the aim of validating the efficiency of the proposed energy management supervisor.