Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “feedback control systems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Extremum seeking for optimal control problems with unknown time-varying systems and unknown objective functions

We consider the problem of optimal feedback control of an unknown, noisy, time-varying, dynamic system that is initialized repeatedly. Examples include a robotic manipulator which must perform the same motion, such as assisting a human, repeatedly and accelerating cavities in particle accelerators which are turned on for a fraction of a second with given initial conditions and vary slowly due to temperature fluctuations. In this paper, we present an approach that applies to systems of practical interest. The method presented here is model independent; does not require knowledge of the objective function; is robust to measurement noise; is applicable for any set of initial conditions; is applicable to simultaneously controlling an arbitrary number of parameters; and may be implemented with a broad range of continuous or discontinuous functions such as sine or square waves. For systems with convex cost functions we prove that our algorithm will produce controllers that approach the minimal cost. For linear systems we reproduce the cost minimizing linear quadratic regulator optimal controller that could have been designed analytically had the system and cost function been known. We demonstrate the effectiveness of the algorithm with simulation studies of noisy and time-varying systems.

42 ENGINEERING↗

A Portable Wave Tank and Wave Energy Converter for Engineering Dissemination and Outreach

Wave energy converters are a nascent energy generation technology that harnesses the power in ocean waves. To assist in communicating both fundamental and complex concepts of wave energy, a small-scale portable wave tank and wave energy converter have been developed. The system has been designed using commercial off-the-shelf components, and all design hardware and software are openly available for replication. This project builds on prior research conducted at Sandia National Laboratories, particularly in the areas of WEC device design and control systems. By showcasing the principles of causal feedback control and innovative device design, SIWEED not only serves as a practical demonstration tool but also enhances the educational experience for users. This paper presents the detailed system design of this tool. Furthermore, via testing and analysis, we demonstrate the basic functionality of the system.

educational↗

Reinforcement Learning of Structured Stabilizing Control for Linear Systems With Unknown State Matrix

This paper delves into designing feedback control gains for a continuous-time linear quadratic regulator (LQR) problem that is constrained to certain predefined structure with unknown state matrix. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. Here we first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the LQR gain computation in the continuous-time setting, and then subsequently, formulate a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. The design enables a distributed learning control design which is necessary for many large-scale cyber-physical systems. Theoretical guarantees are provided for stability and convergence of the structured reinforcement learning (SRL) algorithm. We validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.

42 ENGINEERING↗

Control systems and data management for high-power laser facilities

The next generation of high-power lasers enables repetition of experiments at orders of magnitude higher frequency than what was possible using the prior generation. Facilities requiring human intervention between laser repetitions need to adapt in order to keep pace with the new laser technology. A distributed networked control system can enable laboratory-wide automation and feedback control loops. These higher-repetition-rate experiments will create enormous quantities of data. A consistent approach to managing data can increase data accessibility, reduce repetitive data-software development and mitigate poorly organized metadata. An opportunity arises to share knowledge of improvements to control and data infrastructure currently being undertaken. We compare platforms and approaches to state-of-the-art control systems and data management at high-power laser facilities, and we illustrate these topics with case studies from our community

47 OTHER INSTRUMENTATION↗

Light Water Sustainability Program: Optimizing Information Automation Using a New Method Based on System-Theoretic Process Analysis

This report describes the interim progress for research supporting the design and optimization of information automation systems for nuclear power plants. Much of the domestic nuclear fleet is currently focused on modernizing technologies and processes, including transitioning toward digitalization in the control room and elsewhere throughout the plant, along with a greater use of automation, artificial intelligence, robotics, and other emerging technologies. While there are significant opportunities to apply these technologies toward greater plant safety, efficiency, and overall cost-effectiveness, optimizing their design and avoiding potential safety and performance risks depends on ensuring that human-performance-related organizational and technical design issues are identified and addressed. This report describes modeling tools and techniques, based on sociotechnical system theory, to support these design goals and their application in the current research effort. The report is intended for senior nuclear energy stakeholders, including regulators, corporate management, and senior plant management. We have developed and employed a method to design an optimized information automation ecosystem (IAE) based on the systems-theoretic constructs underlying sociotechnical systems theory in general and the Systems-Theoretic Accident Modeling and Processes (STAMP) approach in particular. We argue that an IAE can be modeled as an interactive information control system whose behavior can be understood in terms of dynamic control and feedback relationships amongst the system’s technical and organizational components. Up to this point, we have employed a Causal Analysis based on STAMP (CAST) technique to examine a performance- and safety-related incident at an industry partner’s plant that involved the unintentional activation of an emergency diesel generator. This analysis provided insight into the behavior of the plant’s current information control structure within the context of a specific, significant event. Our ongoing analysis is focused on identifying near-term process improvements and longer-term design requirements for an optimized IAE system. The latter analyses will employ a second STAMP-derived technique, System-Theoretic Process Analysis (STPA). STPA is a useful modeling tool for generating and analyzing actual or potential information control structures. Finally, we have begun modeling plantwide organizational relationships and processes. Organizational system modeling will supplement our CAST and STPA findings and provide a basis for mapping out a plantwide information control architecture. CAST analysis findings indicate an important underlying contributor to the incident under investigation, and a significant risk to information automation system performance, was perceived schedule pressure, which exposed weaknesses in interdepartmental coordination between and within responsible plant organizations and challenged the resilience of established plant processes, until a human caused the initiating event. These findings are discussed in terms of their risk to overall system performance and their implications for information automation system resilience and brittleness. We present two preliminary information automation models. The proactive issue resolution model is a test case of an information automation concept with significant near-term potential for application and subsequent reduction in significant plant events. The IAE model is a more general representation of a broader, plantwide information automation system. From our results, we have generated a set of preliminary system-level requirements and safety constraints. These requirements will be further developed over the remainder of our project in collaboration with nuclear industry subject matter experts and specialists in the technical systems under consideration. Additionally, we will continue to pursue the system analyses initiated in the first part of our effort, with a particular emphasis on STPA as the main tool to identify weak or weakening control structures that affect the resilience of organizations and programs. Our intent is to broaden the scope of the analysis from an individual use case to a related set of use cases (e.g., maintenance tasks, compliance tasks) with similar human-system performance challenges. This will enable more generalized findings to refine the Proactive Issue Resolution and IAE models, as well as their system-level requirements and safety constraints. We will use organizational system modeling analyses to supplement STPA findings and model development. We conclude the report with a set of summary recommendations and an initial draft list of system-level requirements and safety constraints for optimized information automation systems.

99 GENERAL AND MISCELLANEOUS↗

Pressure feedback control of electro-hydraulic actuators using fixed displacement hydraulic machines

This paper presents the development of a control strategy for Electro-Hydraulic Actuator (EHA) systems based on fixed displacement hydraulic machines. Although some previous studies on EHAs show benefits in terms of energy efficiency and regeneration capability compared to conventional hydraulic systems, few studies focus on the dynamic performance of EHAs. Unlike traditional valve-controlled systems, an EHA based on a fixed displacement pump typically relies on variation of the electric motor shaft speed to control the actuator velocity. This study shows that pressure feedback can be used to control the speed of the electric machine, thus achieving the required actuator/machine dynamic response. A simulation model is developed by including the EM, the hydraulic system, and the actuation system, which can give a realistic prediction of the EHA performance for a typical duty cycle. An open-circuit EHA previously proposed by the authors is used to validate the control strategy, and the simulation results show superior dynamic performance, exhibiting a reduction in response time and oscillatory behavior, compared to a feedforward EHA controller. Following the method presented in this study, it is possible to design a controller with a pressure feedback strategy for EHA systems with different size and actuation requirements

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Failure Mechanism Traceability and Application in Human System Interface of Nuclear Power Plants using RESHA

In recent years, there has been considerable effort to modernize existing and new nuclear power plants with digital instrumentation and control systems (DI&C). However, there has also been considerable concern both by industry and regulatory bodies for the risk and consequence analysis of these systems. Of particular concern are digital common cause failures (CCFs) specifically related to software defects. These “misbehaviors” by the software can occur in both the control and monitoring of a system. While many new methods have been proposed to identify potential software failure modes, such as Systems-theoretic Process Analysis (STPA), Hazard and Consequence Analysis for Digital Systems (HAZCADS), etc., these methods are focused primarily on the control action pathway of a system. In contrast, the information feedback pathway lacks unsafe control actions (UCAs), which are typically related to software basic events; thus, assessment of software basic events in such systems is unclear. In this work, we present the idea of intermediate processors and unsafe information flow (UIF) to help safety analysts trace failure mechanisms in the feedback pathway and how they can be integrated into a fault tree for improved assessment capability. The concepts presented are demonstrated in two comprehensive case studies, a smart sensor integrated platform for unmanned autonomous vehicles and another on a representative advanced human system interface (HSI) for safety critical plant monitoring. The qualitative software basic events are identified, and a fault tree analysis is conducted based on a modified Redundancy-guided Systems-theoretic Hazard Analysis (RESHA) methodology. The case studies demonstrate the use of UIF and intermediate processors in the fault tree to improve traceability of software failures in highly complex digital instrumentation feedback. The improved method can also clarify fault tree construction when multiple component dependencies are present in the system.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Failure Mechanism Traceability and Application in Human System Interface of Nuclear Power Plants using RESHA

In recent years, there has been considerable effort to modernize existing and new nuclear power plants with digital instrumentation and control systems (DI&C). However, there has also been considerable concern both by industry and regulatory bodies for the risk and consequence analysis of these systems. Of particular concern are digital common cause failures (CCFs) specifically related to software defects. These “misbehaviors” by the software can occur in both the control and monitoring of a system. While many new methods have been proposed to identify potential software failure modes, such as Systems-theoretic Process Analysis (STPA), Hazard and Consequence Analysis for Digital Systems (HAZCADS), etc., these methods are focused primarily on the control action pathway of a system. In contrast, the information feedback pathway lacks unsafe control actions (UCAs), which are typically related to software basic events; thus, assessment of software basic events in such systems is unclear. In this work, we present the idea of intermediate processors and unsafe information flow (UIF) to help safety analysts trace failure mechanisms in the feedback pathway and how they can be integrated into a fault tree for improved assessment capability. The concepts presented are demonstrated in two comprehensive case studies, a smart sensor integrated platform for unmanned autonomous vehicles and another on a representative advanced human system interface (HSI) for safety critical plant monitoring. The qualitative software basic events are identified, and a fault tree analysis is conducted based on a modified Redundancy-guided Systems-theoretic Hazard Analysis (RESHA) methodology. The case studies demonstrate the use of UIF and intermediate processors in the fault tree to improve traceability of software failures in highly complex digital instrumentation feedback. The improved method can also clarify fault tree construction when multiple component dependencies are present in the system.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Simultaneous stabilization and control of the n = 1 and n = 2 resistive wall mode

Abstract DIII-D experiments demonstrate simultaneous stability measurements and control of resistive wall modes (RWMs) with toroidal mode numbers n = 1 and n = 2. RWMs with n > 1 are sometimes observed on DIII-D following the successful feedback stabilization of the n = 1 mode, motivating the development of multi- n control. A new model-based multi-mode feedback algorithm based on the VALEN physics code has been implemented on the DIII-D tokamak using a real-time GPU installed directly into the DIII-D plasma control system. In addition to stabilizing RWMs, the feedback seeks to control the stable plasma error field response, enabling compensation of the typically unaddressed DIII-D n = 2 error field component. Experiments recently demonstrated this algorithm’s ability to simultaneously control n = 1 and n = 2 perturbed fields for the first time in a tokamak, using reactor relevant external coils. Control was maintained for hundreds of wall-times above the n = 1 no-wall pressure limit and approaching the n = 1 and n = 2 ideal-wall limits. Furthermore, a rotating non-zero target was set for the feedback, allowing stability to be assessed by monitoring the rotating plasma response (PR) while maintaining control. This novel technique can be viewed as a closed-loop extension of active MHD spectroscopy, which has been used to validate stability models through comparisons of the PR to applied, open-loop perturbations. The closed-loop response measurements are consistent with open-loop MHD spectroscopy data over a wide range of β N approaching the n = 1 ideal-wall limit. These PR measurements were then fit to produce both VALEN and single-mode stability models. These models allowed for important plasma stability information to be determined and have been shown to agree with experimentally observed RWM growth rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimizing Information Automation Using a New Method Based on System-Theoretic Process Analysis: Tool Development and Method Evaluation

This report is an update to a prior report that describes progress and findings for a program of research supporting the design and optimization of information automation systems for nuclear power plants. Much of the domestic nuclear fleet is currently focused on modernizing technologies and processes, including transitioning toward digitalization in the control room and throughout the plant, along with a greater interest in the use of automation, artificial intelligence, robotics, and other emerging technologies. While there are significant opportunities to apply these technologies toward greater plant safety, efficiency, and overall cost-effectiveness, optimizing their design and avoiding potential safety and performance risks depends on ensuring that human performance-related organizational and technical design issues are identified and addressed early in the design process. This report describes modeling tools and techniques, based on sociotechnical systems theory, to support these design goals and their application in the current research effort. The report is primarily intended for senior nuclear energy stakeholders, including regulators, corporate management, and senior plant management. We have developed and employed a method to design an optimized information automation ecosystem (IAE) based on the systems-theoretic constructs underlying sociotechnical systems theory in general and the Systems-Theoretic Accident Modeling and Processes (STAMP) approach in particular. We argue that an IAE can be modeled as an interactive information control system whose behavior can be understood in terms of dynamic control, feedback, and communication relationships amongst the system’s technical and organizational components. We have employed two STAMP-based tools in this effort. The first is Causal Analysis based on STAMP (CAST), an accident and incident analysis technique that was used to examine a performance- and safety-related incident at an industry partner’s plant involving the unintentional activation of an emergency diesel generator. This analysis provided insight into the behavior of the plant’s current information control structure within the context of a specific, significant event. The second tool is Systems Theoretic Process Analysis (STPA) which is a proactive risk analysis tool used to examine existing and potential, planned sociotechnical systems. STPA was used to identify risk factors in the current design of a generic nuclear power plant (NPP) preventive maintenance system. Our analyses focused on identifying near-term system improvements and longer-term design requirements for an optimized IAE system. CAST analysis findings indicate an important underlying contributor to the incident under investigation, and a significant risk to information automation system performance, was perceived time and schedule pressure, which exposed weaknesses in interdepartmental coordination between and within responsible plant organizations and challenged the resilience of established plant processes, until a human caused the eventual event. These findings are discussed in terms of their risk to overall system performance and their implications for information automation system resilience and brittleness. STPA findings exposed several areas of concern in the design of current preventive maintenance systems. We also present two preliminary information automation models. The proactive issue resolution (PIR) model is a test case of an information automation concept with significant near-term potential for application and subsequent reduction in significant plant events. The IAE model is a more general representation of a broader, plantwide information automation system and represents an end-state vision for our work. From our results, we have generated an initial set of preliminary system-level requirements and safety constraints for these models. We have also focused on early development of easy to learn, easy to use “transportable” tools for sociotechnical systems analysis. We intend these to be used by NPP personnel as a means of gaining reliable and relatively quick insight into (1) sociotechnical systems factors impacting incidents and accidents, (2) potential sociotechnical risk factors in existing or planned system designs, and (3) potential weaknesses in a system’s safety and/or information control structure. We conclude the report with a set of summary recommendations, a discussion of planned and potential follow-on research and development, and a draft list of system-level requirements and safety constraints for optimized information automation systems.

99 GENERAL AND MISCELLANEOUS↗

Implementation of high-speed data acquisition at DIII-D

Research at the DIII-D National Fusion Facility in San Diego focuses on short pulse plasma discharges that specialize on various shaping profiles. High-speed data collection is a critical component for the operation of many of DIII-D’s diagnostics and is fundamental for capturing high-resolution data used in experimental data analysis. Differing techniques enable the plasma control system (PCS) to perform complex real-time feedback control on microsecond time scales. This work presents a comprehensive overview of data acquisition, focusing on the hardware and software used in reliable data acquisition at DIII-D. The robust nature of the data acquisition system allows for various techniques to coexist seamlessly. However, as modern systems capable of nanosecond resolution become more common, existing architectures will need to be modified. Here, by addressing the key challenges of high-speed data acquisition, DIII-D is able to provide real-time data used in plasma operation and has the ability to acquire high fidelity data needed for future experimental fusion reactors, such as ITER.

Control↗

Control system and method for tapered structure construction

A control system for forming a tapered structure includes a sensor providing feedback for a machine for forming a tapered structure including at least three rolls having at least one bend roll and at least two guide rolls. The guide rolls may include rollette banks having a plurality of rollettes. The machine may also include an adjustment mechanism to position at least one of the rolls, where a diameter of the tapered structure being formed is controlled by relative positions of the rolls. The machine may also include a joining element to join edges of a stock of material together as it is rolled through the rolls to form the tapered structure. The control system may also include a controller to receive feedback from the sensor and to send a control signal based on the feedback to the adjustment mechanism for positioning at least one of the rolls.

Takata, Rosalind K.↗

Deep learning-assisted modeling for χ (2) nonlinear optics

Modeling second-order (χ(2)) nonlinear optical processes remains computationally expensive due to the need to resolve fast field oscillations and simulate wave propagation using methods such as the split-step Fourier method (SSFM). This can become a bottleneck in real-time applications, such as high-repetition-rate laser systems requiring rapid feedback and control. We present a long short-term memory-based surrogate model trained on SSFM simulations generated from a start-to-end model of the photocathode drive laser at SLAC National Accelerator Laboratory’s Linac Coherent Light Source II. The model achieves over 250× speedup while maintaining high fidelity, enabling future real-time optimization and laying the foundation for data-integrated modeling frameworks and digital twins of laser systems.

Accelerator Physics (physics.acc-ph)↗

Thermal Reservoir Networks for Modularly Expandable Thermal Microgrids

The Department of Defense (DoD) faces the substantial challenge of cost-effectively retrofitting one to two installations per month, each comprising approximately 1,000 buildings, to improve resilience, reduce energy consumption, and enhance energy supply security. Achieving these objectives requires optimal system selection and effective risk mitigation during system integration. To address this need, we introduce Platform-Based Design (PBD), a structured, hierarchical methodology adapted from other industrial sectors to the domain of energy system retrofits. We demonstrate the effectiveness of PBD through a techno-economic feasibility study comparing geothermal-coupled thermal energy networks (TENs) with conventional energy systems for heating, cooling, and powering 17 buildings at Joint Base Andrews (JBA) in Maryland. Our analysis illustrates that the PBD approach enables rigorous, data-driven, sequential decision making, resulting in a family of Pareto-optimal systems, among which the TEN emerged as the most promising solution. The selected TEN design integrates geothermal borefields, heat recovery heat pumps, photovoltaic (PV) arrays, and battery storage. Compared to the baseline system – gas heating combined with air-source chillers – the proposed TEN reduces annual imported energy by 74% and peak electricity demand by 45%, achieves a levelized cost of energy of $\$0.210$/kWh, and substantially enhances resilience. Life-cycle costs increase by approximately 6%, and initial investment costs are about 2.5 times higher than the baseline. However, if central plant infrastructure, district loops, and utility-scale PV and battery systems are privately funded and operated, the initial investment would fall below the baseline system cost. Critical to achieving these significant performance improvements were detailed nonlinear dynamic simulations coupling geothermal heat transfer, energy system operation, and realistic feedback control logic. These simulations identified essential design modifications and control strategy refinements that substantially reduced energy use, peak demand, and compressor shortcycling, thereby improving durability and reliability—issues that would have been significantly more expensive to resolve during operation. Additionally, the verification step highlighted sensitivities to key design parameters that could reduce initial investment by approximately $\$2$ million and reduce annual life-cycle costs more than $\$300,000$. We recommend adopting the PBD methodology for future feasibility studies and TEN pilot projects to gain valuable operational experience. Furthermore, we recommend that DoD invest in transferring and scaling the PBD methodology to other installations. This entails developing standardized computational frameworks and component libraries as well as training industry in conducting PBD. Such investments would enable rapid, robust, reliable, and cost-effective retrofits, supporting DoD’s ambitious energy system modernization goals.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Operating a commercial building HVAC load as a virtual battery through airflow control

Virtual battery (VB) is an innovative method to model flexibility of building loads and effectively coordinate them with other resources at a system level. Unlike a real battery with a dedicated power conversion system for charging control, methods are required for operating building loads to deviate from the baseline to respond to grid signals. This paper presents a VB control for a commercial heating, ventilation, and air conditioning (HVAC) system to follow the desired power consumption in real-time by adjusting zonal airflow rates. The proposed method consists of two parts. At the system level, a mixed feedforward and feedback control is used to estimate the desired total airflow rate. At the zone level, two priority-based algorithms are then proposed to distribute the total airflow rate to individual zones. In particular, a zonal airflow limit estimation method is proposed using machine-learning techniques, in contrast to physics-based thermal models in existing studies, to more accurately capture zonal thermal dynamics and improve temperature control performance. An office building on the Pacific Northwest National Laboratory campus is implemented in EnergyPlus, and used to illustrate and validate the proposed control.

Wang, Jiyu↗

Exploring electron-beam induced modifications of materials with machine-learning assisted high temporal resolution electron microscopy

Directed atomic fabrication using an aberration-corrected scanning transmission electron microscope (STEM) opens new pathways for atomic engineering of functional materials. In this approach, the electron beam is used to actively alter the atomic structure through electron beam induced irradiation processes. One of the impediments that has limited widespread use thus far has been the ability to understand the fundamental mechanisms of atomic transformation pathways at high spatiotemporal resolution. Here, we develop a workflow for obtaining and analyzing high-speed spiral scan STEM data, up to 100 fps, to track the atomic fabrication process during nanopore milling in monolayer MoS 2 . An automated feedback-controlled electron beam positioning system combined with deep convolution neural network (DCNN) was used to decipher fast but low signal-to-noise datasets and classify time-resolved atom positions and nature of their evolving atomic defect configurations. Through this automated decoding, the initial atomic disordering and reordering processes leading to nanopore formation was able to be studied across various timescales. Using these experimental workflows a greater degree of speed and information can be extracted from small datasets without compromising spatial resolution. This approach can be adapted to other 2D materials systems to gain further insights into the defect formation necessary to inform future automated fabrication techniques utilizing the STEM electron beam.

36 MATERIALS SCIENCE↗

Robust Output Feedback Control Design for Inertia Emulation by Wind Turbine Generators

Wind generation has gained widespread use as a renewable energy source. Most wind turbines and other renewables connected to the grid through converters result in a reduction in the natural inertial response to grid frequency changes. The doubly-fed induction generator (DFIG) can be controlled to compensate for this reduction and, in fact, provide faster response than traditional synchronous machines. This paper proposes to design observer based output feedback linear quadratic regulator (LQR) and H control laws to realize the inertia emulation function and deliver fast frequency support. Furthermore, the aim is to track the reference speed by a diesel synchronous generator (DSG) in order to reach the desired inertia. The control signal is computed based on a reduced order model using the balanced truncation technique. A comparison with selective modal analysis (SMA) and balanced truncation model reduction techniques is presented. Comprehensive results show the effective emulation of synthetic inertia by implementing the control laws on a nonlinear three- phase diesel-wind system. The proposed technique is analyzed for different short circuit ratio (SCR) scenarios.

17 WIND ENERGY↗

New Safety Feedback Control Design to Guarantee Adequate Frequency Performance in Microgrids

Safety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel-wind energy system is considered and modeled as a switching system between normal, faulted, and post-fault modes. Further, a safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33-bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness.

barrier function↗