Extremum Seeking Control Method Research Articles

РОЗПОДІЛЕНЕ РЕГУЛЮВАННЯ НАПРУГИ РОЗПОДІЛЬЧОЇ ЕЛЕКТРОМЕРЕЖІ З ВІДНОВЛЮВАНИМИ ДЖЕРЕЛАМИ ЕЛЕКТРОЕНЕРГІЇ

The problems of distributed voltage control in electrical grids (EGs) with renewable sources of electric energy with converter-interfaced generation (CIG). It is proposed to control the EGs modes by controlling the reactive power of converter-interfaced generation. It is proposed to use the mean square deviation of the voltage in the converter inter-faced generation (CIG) installation nodes as the criterion of the target function. The extremum seeking control method was used to solve the problem of dynamic optimization with daily changes in the parameters of the electric network, namely the loads and active power of renewable sources. The examples provided have shown the improvement of the voltage in the EG at different levels of reactive power generation limitation according to the norms of the standard EN50549-1:2019. The optimal values of the average daily value of the rms deviation of the voltage of the ieee33 test EM were obtained with a significant penetration of the RES power. Bibl. 12, fig. 4, table. Keywords.: distributed voltage control, converter interfaced generation, extremum seeking control method.

Self-optimized efficient operation of trans-critical CO2 ejector-expansion heat pump water heater system with two-stage evaporation

In application scenarios with lower ambient temperatures and higher sink temperatures, the trans-critical CO2 heat pump water heater system using an ejector instead of a conventional expansion device offers better performance, and the higher pressure differential allows for partial pressure loss recovery through the ejector. However, the complexity of discharge pressure and ejector matching affects the further application of the system. Therefore an optimization method called Extremum seeking control method is proposed to achieve the lowest power consumption implementation under off-design conditions. The ESC controller applied to the system uses the compressor power consumption as the feedback signal and the discharge pressure is used as operating input set-point. The dynamical model of a trans-critical CO2 heat pump water heater built on Modelica/Dymola is used as the study object and optimized for three scenarios: fixed, sloped step profile, and actual ambient temperature. The simulation results show that the ESC applicable to the proposed system can optimize the matching of discharge pressure and ejector driving nozzle throat area to obtain the best performance. Compared with the benchmark system, the extremum seeking control for actual ambient temperature conditions results in a 5.7% increase in system efficiency.

Extremum seeking control to optimize mineral recovery of a flotation circuit using peak air recovery

A flotation circuit is controlled in simulation using an extremum seeking control (ESC) approach to keep the cells operating at the optimal operating point, as represented by peak air recovery. It is assumed that optimal performance is achieved at this operating point where the froth layer is stable, and the mineral recovery of the flotation cell is maximized. Two gradient-based ESCs, a classical perturbation-based ESC and a time-varying ESC, as well as a non-gradient-based direct search Nelder–Mead simplex ESC, are compared on the flotation circuit to steer the plant through an unknown static map towards the peak in air recovery. The three ESCs can respectively optimize the flotation circuit and find the peak air recovery operating point. The simplex ESC can converge quickly to the optimum but does not adapt to changing conditions. The gradient-based ESCs can track the time-varying peak air recovery operating point and adapt to an external disturbance. Although the three ESC methods are not dependent on a process model to optimize the plant, their convergence times are relatively slow. The ESCs are ideally suited for model-independent long-term automated optimization of a flotation circuit with a slow time-varying optimal operating point.

Cooperative distributed extremum seeking control for coupled multiagent systems based on distributed identification‐gradient tracking

SummaryThis paper proposes a cooperative distributed extremum seeking control (ESC) approach for solving distributed optimization problems in static and dynamical multiagent systems, where the agents' coupled dynamics are unknown and only local cost values can be measured. The approach begins with each agent estimating the local gradient information of the unknown local cost function through recursive identification using measured local cost values. Subsequently, the distributed identification‐gradient tracking (DIGT) algorithm is employed to enable each agent to track the global gradient information of the global cost function, utilizing the estimated local gradient information from itself and its neighbors in the network. The proposed cooperative distributed ESC method enables the multiagent system to reach the extreme point of the global cost function under model‐free scenarios. Furthermore, the convergence properties of the approach are established for both static and dynamical multiagent systems. Finally, numerical examples are presented to demonstrate the effectiveness and stability of the proposed approach.

Optimization of the control paper production system of using the extremum seeking control method

Currently the pulp and paper industry is one of the fastest growing sectors of the economy in Russia and other countries. An important aspect of the further development of this industry is associated with an increase in the efficiency of paper production and the quality of finished products with an economical and rational use of raw materials, fuel and energy and other material resources. This is facilitated by the use of modern means of automation and process control. It was experimentally established that there is an extreme dependence between the ratio of the speeds of the paper pulp and the paper machine and the standard deviation of the linear density of the paper web, which determines the degree of non-uniformity of the paper gap. The use of a noise-resistant algorithm for extreme control of an inertial object based on the combination of synchronous accumulation and synchronous detection methods with subsequent search for the maximum amplitude of the second harmonic of the filtered signal, aimed at reducing the root-mean-square deviation of the mass of a square meter of paper web, is considered. It is proposed to simultaneously stabilize the mass flow rate of paper pulp and the coordinate of the fall of the paper pulp jet onto the conveyor mesh, which made it possible to increase the efficiency of paper production.

Quasi-Newton extremum seeking control based on incremental recursive identification

This paper proposes a novel quasi-Newton extremum seeking control method based on incremental recursive identification for a real-time optimization problem. The optimization of static map and dynamical system are both considered where the dynamics of the nonlinear system and the cost function to be minimized are unknown. Firstly, the proposed method only employs the measured function values to effectively estimate the time-varying gradient of the unknown cost function by using incremental recursive least square identification. Then, an extremum seeking control (ESC) approach based on the quasi-Newton direction is developed to improve convergence speed, which only requires the estimated gradient of the objective function without Hessian information. Furthermore, the convergence properties of the proposed ESC method are established for static map and dynamical system. Finally, we demonstrate the superiority and effectiveness of the proposed method using three examples.

New Formulation of Wave Energy Converter Control Using Extremum Seeking

Ocean wave energy converter (WEC) requires real-time control to maximise energy conversion. Effective control of wave energy converter is particularly challenging, since the ocean wave is highly uncertain and time-varying. Conventionally, instantaneous control methods are utilised, such as Bang-Bang control and model predictive control with wave prediction, which consequently requires fast controller and responses. In this paper, energy generated in a period of time is regarded as an entirety, and the main wave is considered to impose a periodic excitation force to WEC. Then, it is shown that the optimal power take-off force also follows a periodic function, by optimising which WEC is expected to generate maximum power output. The intriguing relationship among the harvested energy, wave properties and control force is derived in this paper. An extremum seeking control method is implemented to solve this reformulated problem. By extensive simulation results, the effectiveness of the proposed framework and control method is validated, which demonstrates high conversion efficiency comparing to Bang-Bang control and short-horizon optimal control.

Efficiency Improvement of Vibration Power Generation by Extremum Seeking Control against Vibration Randomness

Vibration power generation utilizing environmental vibrations to generate electricity has been attracting attention as a sustainable independent power source for such as wireless sensors placed under vibration. For efficient power generation, the resonant frequency of the vibration power generation device must be automatically adjusted to the environmental vibrations. To achieve it, the author's group proposes a method of installing a variable capacitance in the device and adjusting its capacitance by extremum seeking control. In the case of damped vibration applied, even if the amplitude and frequency of the vibration vary randomly if their distributions can be regarded as stationary and identical, an effective extremum seeking control method and its effectiveness are demonstrated using experiments.

Online induction motor rotor time constant estimation using perturbation-based extremum seeking control

<p class="Abstract"><span lang="EN-US">A novel online induction motor (IM) rotor time constant estimator based on a perturbation-based extremum seeking control (ESC) and model reference adaptive system (MRAS) is proposed. Since implementations of fieldoriented control (FOC) requires accurate values of IM parameters, such as rotor time constant, so accurate and robust on-line estimations of such parameters are crucial for any modern industrial IM drives. The proposed MRAS estimator employs ESC method to estimate the IM rotor resistance in various operating conditions. Meanwhile, since extremum seeking control is a model-free scheme, so it is robust to other IM parameter variations. The feasibility and effectiveness of the IM rotor resistance estimation by utilizing ESC scheme has been verified by simulation and experimental results. A 2.2 kW experimental setup has been implemented. </span></p>

Extremum seeking control for optimization of an open-loop grinding mill using grind curves

A semi-autogenous grinding mill is simulated with gradient and non-gradient based extremum seeking controllers to maximize the mill performance using grind curves. Grind curves map the essential performance measures of a grinding mill to the mill load and rotational speed. The curves vary with the changes in the feed ore characteristic but show generic parabolic features with extremums. The extremum seeking controllers search along the unknown input–output map to steer the process towards an unknown optimum. In this study, a classical perturbation-based method, a time-varying parameter estimation-based method and the Nelder–Mead simplex method are employed as extremum seeking control (ESC) methods to search along the grind curves to either optimize the mill throughput or grind by means of manipulating the mill feed or rotational speed. The proposed extremum seeking controller could reduce the need for a plant operator to manually select the optimal operating conditions that maximize the performance measures of a grinding mill. Since the controller is agnostic to the process model, the grinding mill can be optimized without the need for a detailed process model. The simulated results show that the extremum seeking controllers steer the mill operating conditions toward the steady-state optimum and can be used to satisfy operational objectives. However, the slow grinding mill dynamics result in a long convergence rate when the initial conditions are far from the optimal operating conditions.

РЕГУЛЮВАННЯ НАПРУГИ ТА РЕАКТИВНОЇ ПОТУЖНОСТІ В РОЗПОДІЛЬНИХ ЕЛЕКТРИЧНИХ МЕРЕЖАХ ШЛЯХОМ ВИКОРИСТАННЯ РОЗОСЕРЕДЖЕНИХ ВІДНОВЛЮВАНИХ ДЖЕРЕЛ ЕНЕРГІЇ

The problems of mode regulation of distribution networks in Ukraine are investigated in this paper. Authors propose to regulate the modes of distribution networks by the means of convertors of renewable energy sources (solar power plants etc.) connected to this networks according to the Smart Grid concept. The analysis of multicriteria mode optimization results of the distribution network was performed and the most perspective criterion were selected according to the features of structure and functioning of distribution networks in Ukraine. The target function of multicriteria optimization by the criteria of minimization of reactive power on the main section of the line and minimization of standard voltage deviations from the nominal value is formalized by the authors. To calculate the optimal value for the target function, the Multivariable extremum seeking control method was chosen, this method was improved by adding additional filters of individual frequency channels. An example of calculations is given in the paper; it illustrates the efficiency of the proposed method of modes regulating of the distribution networks. References 24, figures 3, tables 2.

Automation of the peripheral resistance valve in a hydro-mechanical cardiovascular pulse duplicator system

This paper considers the modernization of an existing non-commercial Pulse Duplicator in use at the Healing Research Laboratory at the University of Padova, Italy. The system reproduces human systemic circulation and it is used to test heart medical devices. The focus of this study is the full automation of a crucial system component that is the peripheral resistance manual valve that is replaced by a motorized one. First, under certain technological constraints, the problem of the automatic setting adjustment of the valve is tackled by using a Sliding Mode Extremum Seeking Control (ESC) method. This approach guarantees the system fundamental pressure drop to simulate the peripheral resistance to flow in the human systemic circulation in various system configurations and operating conditions. Then, the Sliding Mode ESC algorithm is embedded in an Arduino board driving the motorized valve. Finally, experimental tests are performed to assess the effectiveness of the motorized valve.

A Modified ESC Algorithm for MPPT Applied to a Photovoltaic System under Varying Environmental Conditions

Photovoltaic solar energy is one of the most important renewable energy sources. However, the production of this energy is nonlinear and varies depending on atmospheric parameters. Therefore, the operating point of the photovoltaic panel (PV) does not always coincide with the maximum power point (MPP). A mechanism that allows the research of the maximum power point known as maximum power point tracking (MPPT) algorithm is then needed to yield the maximum power permanently. This paper presents an intelligent control technique based on the ESC (Extremum Seeking Control) method for MPPT under varying environmental conditions. The proposed technique is an improvement of the classical ESC algorithm with an additional loop in order to increase the convergence speed. A detailed stability analysis is given not only to ensure a faster convergence of the system towards an adjustable neighborhood of the optimum point but also to confirm a better robustness of the proposed method. In addition, simulation results using Matlab/Simulink environment and experimental results using Arduino board are presented to demonstrate that the proposed modified ESC method performs better than the classical ESC under varying atmospheric conditions.

A Comparison of DER Voltage Regulation Technologies Using Real-Time Simulations

Grid operators are now considering using distributed energy resources (DERs) to provide distribution voltage regulation rather than installing costly voltage regulation hardware. DER devices include multiple adjustable reactive power control functions, so grid operators have the difficult decision of selecting the best operating mode and settings for the DER. In this work, we develop a novel state estimation-based particle swarm optimization (PSO) for distribution voltage regulation using DER-reactive power setpoints and establish a methodology to validate and compare it against alternative DER control technologies (volt–VAR (VV), extremum seeking control (ESC)) in increasingly higher fidelity environments. Distribution system real-time simulations with virtualized and power hardware-in-the-loop (PHIL)-interfaced DER equipment were run to evaluate the implementations and select the best voltage regulation technique. Each method improved the distribution system voltage profile; VV did not reach the global optimum but the PSO and ESC methods optimized the reactive power contributions of multiple DER devices to approach the optimal solution.

Extremum-seeking control for optimization of time-varying steady-state responses of nonlinear systems

Extremum-seeking control (ESC) is a useful tool for the steady-state performance optimization of plants for which limited knowledge about its dynamical behavior and disturbance situation is known. The case when the steady-state plant responses correspond to equilibrium solutions received a lot of attention. However, in many industrial applications plant performance is characterized by time-varying steady-state behavior. In those cases, no static parameter-to-steady-state performance map can be defined. In this work, we propose an ESC method that employs a so-called dynamic cost function to cope with time-varying steady-state responses of general nonlinear systems. We prove semi-global practical asymptotic stability of the closed-loop ESC scheme in the presence of bounded and time-varying external disturbances. Moreover, the working principle is illustrated by means of the real-time performance optimal tuning of a nonlinear control strategy for a motion control application.

Real-Time Optimization of a CO Preferential Oxidation Reactor Temperature with Extremum Seeking Control Techniques.

A hydrogen (H2)-rich gas mixture is used as the fuel of the proton exchange membrane fuel cell (PEMFC). A small amount of the carbon monoxide (CO) gas in the gas mixture can significantly deactivate the catalyst of the PEMFC, resulting in a reduction in the efficiency of power generation. Preferential oxidation is used to reduce the CO concentration less than 10 ppm in the gas mixture. It has an optimal reaction temperature at which the reaction shows the minimum exit CO concentration with minimum consumption of H2. This optimal temperature continuously changes under the varying conditions of operation and catalyst deactivation. In this study, two modified extremum seeking control (ESC) methods were proposed to continuously seek and maintain this optimal reaction temperature, guaranteeing CO concentration under 10 ppm even under time-varying conditions. The proposed methods have a smaller number of design parameters than the conventional extremum seeking approaches so that tuning the ESC method is much easier, more intuitive, and efficient. In addition, the proposed method can additionally use the secondary measurement to improve the performance of the ESC method by removing the possibility that the modeling error of the linear dynamic block can deteriorate the accuracy of calculating the gradient of the nonlinear static block. The experimental results confirmed that the proposed methods can track the optimal temperature within a short time compared to the conventional approach while successfully maintaining the CO concentration below 10 ppm.

Multidimensional Fractional-Order Newton-Based Extremum Seeking for Online Light-Energy Saving Technique of Lighting System

This article proposes a real-time light-energy saving control technique to reduce unnecessary light-energy consumption (LEC) for varying lighting environment, through regulating brightness of illuminative lamps while providing the expect illumination level. Considering the influence of environmental conditions, a fractional-order Newton-based extremum seeking control (ESC) method in the proposed technique is developed to enhance the tracking accuracy and convergence speed. It can result in the high efficient lighting system and the rapid track of minimum LEC. Moreover, it significantly reduces the impact of selecting an arbitrary Hessian matrix on tracking speed of the algorithm, which is the main drawback in the most conventional ESC algorithms. Experimental results reveal that the proposed method has the ability to track the available minimum LEC under changing environmental conditions.

Optimizing Energy Consumption for Lighting Control System via Multivariate Extremum Seeking Control With Diminishing Dither Signal

Because that the light-energy consumption (LC) is growing quite dramatically over the past decades, the light-energy efficiency is regarded as a key component of the modern energy system in major cities. In this paper, a novel and sophisticated algorism of lighting control is presented to improve light-energy efficiency and cut down energy consumption, when considering the lighting system with multilighting equipment. In this paper, a multivariate extremum seeking controller is used to manipulate, respectively, the luminance of multilighting equipment, in order to track the minimal LC efficiently. Meanwhile, a proportional–integral–differential (PID) approach is adopted to achieve the required level of illumination. The proposed extremum seeking control (ESC) is designed to ensure the amplitude of the dither signal converge exponentially to zero, by making the amplitudes change with the extremum estimation error. The presented frame helps to improve search speed for the minimal LC value and remove the steady-state oscillations. The comparative experiments reveal that, compared with the convergence velocity of the Newton- and gradient-based ESCs, the developed method for the track of the minimal LC can have higher accuracy and faster speed. Note to Practitioners —In a modern large commercial building, the exorbitant LC is an important problem for the engineering technicians and managers, and the hybrid lighting system which combines artificial light with natural light offers a solution to this problem. However, the minimum light-energy optimal control is a very key problem in manipulating multigroup lighting equipment, since the required level of illumination usually varies according to the exterior lighting environment. This paper contributes to a useful multivariate extremum seeking controller to solve these light-energy control problems for multiple-input single-output hybrid lighting system, whereas the PID controller is also designed to maintain the required level of illumination simultaneously. This paper discusses how to seek the minimal energy necessary for the required levels of illumination by separately regulating different light equipment. The research results of this paper will be beneficial for a practical application of extremum seeking control method in enhancing the lighting energy efficiency of lighting system.

A two-variable extremum seeking controller with application to self-tuned vibration energy harvesting∗∗This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

A new control strategy for sliding-mode extremum seeking in two-variables is proposed in this study. The controller converts the two-variable search problem into a single-variable problem in which the direction of changes on the two-dimensional phase plane is used as the sliding mode variable. Simulations are conducted to show that the proposed method is simpler, faster and more accurate than multi-variable sliding mode extremum seeking control methods in the current literature. The proposed controller is utilized for maximum power point tracking in vibration energy harvesters where both damping and stiffness of the harvester can be tuned using power electronic techniques. Experimental results show that the proposed controller is capable of tuning the variables for seeking the extremum point without using any model of the system.

Extremum-Seeking Control for Harmonic Mitigation in Electrical Grids of Marine Vessels

This paper focuses on the minimization of the harmonic distortion in multibus electrical grids of marine vessels using a single active power filter. An active power filter is commonly used for local harmonic mitigation. However, local filtering may lead to a “whack-a-mole” effect, where the reduction of harmonic distortion at the point of installation is coupled to an increase of distortion in other grid nodes. The few existing filtering methods that consider system-wide mitigation are based on an accurate model of the power grid, which may not be available if the complexity and the scale of the grid are large. In this work, we investigate the use of an extremum-seeking control method to optimize the injection current of an active power filter for system-wide harmonic mitigation. Because the extremum-seeking control method is model-free, it can be used without knowledge of the electrical grid. Moreover, the method can be implemented on top of the existing approaches to combine the fast transient response of conventional harmonic-mitigation methods with the optimizing capabilities of extremum-seeking control.