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DOE OSTI2025

Scanless laser waveform measurement in the near-infrared

Field-resolved measurements of few-cycle laser waveforms allow access to ultrafast electron dynamics in light–matter interactions and are key to future lightwave electronics. Recently, sub-cycle gating based on nonlinear excitation in active pixel sensors has allowed the first single-shot measurements of mid-infrared optical fields. Extending the techniques to shorter wavelengths, however, is not feasible using silicon-based detectors with bandgaps in the near-infrared. Here, we demonstrate an all-optical sampling technique for near-infrared laser fields, wherein an intense fundamental field generates a sub-cycle gate through nonlinear excitation of a wide-bandgap crystal, in this case, ZnO, which can sample the electric field of a weak perturbing pulse. By using a crossed-beam geometry, the temporal evolution of the perturbing field is mapped onto a transverse spatial axis of the nonlinear medium, and the waveform is captured in a single measurement of the spatially resolved fluorescence emission from the crystal. The technique is demonstrated through field-resolved measurements of the field reshaping during nonlinear propagation in the ZnO detection crystal.

Truong, Tran-Chau (ORCID:0000000348940635)↗
DOE OSTI2023

Effect of the neutral beam injector operational regime on the Alfven eigenmode saturation phase in DIII-D plasma

The aim of this study is to analyze the effect of the neutral beam injector (NBI) operation regime on the saturation phase of the Alfven Eigenmodes (AEs) in DIII-D plasma. Here, the analysis is done using the linear and nonlinear versions of the gyro-fluid code FAR3d. A set of parametric analyses are performed modifying the nonlinear simulation EP $β$ (NBI injection power), EP energy (NBI voltage) and the radial location of the EP density profile gradient (NBI radial deposition). The analysis indicates a transition from the soft (local plasma relaxation) to the hard MHD (global plasma relaxation) limit if the simulation EP $β$ $\unicode{x2A7E}$ $0.02$, leading to bursting MHD activity caused by radial AEs overlapping. MHD bursts cause an enhancement of the EP transport showing ballistic-like features as avalanche-like events. Simulations in the soft MHD limit show an increment of the EP density gradient as the EP $β$ increases. On the other hand, there is a gradient upper limit in the hard MHD limit, consistent with the critical-gradient behavior. AEs induce shear flows and zonal current leading to the deformation of the flux surfaces and the safety factor profile, respectively, particularly strong for the simulation in the hard MHD limit. Simulations in the hard MHD regime show a decrease of the AE frequency in the saturation phase; this is caused by the destabilization of a transitional mode between a $9/3-10/3$ TAE and a $9/3$ RSAE that may explain the AE frequency down-sweeping observed in some DIII-D discharges. Reducing the EP energy in the nonlinear simulations leads to a weakening of the plasma perturbation. On the other hand, increasing the EP energy causes the opposite effect. Nonlinear simulations of off-axis NBI profiles indicate a lower plasma perturbation as the EP density gradient is located further away from the magnetic axis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

The principle of minimal power

This article is devoted to the memory of Yuri P Raizer, who passed away in 2021. He left a noticeable trace in gas discharge physics. The principle of minimal power (the state that requires minimal power is most probable) is thoroughly used in his books. Although the fundamental laws of physics do not imply this ad hoc principle, a detailed analysis of underlying phenomena can often reveal why nature prefers this path. Raizer illustrated this principle for plasma stratification, formation of electrode spots, discharge constriction, the shape of an arc channel, etc. We argue that the nonlinearity of equations describing gas discharges can often justify the realization of a plasma state maintained at minimal electric power. This nonlinearity appears because small groups of energetic electrons often control the ionization processes. The number of these electrons depends strongly on the ratio of the electric field to gas density, E/N. Under certain conditions, the ionization rate can also depend nonlinearly on electron density due to stepwise ionization and Coulomb collisions. Here, we use the principle of minimal power to illustrate some of Raizer's contributions to gas discharge physics from a single point of view. We demonstrate that nonlinearity of ionization processes in gas discharges can substantiate this principle for plasma stratification. However, striations of s, p, and r types in neon could exist with minimal or no ionization enhancement. This reminds us of Raizer's warning that applying the minimal power principle could lead to erroneous predictions, and a proper theory is required in each case to justify its use. 'The phenomenon of striations satisfies the principle of minimal power' – Yuri Raizer

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simulation of the TAEs’ saturation phase in the Large Helical Device: MHD burst

Here, the aim of the present study is to analyze the saturation regime of the toroidal Alfven eigenmodes (TAE) in the Large Helical Device plasma, particularly the MHD burst. The linear and nonlinear evolution of the TAEs are simulated by the FAR3d code that uses a reduced MHD model for the thermal plasma coupled with a gyrofluid model for the energetic particle (EP) species. The linear simulations indicate the overlapping of 1/2–1/1, 2/3–2/4 and 3/5–3/6 TAEs in the inner-middle plasma region and frequency range of 45–75 kHz, triggered by EPs with an energy of T f = 45 keV and EP β = 0.022. The nonlinear simulations show that 2/3–2/4 and 3/4–3/5 TAEs are further destabilized due to the energy transfer from the 1/1–1/2 TAE, leading to broad TAE radial overlapping and triggering of the MHD burst. The energy of the 1/1–1/2 TAE is also nonlinearly transferred to the thermal plasma destabilizing the 0/0 and 0/1 modes, inducing the generation of shear flows and zonal currents, as well as large deformations in the thermal pressure and EP density radial profiles. The nonlinear simulation reproduces the same succession of instabilities and the same frequency range with respect to the experiment. The instability propagates outward during the bursting phase, showing a large decrease of the EP density profile between the middle-outer plasma, indicating the loss of part of the EP population that explains the decrease in the plasma heating efficiency observed during the MHD burst.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Abstract Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane n e , s e p O M P and the electron temperature at the outer divertor T e , s e p d i v . Note that T e , s e p d i v is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in T e , s e p d i v , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in n e , s e p O M P and 5%–10% in T e , s e p d i v for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in n e , s e p O M P using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Prediction of pellet mass thresholds for ELM triggering in low-collisionality, ITER-like discharges

Abstract In ITER, pellets are calculated to require more than 8 times the mass than currently planned to reliably trigger edge-localized modes (ELMs). Unmitigated heat flux impulses from ELMs are intolerable in ITER at full power and current. Therefore, ITER operation relies on multiple approaches to control ELM heat fluxes. One method is pellet ELM pacing to instigate small rapid ELMs with low heat flux. Predicting the performance of pellet pacing is critical for ITER, which is expected to operate in a regime with a low-collisionality, peeling-limited pedestal. However, to trigger ELMs the local pressure increase in the expanding pellet cloud pushes the equilibrium over the ballooning stability limit. In this work, linear and nonlinear M3D-C1 simulations are used to predict pellet mass thresholds in DIII-D discharges and ITER scenarios with peeling-limited pedestals. It is found that the distance of the equilibrium’s operational point from the ballooning branch of the pedestal stability boundary strongly changes thresholds. Linear M3D-C1 simulations find a strong dependence of the pellet mass threshold on the poloidal injection location for ITER’s 15 MA, Q = 10 scenario. The required pellet mass at the planned injection locations is 8 to 17 times larger than currently considered. However, such linear simulations do not include pellet ablation physics or time evolution of density and temperature. A new scheme of 2D nonlinear simulations, coupled with linear stability analysis at various steps throughout the nonlinear time evolution, was developed to include such physics and improve on the linear results. These new nonlinear-to-linear simulations confirm previous findings. This result suggests that pellet ELM triggering in ITER could require pellets much larger than those currently planned, which makes ELM-pacing operationally challenging. On the other hand, fueling pellets injected from the high-field side will likely not unintentionally trigger ELMs in an otherwise ELM-stable plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Verification of Floating Offshore Wind Linearization Functionality in OpenFAST

The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations, e.g., for design standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system properties and exploit well-established methods and tools for analyzing linear systems. Previous work in this area has focused on the development of the new linearization functionality of the open-source engineering tool OpenFAST for floating offshore wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly. This paper focuses on the verification of this new linearization functionality, which is carried out by comparing results to previous stable versions of FAST. A nonlinear time-domain simulation for a floating offshore platform is also compared to the time-domain response of the linearized state-space model. The linearized results show good alignment between OpenFAST and previous versions of FAST, as well as with the time-domain simulations, thereby showing the accuracy of the new features in OpenFAST.

17 WIND ENERGY↗
DOE OSTI2021

Minimal two-body quantum absorption refrigerator

Here, we study the phenomenon of absorption refrigeration, where refrigeration is achieved by heating instead of work, in two different setups: a minimal set up based on coupled qubits and two nonlinearly coupled resonators. Considering ZZ interaction between the two qubits, we outline the basic ingredients required to achieve cooling. Using local as well as global master equations, we observe that inclusion of an XX type term in the qubit-qubit coupling is detrimental to cooling. We compare the cooling effect obtained in the qubit case with that of nonlinearly coupled resonators (multilevel system) where the ZZ interaction translates to a Kerr-type nonlinearity. For small to intermediate strengths of nonlinearity, we observe that multilevel quantum systems, for example qutrits, give better cooling effect compared to the qubits. Using Keldysh nonequilibrium Green's function formalism, we go beyond first order sequential tunneling processes and study the effect of higher order processes on refrigeration. We find a reduced cooling effect compared to the master equation calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Drude weights in one-dimensional systems with a single defect

Ballistic transport of a quantum system can be characterized by Drude weight, which quantifies the response of the system to a uniform electric field in the infinitely long timescale. The Drude weight is often discussed in terms of the Kohn formula, which gives the Drude weight by the derivative of the energy eigenvalue of a finite-size system with the periodic boundary condition in terms of the Aharonov-Bohm flux. Recently, the Kohn formula is generalized to nonlinear responses. However, the nonlinear Drude weight determined by the Kohn formula often diverges in the thermodynamic limit. In order to elucidate the issue, in this work we examine a simple example of a one-dimensional tight-binding model in the presence of a single defect at zero temperature. We find that its linear and nonlinear Drude weights given by the Kohn formula (i) depend on the Aharonov-Bohm flux and (ii) diverge proportionally to a power of the system size. Here, we argue that the problem can be attributed to different order of limits. The Drude weight according to the Kohn formula (“Kohn-Drude weight”) indicates the response of a finite-size system to an adiabatic insertion of the Aharonov-Bohm flux. While it is a well-defined physical quantity for a finite-size system, its thermodynamic limit does not always describe the ballistic transport of the bulk. The latter should be rather characterized by a “bulk Drude weight” defined by taking the thermodynamic limit first before the zero-frequency limit. While the potential issue of the order of limits has been sometimes discussed within the linear response, the discrepancy between the two limits is amplified in nonlinear Drude weights. We demonstrate the importance of the low-energy excitations of O(1/L), which are excluded from the Kohn-Drude weight, in regularizing the bulk Drude weight.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Dark Energy Survey Year 3 results: Cosmology from combined galaxy clustering and lensing validation on cosmological simulations

In this work, we present a validation of the Dark Energy Survey Year 3 (DES Y3) 3×2-point analysis choices by testing them on Buzzard2.0, a new suite of cosmological simulations that is tailored for the testing and validation of combined galaxy clustering and weak-lensing analyses. We show that the buzzard2.0 simulations accurately reproduce many important aspects of the DES Y3 data, including photometric redshift and magnitude distributions, and the relevant set of two-point clustering and weak-lensing statistics. We then show that our model for the 3×2-point data vector is accurate enough to recover the true cosmology in simulated surveys assuming the true redshift distributions for our source and lens samples, demonstrating robustness to uncertainties in the modeling of the nonlinear matter power spectrum, nonlinear galaxy bias, and higher-order lensing corrections. Additionally, we demonstrate for the first time that our photometric redshift calibration methodology, including information from photometry, spectroscopy, clustering cross-correlations, and galaxy–galaxy lensing ratios, is accurate enough to recover the true cosmology in simulated surveys in the presence of realistic photometric redshift uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT and P l a n c k . II. Cross-correlation measurements and cosmological constraints

Cross-correlations of galaxy positions and galaxy shears with maps of gravitational lensing of the cosmic microwave background (CMB) are sensitive to the distribution of large-scale structure in the Universe. Such cross-correlations are also expected to be immune to some of the systematic effects that complicate correlation measurements internal to galaxy surveys. We present measurements and modeling of the cross-correlations between galaxy positions and galaxy lensing measured in the first three years of data from the Dark Energy Survey with CMB lensing maps derived from a combination of data from the 2500 deg 2 SPT-SZ survey conducted with the South Pole Telescope and full-sky data from the Planck satellite. The CMB lensing maps used in this analysis have been constructed in a way that minimizes biases from the thermal Sunyaev Zel’dovich effect, making them well suited for cross-correlation studies. The total signal-to-noise of the cross-correlation measurements is 23.9 (25.7) when using a choice of angular scales optimized for a linear (nonlinear) galaxy bias model. Here we use the cross-correlation measurements to obtain constraints on cosmological parameters. For our fiducial galaxy sample, which consist of four bins of magnitude-selected galaxies, we find constraints of Ω m =0.272$^{+0.032}_{-0.052}$ and S 8 ≡σ8$\sqrt{Ω_m/0.3}$=0.736$^{+0.032}_{-0.028}$ (Ω m =0.245$^{+0.026}_{-0.044}$ and S 8 =0.734$^{+0.035}_{-0.028}$) when assuming linear (nonlinear) galaxy bias in our modeling. Considering only the cross-correlation of galaxy shear with CMB lensing, we find Ω m =0.270$^{+0.043}_{-0.061}$ and S 8 =0.740$^{+0.034}_{-0.029}$. Our constraints on S8 are consistent with recent cosmic shear measurements, but lower than the values preferred by primary CMB measurements from Planck.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atom-based sensing

Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics U ( φ ) (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of φ even when the nonlinearities are applied for times much shorter than required to produce Schrödinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator n → · J → . We consider the following physical settings: all-to-all interactions generated by one-axis twisting J z 2 (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cramér-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of L without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an L layer quantum alternating operator ansatz.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Potential quantum advantage for simulation of fluid dynamics

Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·$\triangledown$u) to lattice-Boltzmann nonlinearity (u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

42 ENGINEERING↗
DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗
DOE OSTI2020

Linear Approximation Line Pack Model for Integrated Electricity and Natural Gas Systems OPF

With the increasing installation of renewable energy electricity generation capacity, the penetration of natural gas fired generation is also substantailly increasing in power systems due to their fast response capability to mitigate system variability and uncertainty. The dependencies between the electricity system and the natural gas system are becoming more important to maintain the reliability of both systems. In integrated electricity and natural gas systems (IEGSs) operations, the nonlinearity of the natural gas system brings challenges to the system operators. In this paper, the IEGSs optimal power flow (OPF) model is proposed that includes the line pack of the gas system via linear approximation. The simulation results demonstrate that the proposed model can obtain optimal solutions efficiently that are comparable in accuracy as the nonlinear line pack model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Analytical Large-Signal Modeling of Inverter-Based Microgrids With Koopman Operator Theory for Autonomous Control

The microgrid (MG) plays a crucial role in the energy transition, but its nonlinearity presents a significant challenge for large-signal power systems studies in the electromagnetic transient (EMT) time scale. In this paper, we develop a large-signal linear MG model that considers the detailed dynamics of the primary and zero-control levels based on the Koopman operator (KO) theory. Firstly, a set of observable functions is carefully designed to capture the nonlinear dynamics of the MG. The corresponding linear KO is then analytically derived based on these observables, resulting in the linear representation of the original nonlinear MG with observables as the new coordinate. The influence of external input on the system dynamics is also considered during the derivation, enabling control of the MG. We solve the voltage control problem using the traditional linear quadratic integrator (LQI) method to demonstrate that textbook linear control techniques can accurately control the original nonlinear MG via the developed KO-linearized MG model. Our proposed KO linearization method is generic and can be easily extended for different control objectives and MG structures using our analytical derivation procedure. Here, we validate the effectiveness of our methodology through various case studies.

25 ENERGY STORAGE↗
DOE OSTI2020

Water and vapor transport in algal‐fungal lichen: Modeling constrained by laboratory experiments, an application for Flavoparmelia caperata

ABSTRACT Algal‐fungal symbionts share water, nutrients, and gases via an architecture unique to lichens. Because lichen activity is controlled by moisture dynamics, understanding water transport is prerequisite to understand their fundamental biology. We propose a model of water distributions within foliose lichens governed by laws of fluid motion. Our model differentiates between water stored in symbionts, on extracellular surfaces, and in distinct morphological layers. We parameterize our model with hydraulic properties inverted from laboratory measurements of Flavoparmelia caperata and validate for wetting and drying. We ask: (1) Where is the bottleneck to water transport? (2) How do hydration and dehydration dynamics differ? and (3) What causes these differences? Resistance to vapor flow is concentrated at thallus surfaces and acts as the bottleneck for equilibrium, while internal resistances are small. The model captures hysteresis in hydration and desiccation, which are shown to be controlled by nonlinearities in hydraulic capacitance. Muting existing nonlinearities slowed drying and accelerated wetting, while exaggerating nonlinearities accelerated drying and slowed wetting. The hydraulic nonlinearity of F. caperata is considerable, which may reflect its preference for humid and stable environments. The model establishes the physical foundation for future investigations of transport of water, gas, and sugar between symbionts.

Potkay, Aaron↗
DOE OSTI2022

Control Design for a Marine Hydrokinetic Cycloturbine Vehicle

Abstract Marine Hydrokinetic (MHK) cycloturbines generate sustainable power by exploiting tidal currents. By powering the turbines and using pitching foils for control, a vehicle comprised of MHK cycloturbines also has the ability to station keep and maneuver. The vehicle consists of four counter-rotating cycloturbines, with hydrofoils oriented perpendicular to the flow in a paddlewheel configuration. Lift and drag generated from these foils sum together to produce thrust. An experimentally tuned simulation model that solves the six-degrees-of-freedom rigid body equations of motion for the MHK vehicle subject to hydrodynamic, hydrostatic, and propulsive forces is used to aid the design of vehicle controllers. Global feedback controllers are initially designed by applying classical control methods to an approximate linear model of the system dynamics. A higher performing nonlinear controller is designed using the nonlinear dynamic inversion (NDI) method. NDI accounts for the nonlinearities of the MHK system and therefore is suitable for a wide range of operating conditions. The response of the classical and NDI controllers to speed, depth, roll, pitch, and yaw commands are evaluated and compared in simulation. The classical controller outperforms the NDI controller for small amplitude maneuvers, although the degradation with NDI is minor. However, in the nonlinear operating regime the NDI controller outperforms the classical controller and the classical controller exhibits instability.

Automation & Control Systems↗