Reduced-order Dynamic Model Research Articles

Model Predictive Control and Service Life Monitoring for Molten Salt Solar Power Towers

A two-component system for control and monitoring of solar power towers with molten salt receivers is proposed. The control component consists of a model predictive control application (MPC) with a flexible objective function and on-line tunable weights, which runs on a Industrial PC and uses a reduced order dynamic model of the receiver’s thermal and flow dynamics. The second component consists of a service-life monitoring unit, which estimates the service-life consumption of the absorber tubes depending on the current mode of operation based on thermal stresses and creep fatigue in the high temperature regime. The calculation of stresses is done based on a detailed finite element study, in which a digital twin of the receiver was developed. By parallelising the model solver, the estimation of service-life consumption became capable of real-time operation. The system has been implemented at a test facility in Jülich, Germany, and awaits field experiments. In this paper, the modeling and architecture are presented along simulation results, which were validated on a hardware-in-the-loop test bench. The MPC showed good disturbance rejection while respecting process variable constraints during the simulation studies.

Dynamic modeling and trajectory optimization for the rigid-flexible coupled spacecraft with the free-floating manipulator and solar panels

The rigid-flexible coupled spacecraft, composed of flexible solar panels and a multilink manipulator, has gained prominence in on-orbit servicing due to rapid advancements in space technology. However, the intricate effects of rigid-flexible coupling pose significant challenges for dynamic modeling, trajectory planning, and control. This paper aims to develop general dynamic approaches for modeling and trajectory planning in such spacecraft, considering large deformations. The main distinguishing feature is the use of the referenced nodal coordinate formulation to accurately describe the large-deformed solar panels rather than directly treating them as disturbance for the free-floating system. Additionally, the common recursive model for the multilink manipulator is integrated into the same framework. The modal reduction method with modal derivatives techniques is employed to address geometric nonlinearity resulting from large deformations. Polynomial trajectory parameters with different performance characteristics are obtained by defining various optimization objectives. The coupling analysis is conducted based on an accurate reduced-order dynamic model, the results of which can be used for designing manipulator tasks. Coupling values are defined as the objective for trajectory optimization, offering advantages such as insensitivity to dynamic model accuracy and a fast optimization process. After validating the accuracy of the proposed dynamic model through simulations, the performances of different optimized trajectories are demonstrated using numerical examples.

Robust adaptive fault-tolerant tracking for uncertain output-constrained nonlinear systems with unknown time-varying powers and application to the reduced-order dynamical model of a boiler-turbine unit

Robust adaptive fault-tolerant tracking for uncertain output-constrained nonlinear systems with unknown time-varying powers and application to the reduced-order dynamical model of a boiler-turbine unit

Effect of background noise characteristics on early warning indicators of thermoacoustic instability

In this work, we investigate the effects of background noise characteristics — specifically noise color (or correlation time) and intensity — arising from velocity-coupled and additive noise sources, on the early warning indicators (EWIs) of thermoacoustic instability. We employ a nonlinear reduced-order combustion dynamics model for our investigation. In the absence of noise, the nonlinear model undergoes a subcritical Hopf bifurcation, and our focus lies within the linearly stable region of the system (subthreshold region). The studied class of EWIs encompasses those derived from time series (variance), spectral analysis (coherence factor), Hurst exponent, and nonlinear methods (permutation entropy). We find that when the background noise is purely multiplicative, the trends in EWIs are primarily influenced by noise characteristics rather than the control parameter. Further, the EWIs cannot be estimated at low noise levels for large correlation times. In case of purely additive noise driven system, the coherence factor and variance are reliable EWIs across all range of investigated noise characteristics. The Hurst exponent can serve as effective EWI when the system features large noise correlation times, while permutation entropy is effective only when the system features small noise correlation time, i.e., where white noise assumption is acceptable. When the background noise includes contributions from both multiplicative and additive sources, coherence factor and variance emerges as the most reliable EWIs. These results provide insights for selecting appropriate EWIs to be employed in practical systems, considering potential variations in noise characteristics with simultaneous changes in combustor operating conditions.Novelty and significanceThis study conclusively shows that background noise (multiplicative and additive) characteristics – noise correlation time (color) and intensity – can significantly change the trends in early warning indicators (EWIs) for predicting the impending thermoacoustic oscillations. In gas turbine combustors, where thermoacoustic instability poses a critical challenge, inherent noise dynamics undergo variations with changing operating conditions and combustor designs. The development of effective EWIs to foresee the onset of thermoacoustic instability is crucial for preventing potential damage and ensuring the reliable operation of combustion systems. Previous works on stochastic dynamics of combustors simplify noise with the additive white noise assumption. Thus, our results demonstrated on a nonlinear combustion dynamics model advance the state-of-the-art with respect to the early prediction and control of thermoacoustic instability. The results provide valuable insights for selecting appropriate EWIs for engine monitoring in the absence of information on noise properties and their variation with operating conditions. This practical information is of direct relevance and interest to any gas turbine manufacturer/user.

A comprehensive analysis and closed-loop control of a non-isolated boost three-port converter for stand-alone PV system

This study critically investigates analysis and control of non-isolated boost three-port DC to DC converter (TPC) forstandalone PV system. The converter is controlled such that regulates flow of power from PV array to load and batteries as storage devices.According to PV power, there are four operating modes of operation of converter. Simple reduced-order dynamic models of the converter in various modes of operation are obtained using state-space averaging and small-signal techniques. In this work, the controllers of the closed-loop scheme are designed and only two controllers are used to achieve output voltage regulation, and to extract maximum power from PV array under different operating conditions. Closed-loop system simulation is studied to verify the operation of converter with the designed controllers in different modes. Transition between modes is presented with solar radiation variation and change of connected loads. Experimental verification of control systems at different modes of operation is investigated. The experimental results show that the controllers can regulate the power flow between TPC three ports and regulate output voltage under PV irradiance variation and load changing. The controller shows good performance measures such as maximum settling time of 0.06 s, maximum steady-state ripples of ±0.8 %, and 99.3 % power efficiency.

Simultaneous design optimisation methodology for floating offshore wind turbine substructure and feedback-based control strategy

This research article explores the application of control co-design methodologies for optimising floating offshore wind turbine systems concurrently. The primary objective is to offer insights into concurrent design approaches employing an advanced genetic optimisation algorithm. To achieve this, a reduced-order dynamic model is employed to minimise computational time requirements, complemented by a modified version of the levelized cost of energy equation serving as the cost function. Furthermore, various optimisation scenarios are investigated under diverse wind and wave conditions to assess the advantages and drawbacks of increasing the complexity of dynamic cases used in evaluating the cost function. The optimised system designs are then compared against baseline floating system designs to underscore the advantages of employing this approach to floating wind turbine design.

On Dynamic Reduced Order Model for the Flexural Characteristics of Polyvinylidene Fluoride Composite-Based Functional Prototypes

On Dynamic Reduced Order Model for the Flexural Characteristics of Polyvinylidene Fluoride Composite-Based Functional Prototypes

Wireless Power Transfer System Model Reduction with Split Frequency Matching

Reduced-order dynamic models of wireless power transfer (WPT) systems are desired to simplify the analysis and design of power control, phase synchronization, and maximum efficiency tracking. The reduced-order dynamic phasor model is a good choice because of its straightforward physical meaning and concise mathematical formula. However, the model relies on the assumption of loose coupling and loses accuracy when the coupling becomes stronger. In this paper, a model reduction method with split frequency matching is proposed to improve model accuracy under relatively strong coupling conditions, which is suitable for most short-distance WPT applications, such as wireless electrical vehicle charging. Split frequency matching is achieved through a pair of conjugate equivalent mutual inductances, which are derived from the asymmetry characteristics of the full-order dynamic phasor model in the positive and negative frequency domains. The proposed model retains the advantages of the existing model while significantly improving the accuracy under strong coupling conditions. Its characteristics are verified by comparing the experimental results and model predictions under both large step changes and small-signal perturbations.

A generalized wind turbine cross section as a reduced-order model to gain insights in blade aeroelastic challenges

In this work, we present an approach to study the aeroelastic stability of a wind turbine by focusing on the dynamics of a blade cross section. We present a methodology to obtain a reduced-order model of the blade dynamics in the form of generalized cross-sectional quantities that approximates the aerodynamic and structural properties of the full blade. The motivation for the work is to gain a physical understanding of the influence of aerodynamic models such as dynamic wake and dynamic stall on the frequency and damping of the structure using a reduced-order model with low computational cost. The model may be coupled to two-dimensional computational fluid dynamics softwares or engineering unsteady airfoil aerodynamics models accounting for dynamic wake and dynamic stall. In the latter case, we can obtain monolithic state-space forms of the aeroelastic system of equations, which simplifies the determination of the modal parameters and therefore the study of stability. The work investigates wind turbines in operation or at standstill, where vortex-induced vibrations and stall-induced vibrations, respectively, might be an issue. The implementation is made available as part of the open-source Python package WELIB and as part of the open-source unsteady aerodynamic driver of OpenFAST.

Enhanced Tracking in Legged Robots through Model Reduction and Hybrid Control Techniques: Addressing Disturbances, Delays, and Saturation

This study introduces a reduced-order leg dynamic model to simplify the controller design and enhance robustness. The proposed multi-loop control scheme tackles tracking control issues in legged robots, including joint angle and contact-force regulation, disturbance suppression, measurement delay, and motor saturation avoidance. Firstly, model predictive control (MPC) and sliding mode control (SMC) schemes are developed using a simplified model, and their stability is analyzed using the Lyapunov method. Numerical simulations under two disturbances validate the superior tracking performance of the SMC scheme. Secondly, an Nth-order linear active disturbance rejection control (LADRC) is designed based on a simplified model and optimization problems. The second-order LADRC-SMC scheme reduces the contact-force control error in the SMC scheme by ten times. Finally, a fourth-order LADRC-SMC with a Smith Predictor (LADRC-SMC-SP) scheme is formulated, employing each loop controller independently. This scheme simplifies the design and enhances performance. Compared to numerical simulations of the above and existing schemes, the LADRC-SMC-SP scheme eliminates delay oscillations, shortens convergence time, and demonstrates fast force-position tracking responses, minimal overshoot, and strong disturbance rejection. The peak contact-force error in the LADRC-SMC-SP scheme was ten times smaller than that in the LADRC-SMC scheme. The integral square error (ISE) values for the tracking errors of joint angles θ1 and θ2, and contact force f, are 1.6636×10−28 rad2⋅s, 1.7983×10−28 rad2⋅s, and 1.8062×10−30 N2⋅s, respectively. These significant improvements in control performance address the challenges in single-leg dynamic systems, effectively handling disturbances, delays, and motor saturation.

The generalized spring-loaded inverted pendulum model for analysis of various planar reduced-order models and for optimal robot leg design

This paper proposes a generalized spring-loaded inverted pendulum (G-SLIP) model to explore various popular reduced-order dynamic models’ characteristics and suggest a better robot leg design under specified performance indices. The G-SLIP model’s composition can be varied by changing the model’s parameters, such as ground contacting type and spring property. It can be transformed into four widely used models: the spring-loaded inverted pendulum (SLIP) model, the two-segment leg model, the SLIP with rolling foot model, and the rolling SLIP model. The effects of rolling contact and spring configuration on the dynamic behavior and fixed-point distribution of the G-SLIP model were analyzed, and the basins of attraction of the four described models were studied. By varying the parameters of the G-SLIP model, the dynamic behavior of the model can be optimized. Optimized for general locomotion running at various speeds, the model provided leg design guidelines. The leg was empirically fabricated and installed on the hexapod for experimental evaluation. The results indicated that the robot with a designed leg runs faster and is more power-efficient.

Simulation-based digital twin of a high-speed turbomachine (fan) used in avionics cooling

In this contribution, the simulation-based digital twin of a high-speed turbomachine, i.e. a fan with a nominal speed of 16500 rpm, that has been developed for the aerospace industry with multiple uses in various platforms, and the corresponding findings are presented. The relevant simulation-based digital twin is created by first running various multi-physics engineering simulations, i.e. computational solid mechanics, computational fluid dynamics, and low-frequency electromagnetic analyses with Ansys software. Subsequent dynamic reduced order models (ROM) are formed and integrated together to create the digital twin that are bidirectionally connected with the asset. The digital twin is also validated via experimental data that are obtained with various setups for several parameters read at discrete locations via sensors, based on fidelity comparisons both between experiments and simulations, and between simulations and ROMs. Several operational scenarios including those with stress tests are run and the asset is checked against fatigue and thermal requirements for the rotor-stator assembly and the motor circuit respectively. This is done with an inhouse program that incrementally reads time, temperature, and rotational speed data and in which the relevant fatigue and thermal criteria are defined. This program is also used to simulate and analyse what-if scenarios. It is seen that vibration fatigue dominates all possible sources of failure in most cases. As a novel aspect, the fatigue induced by starts and stops of the fan is expressed as equivalent operating hours (EOH) depending on time and temperature parameters of the corresponding scenarios, as opposed to be taken as a constant value for all scenarios. Using this novelty, it is also conceptually demonstrated that simulation-based digital twins can play a significant role in operation and maintenance (O&M) when combined with conventional data-driven predictive maintenance techniques, not only for O&M teams but also asset owners and original equipment manufacturers (OEMs) particularly with the use of what-if analyses. Approaches to simulation-based digital twins in context with multi-physics and ROM fidelity are also discussed based on several digital twin maturity models.

Ensuring the accuracy of indirect nonlinear dynamic reduced-order models

Numerous powerful methods exist for developing reduced-order models (ROMs) from finite element (FE) models. Ensuring the accuracy of these ROMs is essential; however, the validation using dynamic responses is expensive. In this work, we propose a method to ensure the accuracy of ROMs without extra dynamic FE simulations. It has been shown that the well-established implicit condensation and expansion (ICE) method can produce an accurate ROM when the FE model’s static behaviour are captured accurately. However, this is achieved via a fitting procedure, which may be sensitive to the selection of load cases and ROM’s order, especially in the multi-mode case. To alleviate this difficulty, we define an error metric that can evaluate the ROM’s fitting error efficiently within the displacement range, specified by a given energy level. Based on the fitting result, the proposed method provides a strategy to enrich the static dataset, i.e. additional load cases are found until the ROM’s accuracy reaches the required level. Extending this to the higher-order and multi-mode cases, some extra constraints are incorporated into the standard fitting procedure to make the proposed method more robust. A curved beam is utilised to validate the proposed method, and the results show that the method can robustly ensure the accuracy of the static fitting of ROMs.

Sparse identification modeling and predictive control of wafer temperature in an atomic layer etching reactor

To address the escalating demand and supply constraints for semiconductor devices, manufacturing techniques such as thermal atomic layer etching (ALE) have been utilized, which require robust temperature control systems. Radiative heating with lamps is a promising method for achieving fast and precise temperature control. However, there is limited research in analyzing the dynamic control of radiative lamp heating systems. In this study, a transient, two-dimensional (2-D) radiative heating model in a cross-flow thermal ALE reactor is constructed through Ansys Fluent. A sparse identification (SINDy) modeling approach is applied to build a reduced-order dynamic model for the prediction of system states in the control system. A model predictive controller (MPC) is then developed to bring the wafer surface temperature to the target temperature while preserving the uniformity of the temperature on the wafer surface. Control is implemented by adjusting the powers of three groups of heating lamps independently. Notably, a novel feedback-based time-varying steady-state penalty approach is applied with the MPC in this study, which enables the system to reach the target temperature range within 10 s while maintaining temperature uniformity for 1000 s.

Flexibility extension in hydropower for the provision of frequency control services within the European energy transition

This paper presents a comprehensive assessment of the large-scale deployment of hydropower on the provision of frequency regulation services, when equipped with the extended flexibility solutions being developed and/or tested within the scope of the XFLEX HYDRO project. The current analysis is performed on the Iberian Peninsula (IP) power grid considering its interconnection to the Continental Europe (CE) system, since this power system zone is expected to have the most severe frequency transient behaviour in future scenarios with increased shares of variable renewable energies. For this purpose, prospective scenarios with increased shares of time variable renewable generation were identified and analysed. To assess the impacts of the hydropower flexibility solutions on frequency dynamics after a major active power loss, extensive time domain simulations were performed of the power system, including reliable reduced order dynamic models for the hydropower flexibility solutions under evaluation. This research assesses the effects of synchronous and synthetic inertia, and of the Frequency Containment Reserve (FCR) and Fast Frequency Response (FFR) services as specified in European grid codes. The main findings highlight the potential of hydropower inertia and of adopting a variable speed technology for enhancing frequency stability, while contribute to better understand the role of hydropower plants in future power systems.

Dynamic modelling of cross-flow printed circuit heat exchangers for multistage reactor intercooling

A reduced-order dynamic model of a cross-flow printed circuit heat exchanger was developed to study both steady-state and transient performance under conditions that would be encountered in multistage catalytic combustion reactors to better understand how they can be used to minimize fluctuations in heat-integrated reactors and intensified processes. Previous transient models for cross-flow heat exchangers rely on an initial steady state and apply only for changes in inlet temperature, but this work presents a model that can be applied to intermediate states or multiple concurrent upstream process changes. Steady-state simulations showed that larger channels reduce volumetric heat transfer performance and effectiveness due to convective resistance. Furthermore, larger channel spacing increases effectiveness but also reduces compactness. Operating temperature was found to have a minimal effect on the overall heat transfer coefficient and effectiveness within the range of conditions studied, and operating pressure was found to have no effect on heat transfer. Transient analyses showed that the response to a unit step in temperature matches closely with an analytical infinite gas velocity model, both for time constants and the overall thermal response, with initial variations in outlet temperatures from ideal-case models below 3.8 % of unit step magnitudes, and average differences below 0.75 %. Transient analyses also show the effects of a finite fluid velocity which is critical in the transient response of large heat exchangers. The presented numerical model can also be more easily extended to complex configurations and can be applied to other changes in inlet conditions such as changing composition and flow rates as are found in combustion applications. A three-fluid thermal management system for a multistage packed-bed microreactor using printed circuit heat exchangers is proposed and modelled to provide a method for temperature regulation and pre-heating of fresh reactor feed.

Dynamic mode decomposition for data-driven analysis and reduced-order modeling of E × B plasmas: II. Dynamics forecasting

In part I of the article, we demonstrated that a variant of the dynamic mode decomposition (DMD) algorithm based on variable projection optimization, called optimized DMD (OPT-DMD), enables a robust identification of the dominant spatiotemporally coherent modes underlying the data across various test cases representing different physical parameters in an E × B simulation configuration. We emphasized that the OPT-DMD significantly improves the analysis of complex plasma processes, revealing information that cannot be derived using conventionally employed analyses such as the fast Fourier transform. As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs) by construction, in this paper, we extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics in configurations representative of the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and over a range of simulation parameters in each test case. The predictive capacity of the OPT-DMD ROM is assessed primarily in terms of short-term dynamics forecast or, in other words, for large ratios of training-to-test data. However, the utility of the ROM for long-term dynamics forecasting is also presented for an example case in the radial-azimuthal configuration. The model’s predictive performance is heterogeneous across various test cases. Nonetheless, a remarkable predictiveness is observed in the test cases that do not exhibit highly transient behaviors. Moreover, in all investigated cases, the error between the ground-truth and the reconstructed data from the OPT-DMD ROM remains bounded over time within both the training and the test window. As a result, despite its limitation in terms of generalized applicability to all plasma conditions, the OPT-DMD is proven as a reliable method to develop low computational cost and highly predictive data-driven ROMs in systems with a quasi-periodic global evolution of the plasma state.

On digital twinning of fused filament fabrication for tensile properties of polyvinylidene fluoride composites-based functional prototypes

In the last two decades, several studies have been conducted for the process parametric optimization of fused filament fabrication (FFF) with a variety of thermoplastic composites, especially for mechanical properties. But hitherto less has been conveyed, on the development of dynamic reduced order models (ROMs) for digital twining (DT) of tensile properties (of 3D printed implants/scaffolds) with novel thermoplastic-based composites. In this study, for the generation of dynamic ROM (for hybrid analytics), the signal-to-noise (S/N) ratio was used to ascertain the best settings of parameters for tensile properties of polyvinylidene fluoride (PVDF) composite. The study suggests that the best setting of the FFF process, for the 3D printing of PVDF composite (90% PVDF, 8% hydroxyapatite (HAp), and 2% Chitosan (CS) (for maximizing the tensile properties as per ASTM-D638-Type-V) are nozzle temperature (NT) of 235°C, raster angle (RA) 45°, printing speed (PS) of 60 mm/s respectively resulting in peak load (PL) 394.87 N, peak stress (PSt) 33.92 MPa, Young’s modulus (E) 2.606 MPa. For a modulus of toughness (MOT) of 0.484 MPa, the best settings are NT 230°C, RA 90°, and PS 50 mm/s. The results are supported by the morphological analysis.

Two-Step Adaptive Control for Planar Type Docking of Autonomous Underwater Vehicle

Planar type docking enables a convenient underwater energy supply for irregularly shaped autonomous underwater vehicles (AUVs), but the corresponding control method is still challenging. Conventional control methods for torpedo-shaped AUVs are not suitable for planar type docking due to the significant differences in system structures and motion characteristics. This paper proposes a two-step adaptive control method to solve the planar type docking problem. The method makes a seamless combination of horizontal dynamic positioning and visual servo docking considering ocean current disturbance. The current disturbance is estimated and canceled in the pre-docking step using a current observer, and the positioning error is further compensated for by the vertical visual servo technique in the docking step. Reduced order dynamic models are distinctively established for different docking steps according to the motion characteristics, based on which the dynamic controllers are designed considering the model parameter uncertainties. Simulation is conducted with an initial distance of 10 m in the horizontal direction and 3 m in depth. Stable and accurate dynamic positioning under up to 0.4 m/s of current disturbances with different directions is validated. A 0.5 m lateral positioning error is successfully compensated for by the visual servo docking step. The proposed control method provides a valuable reference for similar types of docking application.

Approximate Analytical Solutions for Launch-Vehicle Ascent Trajectory

Approximate analytical solutions for the ascent trajectory of a solid-fuel launch vehicle are derived. To the best of the authors' knowledge, the solutions are the ones achieving the highest accuracy in ascent-trajectory prediction under the condition of high angle-of-attack (AOA) maneuvers, where the magnitude of AOA can even be greater than 60 deg at high altitudes. As the first step of deriving the solutions, a reduced-order dynamics model with a normalized mass as the independent variable is put forward for longitudinal-plane flight. To further simplify the model, the sine of AOA is chosen as the key parameter for trajectory control and designed as a polynomial of the normalized mass. Meanwhile, an improved aerodynamic model with the sine of AOA as the independent variable is developed. Due to high AOA, the simplified dynamics model is still highly nonlinear and difficult to solve. To overcome this difficulty, by performing force analysis, several approximate polynomials and first-order Taylor series expansions are created to replace some highly nonlinear but relatively small terms in the dynamical equations, while the errors of the approximate formulae relative to the original nonlinear terms are retained and treated as minor perturbations. The benefit is that the modified dynamics model can be divided into two analytically solvable subsystems using a perturbation method. By solving the subsystems, the approximate analytical solutions for downrange, altitude, velocity and flight-path angle (FPA) of the vehicle are obtained successfully. Simulation results verify that the proposed solutions are much more accurate than the existing solutions in the scenario of high AOA flight.