Extremum Seeking Control Scheme Research Articles

Real-time multi-variable optimization of the interstage subcooling vapor-injection based transcritical CO2 HPWH: An integrated model predictive control approach

The interstage subcooling vapor-injection technique has been introduced to transcritical CO2 heat pumps to alleviate performance degradation under conditions of low ambient temperature and high water-outlet temperature. This type of solution holds considerable appeal and finds utility across a wide range of applications. However, the efficacy and efficiency of such systems are contingent upon their management, which frequently requires the implementation of suitable control systems. The primary objective is to enhance the overall system operational performance, resulting in tangible advantages in terms of economic viability, energy conservation, and environmental sustainability. To achieve these objectives, one can utilize both explicit and implicit optimization methods ranging from Model Predictive Control (MPC) to Extremum Seeking Control (ESC), each with its strengths and weaknesses. This paper compares the performance of an ad hoc integrated MPC strategy and a multi-variable ESC one. Based on the results of the system operation employing the latter strategy, a significant linear correlation was discovered between the optimal medium pressure and the optimal discharge and suction pressure. Consequently, an intrinsic self-optimization strategy for the medium pressure was developed. Subsequently, a dynamic system identification was performed on the new system, incorporating this proposed strategy. To optimize the system Coefficient of Performance (COP) while maintaining the water outlet temperature, ensuring the thermal load constraint, the MPC strategy was employed. The main focus of the MPC was to determine the optimal Electronic Expansion Valve (EEV) opening degree and water pump settings. The integrated MPC strategy was evaluated and compared to the multi-variable ESC strategy under various conditions, including fixed design conditions, changing ambient conditions, and step-change water outlet temperature. The results clearly demonstrated the effectiveness and superiority of the integrated MPC.

A switched extremum seeking control without steady-state oscillation using gradient-based adaptive-amplitude perturbation

To enhance the steady-state and dynamic performance of the extremum seeking control (ESC), a switched ESC scheme is proposed in this paper. Firstly, to solve nonconvex optimization problems, a novel adaptive law for perturbation is established utilizing the hybrid gradient information to accomplish a trade-off between the dynamic and steady-state performance. It is shown that the adaptive-amplitude ESC achieves global optimization despite the existence of local extrema. Then, to overcome the adverse effect of inaccurate gradient estimation on steady-state accuracy, a Lyapunov-based switched strategy is employed to start the bisection-based ESC. The plant output converges to the equilibrium rapidly and accurately without steady-state oscillation. Furthermore, the stability of the proposed scheme is theoretically proved. Numerical simulation examples are carried out to demonstrate the effectiveness of the proposed scheme.

Extremum seeking control for real-time optimization of high temperature heat pump systems incorporating vapor injection

In order to minimize the power consumption of a vapor-injected high temperature heat pump system with R245fa as refrigerant, a control strategy, namely Extremum seeking control, is proposed. It can implement real-time model-free optimization control of plants with concave and convex properties. Modelica-based dynamic simulation model of the proposed system is developed. The Newton-based Extremum seeking control is used to optimize the intermediate pressure of the proposed system to obtain the minimum power consumption of the compressor at a fixed heating capacity (200 kW). The adopted ESC strategy requires four measured quantities, namely, injection pressure, condenser outlet water temperature, evaporator outlet superheat and compressor power consumption, to achieve optimal control of the system in real time. Two operation scenarios are simulated: stable and freely variable heat source temperature. For both scenarios, the condenser outlet water temperature was set to 140 °C. The simulation results show that at stable heat source temperature, the power consumption is reduced by 5.2% and the COP is increased by 7.7% compared to a fixed initial intermediate pressure. Under the free-variable heat source condition, the power consumption can be reduced by up to 5 kW compared to a constant input. A total of 283 kWh of power was saved during the 48 h simulation. Thus, the Newton-based extremum seeking control strategy can optimize the intermediate pressure to achieve the minimum power consumption while maintaining excellent transient performance, and demonstrate the superiority of the ESC strategy for real-time optimization..

Multi-variable extremum seeking control for high temperature heat pump system incorporating double refrigerant injection

The use of refrigerant injection technology to enhance the heating efficiency of heat pumps with larger temperature lifts is becoming more common. Heat pumps with double refrigerant injection loops have better energy efficiency than traditional ones with single refrigerant injection loops. A multi-variable extremum seeking control (ESC) strategy for a high-temperature heat pump system with double refrigerant injection technology is proposed in this study. A Modelica-based dynamic simulation model of the considering system is established in Dymola, and a co-simulation with the proposed ESC strategy is built to validate the effectiveness of this control strategy to minimize power consumption. The strategy uses compressor power consumption as the feedback. The effective throttling area of the upper and lower EEVs is adjusted by a PI controller to manipulate the low and high-pressure vapor injection pressures. Three scenarios were simulated for control: stable, step curve, and freely variable heat source temperature conditions. The simulation results demonstrate that the multi-variable ESC has excellent convergence performance and confirm its effectiveness in searching for the optimal operating point.

Nondisturbing Extremum Seeking Control for Multiagent Industrial Systems

Industrial applications of extremum seeking control (ESC) can be a hit and miss affair. Although a gain in performance can be achieved, the dither applied to excite the system causes unwanted fluctuations in the performance of the system. The fluctuations in systems with a single extremum seeking loop are generally small. However, for systems with many extremum seeking loops, the fluctuations in each loop may add up to an intolerable amount of fluctuation in the total performance. In this article, we propose a method to cancel the dither-induced fluctuations in the overall system performance to a large extent by smartly constructing the dither signals in each extremum seeking loop using a centralized coordinator. The novelty of our method lies in the direct calculation of the dither signals that avoids the heavy computations required by other methods. Moreover, we provide a solvability analysis for the problem of cancelling dither-induced fluctuations in the total performance of the system. Furthermore, a complete stability analysis of the overall ESC scheme with dither coordination is given.

Integration design and control strategy of sCO 2 Brayton cycle for concentrated solar power system

The concentrated solar power (CSP) system integrated with supercritical carbon dioxide (sCO 2) Brayton cycle is considered as the major development trend of clean energy technology in mitigating climate change and promoting sustainable energy owing to its more compact structure, higher efficiency and lower cost. While the system integration and control are more complex because the thermal energy storage and heat exchange units are obliged to be provided with capacity and property matching with sCO 2 compression and expansion units. Therefore, there is an urgent need for the whole system modeling and dynamic simulation of sCO 2-CSP plants. In the paper, running logic of the integrated system is determined and novel system dynamic simulation platform is built. Moreover, for the sake of optimizing the system design, different control strategies are further studied. When the extremum-seeking control strategy is used, the average daily generating capacity of the system is 2.06% higher than that of the traditional fixed inventory control strategy; and when iterative learning control strategy is used, the average daily generating capacity of the system is 2.15% higher than that of the traditional fixed inventory control strategy. The progress of the technology will promote the development of new power systems and early realization of carbon neutrality.

Optimal Positioning of Snake Robots in Vortex Wakes using Extremum-Seeking Control

In this paper we explore the optimal positioning of an underwater snake robot (USR) for energy harvesting in the wake of a bluff body. The USR and fluid are simulated jointly using a coupled vortex particle-mesh method and multi-body system solver. The power dissipated in the damped joints of the robot is used as a proxy for the harvested energy. Furthermore, the effect of different damper coefficients on power dissipation is explored. An extremum-seeking control (ESC) scheme for nonlinear systems with time-varying steady-state solutions is employed to optimize the horizontal placement of the robot. The results show that the dissipated power does have a clear optimum. Moreover, the horizontal position of the USR under the ESC scheme is demonstrated to converge to a vicinity of the optimal position.

Optimizing Surplus Heat Recovery using Fast Fourier Transform-based Extremum Seeking Control

In large industrial parks, the surplus heat generated by the different manufacturing and processing plants can be recovered and utilized (e.g. for district heating) using a network of heat exchangers. Efficient management of the heat exchanger network is an important factor in maximizing the surplus heat recovery. This is accomplished by adjusting the flow of cold stream through the heat exchangers as the amount of heat generated by the different heat sources vary over time. Traditional real time optimization typically requires detailed process models, production schedules, and real-time process measurements in order to optimize the process. However, in an eco-industrial park with multiple heat sources operated by different companies, data sharing may not be desirable. This paper proposes the use of a multivariable extremum seeking control scheme using fast Fourier transform (FFT) to optimize waste heat recovery using only a single temperature measurement, measured at the end of the heat exchanger network. By mapping the time series data into a series of frequencies, we show that FFT allows us to easily extract the effect of different input perturbations from the single temperature measurement, and use it to optimize surplus heat recovery from an industrial cluster.

Gradient-Based Extremum Seeking Control Applied to a Dark Fermentation Process

In this paper we use an extremum seeking control strategy to maximize the produced ethanol in a dark fermenter. Such a strategy avails of a continuous estimation of the reactor’s input-output gradient to compute the dilution rate applied to the reactor. This dilution rate, however, is updated at discrete moments. We consider a scenario in which tequila vinasse is the raw material for this fermentation process; thereby reducing the concentrations of sugars in the vinasse and at the same time obtaining ethanol. Via numerical simulations we show the applicability of the strategy when the optimal concentration of ethanol varies in time as step functions.

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>

Intelligent Reflecting Surface Configurations for Smart Radio Using Deep Reinforcement Learning

Intelligent reflecting surface (IRS) is envisioned to change the paradigm of wireless communications from “adapting to wireless channels” to “changing wireless channels”. However, current IRS configuration schemes, consisting of sub-channel estimation and passive beamforming in sequence, conform to the conventional model-based design philosophies and are difficult to be realized practically in the complex radio environment. To create the smart radio environment, we propose a model-free design of IRS control that is independent of the sub-channel channel state information (CSI) and requires the minimum interaction between IRS and the wireless communication system. We firstly model the control of IRS as a Markov decision process (MDP) and apply deep reinforcement learning (DRL) to perform real-time coarse phase control of IRS. Then, we apply extremum seeking control (ESC) as the fine phase control of IRS. Finally, by updating the frame structure, we integrate DRL and ESC in the model-free control of IRS to improve its adaptivity to different channel dynamics. Numerical results show the superiority of our proposed joint DRL and ESC scheme and verify its effectiveness in model-free IRS control without sub-channel CSI.

Numerical optimization‐based extremum seeking control of a class of constrained nonlinear systems via finite‐time state transition

AbstractThis article studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints that allows to reformulate the original nonlinear system in the so‐called input–output normal form. To steer the system to optimize a performance function without knowing its explicit form, we propose a novel numerical optimization‐based extremum seeking control (NOESC) design consisting of a constrained numerical optimization method and an inversion‐based feedforward controller. In particular, a projected gradient descent algorithm is exploited to produce the state sequence to optimize the performance function, whereas a suitable boundary value problem accommodates the finite‐time state transition between each two consecutive points of the state sequence. Compared to available NOESC methods, the proposed approach (i) can explicitly deal with output constraints; (ii) can consider a direct dependence on the states of the internal dynamics in the performance function; (iii) the internal dynamics do not have to be necessarily stable. The effectiveness of the proposed ESC scheme is shown through extensive numerical simulations and design of antilock braking systems.

Robustness and averaging properties of a large-amplitude, high-frequency extremum seeking control scheme

We investigate robustness and averaging properties of an extremum seeking scheme which employs oscillatory dither signals with sufficiently large amplitudes and frequencies. Our study takes both input and output disturbances into account. We consider general L∞-disturbances, which may correlate with the oscillatory dither signals. A suitable change of variables followed by an averaging procedure reveals that the closed-loop system approximates the behavior of an averaged system. The disturbances in the averaged system are directly linked to the disturbances in the closed-loop system. This allows us to conclude stability and robustness properties of closed-loop system from respective properties of the averaged system. In particular, we show that, if the averaged system tolerates L∞-disturbances of a certain magnitude, then the same is true for the approximating closed-loop system. Another feature of the proposed method is that it steers the closed-loop system approximately into descent directions of an averaged objective function. This property can be beneficial for the purpose of global optimization because an averaged objective function is expected to have fewer undesired critical points than the original objective function.

Dither extremum seeking control of a variable refrigerant flow system with equality constraint handling

In this paper, we apply an extremum-seeking control strategy to a variable refrigerant flow (VRF) system, where the total power consumption is minimized by adjusting the compressor discharge pressure setpoint and the outdoor unit fan mass flow rate, incorporating constraints on the zonal temperature setpoint regulation. A simulation study is conducted using a Modelica dynamic simulation model of a VRF system with one outdoor unit and four indoor units. Simulation results validate the effectiveness of the proposed method of power minimization with the constraint of zone-temperature regulation. The ESC strategy incorporates online penalty-weight estimation and loop-gain adaption, which are shown to improve convergence.

Model guided extremum seeking control of electromagnetic micromirrors

In this paper, a simplified dynamic model is constructed to describe the main characteristic of electromagnetic micro-mirror. Then, based on the information provided by the derived simplified model, a model-guided extremum seeking control (MGESC) scheme with backtracking line search is developed, which can automatically estimate the best value of step-size at each search iteration to improve the performance of the control system for target tracking. Then, the convergence of the proposed MGES algorithm is proved. Finally, the experimental results and the simulations are presented to verify the proposed method.

Development of real-time adaptive model-free extremum seeking control for CFD-simulated thermal environment

Building automation and control are of great importance for maintaining a satisfactory thermal environment. Model-based strategies for building climate control require a large amount of effort to construct and to update the building models to address the uncertainties caused by changes in weather conditions and indoor activities, which make it difficult to be applied in real applications. In this study, to overcome limitations of model-based strategies, a model-free control strategy based on extremum seeking control (ESC) without reliance on building models was proposed for real-time control of thermal environment. A dynamic simulation platform based on ESC and computational fluid dynamics (CFD) was developed to investigate the control performance of the ESC scheme. To investigate the effectiveness of the ESC scheme in different indoor thermal environments, the effectiveness of the ESC controller in two different cases including a confined space under mixing convection and an office with displacement ventilation was evaluated, respectively. The ESC controller showed good performance in terms of convergence speed and control accuracy in both cases. This study revealed that the proposed ESC-based control strategy has the potential to effectively control thermal environment in real applications due to its model-free advantage.

Extremum Seeking With Enhanced Convergence Speed for Optimization of Time-Varying Steady-State Behavior of Industrial Motion Stages

Recently, an extremum-seeking control (ESC) approach has been developed for optimization of generically time-varying steady-state responses of nonlinear systems. A generic filter structure was introduced, the so-called dynamic cost function, which has been instrumental in facilitating the use of ESC in the more generic, time-varying context. However, the dynamic cost function must operate sufficiently slow compared to the time-varying nature of the system responses, thereby compromising the convergence speed of the ESC scheme. In this work, a modified ESC approach is proposed that incorporates explicit knowledge about the user-defined dynamic cost function, able to enhance the convergence speed of the ESC scheme. Moreover, we provide a stability analysis for this extended approach. The main contribution of this work is the experimental demonstration of both ESC approaches for the performance optimal tuning of a variable-gain control (VGC) strategy employed on a high-accuracy industrial motion stage setup, exhibiting generically time-varying steady-state responses. VGC is able to enhance the system performance by balancing the typical linear control tradeoff between low-frequency disturbance suppression properties and sensitivity to high-frequency disturbances in a more desirable manner. We experimentally show that, for the unknown disturbance situation at hand, the variable-gain controller can be automatically tuned using both ESC approaches to achieve the optimal system performance. In addition, enhanced convergence speed with the modified ESC approach is evidenced experimentally.

Adaptive Extremum Seeking Control of Urban Area Wind Turbines

Maximum-power point tracking of wind turbines is a challenging issue considering fast changing wind conditions of urban areas. For this purpose, an adaptive control approach that is fast and robust is required. Conventional approaches based on simple step perturbations and subsequent observation, however, are difficult to design and too slow for the demanding wind conditions of urban areas including gusts and turbulence. In this paper, an extremum seeking control scheme to the recently developed wind turbine MOWEA (Modulare Windenergieanlagen GmbH) is proposed and successfully applied. To this end, a comprehensive aero-electromechanical model of the wind turbine under study including basic control is formulated. Next, the extremum seeking control scheme is adapted to the system. Several aspects to increase adaptation speed are highlighted, including a novel phase compensation. Finally, a validation of the proposed approach is performed considering real wind data, thus demonstrating its fast and robust adaptability. The proposed control scheme is computationally efficient and can be easily implemented on the existing onboard electronics.

Energy‐efficient operation of indirect adiabatic data center cooling systems via Newton‐like phasor extremum seeking control

SummaryThis paper considers the problem of optimizing the operation of Indirect Adiabatic Cooling (IAC) systems with application to data centers. Optimal operation is achieved when the required cooling demand is satisfied at the minimum energy cost. For this purpose, we design a supervisory control system, where the higher layer determines the optimal set‐points for the local controllers by employing an Extremum Seeking Control (ESC) scheme. In particular, we consider a Newton‐like phasor ESC, which augments the derivative estimator underlying the phasor approach to capture also the Hessian of the plant index and then it uses these estimates to steer the system along a Newton‐like direction. The effectiveness of the considered approach is tested in simulation by exploiting a Matlab‐based simulation environment including an IAC system and a computer room.

Extremum seeking control with attenuated steady-state oscillations

We propose two perturbation-based extremum seeking control (ESC) schemes for general single input single output nonlinear dynamical systems, having structures similar to that of the classical ESC scheme. We propose novel adaptation laws for the excitation signal amplitudes in each scheme that drive the amplitudes to zero. The rates of decay for both the laws are governed by the gradient measures of the unknown reference-to-output equilibrium map We show that the proposed ESC schemes achieve practical asymptotic convergence to the extremum with a proper tuning of the parameters in the proposed schemes. As the extremum is reached, and the magnitudes of the gradient measures become small, the excitation signal amplitudes converge to zero. Thus, the proposed schemes ensure that the excitation signal is driven to zero as the system output converges to a neighborhood of the extremum and the steady-state oscillations about the extremum, typically observed for the classical ESC schemes, are attenuated. Simulation examples are included to illustrate the effectiveness of the proposed schemes.