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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.

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NASA NTRS2019

The Effects of an Improved Dynamic Vegetation Phenology Representation in a Global Land Surface Model

Evapotranspiration (ET) is a major driver of the interaction between the land surface and the atmosphere through its component mechanisms, including plant transpiration (T) and soil evaporation. To accurately capture land-atmosphere interactions in global Earth System Models, it is thus critical that the underlying land surface models accurately model both the land hydrology as well as the dynamic response of vegetation to environmental drivers. In an effort to introduce a more realistic vegetation representation, the NASA Catchment land surface model, which is part of the Goddard Earth Observing System (GEOS), has previously been merged with the carbon and nitrogen physics modules of the Community Land Model version 4, resulting in the new Catchment-CN model. Catchment-CN has inherited the advanced treatment of land surface hydrology of Catchment, but is additionally able to dynamically model the response of vegetation to environmental drivers, in contrast to the fixed vegetation climatology that was prescribed in Catchment. Recently, the parameterization of Catchment-CN vegetation has been augmented to better account for variability of vegetation responses to external forcings within existing plant functional types, and vegetation parameters have been calibrated against Moderate Resolution Imaging Spectrometer observations of the fraction of absorbed photosynthetically radiation. These efforts have led to a significant reduction in the RMSE of modeled photosynthetic activity with respect to observations.This presentation investigates the effect of the improved vegetation representation on the partitioning of ET within Catchment-CN. Specifically, we compare global maps of the T:ET ratio across different temporal scales in (1) the original Catchment model, (2) the original Catchment-CN model, and (3) the augmented and calibrated Catchment-CN model. The modeled T and ET estimates are compared against a comprehensive set of ground observations from various field studies, as well as independent global T:ET estimates from different ET algorithms provided in the context of the Water Cycle Observation Multi-mission Strategy ? Evapotranspiration (WACMOS-ET) initiative.

Kolassa, J.↗
NASA NTRS2020

An Observation‐Driven Approach to Improve Vegetation Phenology in a Global Land Surface Model

An empirical model calibration approach is presented that aims to approximate missing biosphere processes in a global land surface model without the need for substantial model structural changes. The strategy is implemented here using the NASA Catchment‐CN land surface model and Moderate Resolution Imaging Spectroradiometer (MODIS) observations of the fraction of absorbed photosynthetically active radiation (FPAR). Existing plant functional types (PFTs) of the Catchment‐CN model are divided into three subtypes, based on the bias between the model‐simulated and MODIS‐observed FPAR. Separate sets of vegetation parameters for each subtype are then calibrated at a small number of grid cells with homogeneous, single‐PFT land cover, using MODIS FPAR reference observations from 2003 to 2009. The effectiveness of the empirical approach at improving the realism of modeled vegetation dynamics is investigated with two global model simulations for the period 2010–2016, one using the newly calibrated parameter values and the other using the original values. Globally, the calibrated parameters reduce the root mean square error (RMSE) of the modeled FPAR with respect to MODIS by 0.029 (∼10%) on average. In some regions, substantially larger RMSE reductions are achieved. RMSE reductions are primarily driven by model bias reductions, with neutral effects on the temporal correlation skill. While the empirical approach is suitable for achieving consistent model improvements, it is shown to be sensitive to the characteristics of the model error, specifically a dominance of the bias component in the case of Catchment‐CN. Ultimately, more fundamental model structural changes may be required to achieve better improvements.

J. Kolassa↗
NASA NTRS2021

Cutting out the Middleman: Calibrating and Validating a Dynamic Vegetation Model (ED2-PROSPECT5) Using Remotely Sensed Surface Reflectance

Canopy radiative transfer is the primary mechanism by which models relate vegetation composition and state to the surface energy balance, which is important to light- and temperature-sensitive plant processes as well as understanding land–atmosphere feedbacks. In addition, certain parameters (e.g., specific leaf area, SLA) that have an outsized influence on vegetation model behavior can be constrained by observations of shortwave reflectance, thus reducing model predictive uncertainty. Importantly, calibrating against radiative transfer outputs allows models to directly use remote sensing reflectance products without relying on highly derived products (such as MODIS leaf area index) whose assumptions may be incompatible with the target vegetation model and whose uncertainties are usually not well quantified. Here, we created the EDR model by coupling the two-stream representation of canopy radiative transfer in the Ecosystem Demography model version 2 (ED2) with a leaf radiative transfer model (PROSPECT-5) and a simple soil reflectance model to predict full-range, high-spectral-resolution surface reflectance that is dependent on the underlying ED2 model state. We then calibrated this model against estimates of hemispherical reflectance (corrected for directional effects) from the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and survey data from 54 temperate forest plots in the northeastern United States. The calibration significantly reduced uncertainty in model parameters related to leaf biochemistry and morphology and canopy structure for five plant functional types. Using a single common set of parameters across all sites, the calibrated model was able to accurately reproduce surface reflectance for sites with highly varied forest composition and structure. However, the calibrated model's predictions of leaf area index (LAI) were less robust, capturing only 46 % of the variability in the observations. Comparing the ED2 radiative transfer model with another two-stream soil–leaf–canopy radiative transfer model commonly used in remote sensing studies (PRO4SAIL) illustrated structural errors in the ED2 representation of direct radiation backscatter that resulted in systematic underestimation of reflectance. In addition, we also highlight that, to directly compare with a two-stream radiative transfer model like EDR, we had to perform an additional processing step to convert the directional reflectance estimates of AVIRIS to hemispherical reflectance (also known as “albedo”). In future work, we recommend that vegetation models add the capability to predict directional reflectance, to allow them to more directly assimilate a wide range of airborne and satellite reflectance products. We ultimately conclude that despite these challenges, using dynamic vegetation models to predict surface reflectance is a promising avenue for model calibration and validation using remote sensing data.

Alexey N Shiklomanov↗
NASA NTRS2022

Aboveground biomass density models for NASA’s Global Ecosystem Dynamics Investigation (GEDI) lidar mission

NASA’s Global Ecosystem Dynamics Investigation (GEDI) is collecting spaceborne full waveform lidar data with a primary science goal of producing accurate estimates of forest aboveground biomass density (AGBD). This paper presents the development of the models used to create GEDI’s footprint-level (~25 m) AGBD (GEDI04_A) product, including a description of the datasets used and the procedure for final model selection. The data used to fit our models are from a compilation of globally distributed spatially and temporally coincident field and airborne lidar datasets, whereby we simulated GEDI-like waveforms from airborne lidar to build a calibration database. We used this database to expand the geographic extent of past waveform lidar studies, and divided the globe into four broad strata by Plant Functional Type (PFT) and six geographic regions. GEDI’s waveform-to-biomass models take the form of parametric Ordinary Least Squares (OLS) models with simulated Relative Height (RH) metrics as predictor variables. From an exhaustive set of candidate models, we selected the best input predictor variables, and data transformations for each geographic stratum in the GEDI domain to produce a set of comprehensive predictive footprint-level models. We found that model selection frequently favored combinations of RH metrics at the 98th, 90th, 50th, and 10th height above ground-level percentiles (RH98, RH90, RH50, and RH10, respectively), but that inclusion of lower RH metrics (e.g. RH10) did not markedly improve model performance. Second, forced inclusion of RH98 in all models was important and did not degrade model performance, and the best performing models were parsimonious, typically having only 1-3 predictors. Third, stratification by geographic domain (PFT, geographic region) improved model performance in comparison to global models without stratification. Fourth, for the vast majority of strata, the best performing models were fit using square root transformation of field AGBD and/or height metrics. There was considerable variability in model performance across geographic strata, and areas with sparse training data and/or high AGBD values had the poorest performance. These models are used to produce global predictions of AGBD, but will be improved in the future as more and better training data become available.

Laura Duncanson↗
NASA NTRSDate not supplied

Can We Model Forest Demography Globally? Benchmarking of State-of-the-Art Demographic DGVMs

Forests in Dynamic Global Vegetation Models (DGVMs) have historically been simulated as area-averaged plant functional types in each gridcell instead of representing communities of trees of different sizes and ages (demography). Just as the behaviour of a tree differs according to its ontogeny, so the behaviour of forests is known to differ depending on their demography. Accurately simulating demography is therefore key in order to address questions on afforestation and management strategies, as well as assessments of resilience of forests to disturbances such as drought and fire or diversity changes after a disturbance. Ultimately, demography determines the overall forest biomass in natural forests and is a key arbiter of growth and mortality rates. DGVMs are now able to simulate size and age structure of the trees in forests. However, these models have so far not been benchmarked alongside each other. We evaluate 6 DGVMs (BiomeE, CABLE-POP, FATES, LPJ-GUESS, JULES-RED, ORCHIDEE) against observations on regrowth dynamics as well as natural forests at boreal, temperate and tropical sites. We examine whether the models capture observed regrowth dynamics after disturbance, well-known stand size structure and well-established processes such as self-thinning. We outline the planned route forward towards a standardised international benchmarking framework for demographic DGVMs.

Dynamic Global Vegetation Models↗
NASA NTRS2024

Unveiling the Transferability of PLSR Models for Leaf Trait Estimation: Lessons from a Comprehensive Analysis with a Novel Global Dataset

Leaf traits are essential for understanding many physiological and ecological processes. Partial least-squares regression (PLSR) models with leaf spectroscopy are widely applied for trait estimation, but their transferability across space, time and plant functional types (PFTs) remains unclear. We compiled a novel dataset of paired leaf traits and spectra, with 47,393 records for >700 species and eight PFTs at 101 globally-distributed locations across multiple seasons. Using this dataset, we conducted an unprecedented comprehensive analysis to assess the transferability of PLSR models in estimating leaf traits. While PLSR models demonstrate commendable performance in predicting chlorophyll content, carotenoid, leaf water and leaf mass per area prediction within their training data space, their efficacy diminishes when extrapolating to new contexts. Specifically, extrapolating to locations, seasons, and PFTs beyond the training data leads to reduced R 2 (0.12-0.49, 0.15-0.42, and 0.25-0.56) and increased NRMSE (3.58-18.24%, 6.27-11.55% and 7.0-33.12%) compared to nonspatial random cross-validation (NRCV). The results underscore the importance of incorporating greater spectral diversity in model training to boost its transferability. These findings highlight potential errors in estimating leaf traits across large spatial domains, diverse PFTs and time due to biased validation schemes and provide guidance for future field sampling strategies and remote sensing applications.

Leaf traits↗
NASA NTRS1951

Flight Performance of a Jet Power Plant: operating characteristics of a jet power plant as a function of altitude - III

The performance of a jet power plant consisting of a compressor and a turbine is determined by the characteristic curves of these component parts and is controllable by the characteristics of the compressor and the turbine i n relation t o each other. The normal. output, overload, and throttled load of the Jet power plant are obtained on the basis of assumed straight-line characteristics.

Weinig, F.↗
NASA NTRS1997

Functional domains of plant chimeric calcium/calmodulin-dependent protein kinase: regulation by autoinhibitory and visinin-like domains

A novel calcium-binding calcium/calmodulin-dependent protein kinase (CCaMK) with a catalytic domain, calmodulin-binding domain, and a neural visinin-like domain was cloned and characterized from plants [Patil et al., (1995) Proc. Natl. Acad. Sci. USA 92, 4797-4801; Takezawa et al. (1996) J. Biol. Chem. 271, 8126-8132]. The mechanisms of CCaMK activation by calcium and calcium/calmodulin were investigated using various deletion mutants. The use of deletion mutants of CCaMK lacking either one, two, or all three calcium-binding EF hands indicated that all three calcium-binding sites in the visinin-like domain were crucial for the full calcium/calmodulin-dependent kinase activity. As each calcium-binding EF hand was deleted, there was a gradual reduction in calcium/calmodulin-dependent kinase activity from 100 to 4%. Another mutant (amino acids 1-322) which lacks both the visinin-like domain containing three EF hands and the calmodulin-binding domain was constitutively active, indicating the presence of an autoinhibitory domain around the calmodulin-binding domain. By using various synthetic peptides and the constitutively active mutant, we have shown that CCaMK contains an autoinhibitory domain within the residues 322-340 which overlaps its calmodulin-binding domain. Kinetic studies with both ATP and the GS peptide substrate suggest that the autoinhibitory domain of CCaMK interacts only with the peptide substrate binding motif of the catalytic domain, but not with the ATP-binding motif.

Non-NASA Center↗
NASA NTRS1960

The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.

Schmidt, Stanley F.↗
NASA NTRS2022

Assurance Equations: A Cost and Criticality Model for Optimizing Quality Assurance Surveillance

The cost of quality vs cost of failure correction has been a long-running topic of discussion within the Aerospace community. It leads directly to concepts of “risk tolerance”, and risk-based decision-making. It would be valuable if there was a way to compute the optimal investment in customer-executed quality assurance activities using defect significance with respect to performance objectives, the activities’ defect detection effectiveness, and the cost-penalty for late discovery of impactful defects. This optimization is particularly of interest to projects whose budget constraints significantly limit their risk management options.The cost to fix defects (i.e., failure correction) escalates as the project matures. There have been studies attempting to determine the relative cost of fixing defects discovered during various phases of a project life cycle with important implications, all of which suggest growth factors are large. The commonly referred to 1:10:100 rule represents a cost multiplier for repair/rework across the Design to Fab to Test hardware development phases. Cost premiums for QA activities also accumulate when they are treated as mandatory (due to schedule drag) or are performed later than their assigned phase.This paper describes the modeling of development phase -dependencies in the conduct of typical customer-executed quality assurance activities. Our initial modeling encompasses:• Distinct phases of the production lifecycle• Multiple kinds of Defects, each with some a-priori likelihood of being present• Each defect’s impact on performance Objectives for a type of hardware• The cost and efficacy of assurance techniques at detecting such Defects• The costs of fixing those Defects detected in a given phase of the production lifecycleThe model captures assurance activities’ abilities to Detect defects. Upon detection it is assumed that the Defect is immediately fixed. Defects that “escape” detection by some activity may thereafter be detected by a later activity, but by then the cost of fixing the Defect may have escalated. Defects are related to the performance Objectives they would detract from, were those Defects to remain present in the operating system.We have constructed and are exploring, a model that relates the importance of hardware system elements to mission objectives, the impact of types of Defects on those hardware types, the cost of customer-executed assurance activities (i.e., supplier controls) and their effectiveness towards reducing an impactful quality escape, and the cost of Defect correction across production phase. We describe the approach taken to select the key model aspects, why they are relevant to our NASA mission, and our efforts to populate it with relevant and contemporary data. We use a notional example to illustrate model design and function.

Plante, Jeannette↗
NASA NTRS1994

Modeling the bidirectional reflectance distribution function of mixed finite plant canopies and soil

An analytical model of the bidirectional reflectance for optically semi-infinite plant canopies has been extended to describe the reflectance of finite depth canopies contributions from the underlying soil. The model depends on 10 independent parameters describing vegetation and soil optical and structural properties. The model is inverted with a nonlinear minimization routine using directional reflectance data for lawn (leaf area index (LAI) is equal to 9.9), soybeans (LAI, 2.9) and simulated reflectance data (LAI, 1.0) from a numerical bidirectional reflectance distribution function (BRDF) model (Myneni et al., 1988). While the ten-parameter model results in relatively low rms differences for the BRDF, most of the retrieved parameters exhibit poor stability. The most stable parameter was the single-scattering albedo of the vegetation. Canopy albedo could be derived with an accuracy of less than 5% relative error in the visible and less than 1% in the near-infrared. Sensitivity were performed to determine which of the 10 parameters were most important and to assess the effects of Gaussian noise on the parameter retrievals. Out of the 10 parameters, three were identified which described most of the BRDF variability. At low LAI values the most influential parameters were the single-scattering albedos (both soil and vegetation) and LAI, while at higher LAI values (greater than 2.5) these shifted to the two scattering phase function parameters for vegetation and the single-scattering albedo of the vegetation. The three-parameter model, formed by fixing the seven least significant parameters, gave higher rms values but was less sensitive to noise in the BRDF than the full ten-parameter model. A full hemispherical reflectance data set for lawn was then interpolated to yield BRDF values corresponding to advanced very high resolution radiometer (AVHRR) scan geometries collected over a period of nine days. The resulting parameters and BRDFs are similar to those for the full sampling geometry, suggesting that the limited geometry of AVHRR measurements might be used to reliably retrieve BRDF and canopy albedo with this model.

Schluessel, G.↗
NASA NTRS1976

Computer program for single input-output, single-loop feedback systems

Additional work is reported on a completely automatic computer program for the design of single input/output, single loop feedback systems with parameter uncertainly, to satisfy time domain bounds on the system response to step commands and disturbances. The inputs to the program are basically the specified time-domain response bounds, the form of the constrained plant transfer function and the ranges of the uncertain parameters of the plant. The program output consists of the transfer functions of the two free compensation networks, in the form of the coefficients of the numerator and denominator polynomials, and the data on the prescribed bounds and the extremes actually obtained for the system response to commands and disturbances.

Source record↗
NASA NTRS1971

Synthesis of feedback systems with large plant ignorance for prescribed time domain tolerances

There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values. The plant is imbedded in a two-degree-of freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor noise at the input to the plant. This report presents a design procedure for this purpose, based on frequency response concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop transmission function in the form of continuous curves on the Nichols chart. The properties of the loop transmission function which satisfy these bounds with minimum effect of sensor noise, are derived.

Horowitz, I. M.↗
NASA NTRS2010

Practical Loop-Shaping Design of Feedback Control Systems

An improved methodology for designing feedback control systems has been developed based on systematically shaping the loop gain of the system to meet performance requirements such as stability margins, disturbance attenuation, and transient response, while taking into account the actuation system limitations such as actuation rates and range. Loop-shaping for controls design is not new, but past techniques do not directly address how to systematically design the controller to maximize its performance. As a result, classical feedback control systems are designed predominantly using ad hoc control design approaches such as proportional integral derivative (PID), normally satisfied when a workable solution is achieved, without a good understanding of how to maximize the effectiveness of the control design in terms of competing performance requirements, in relation to the limitations of the plant design. The conception of this improved methodology was motivated by challenges in designing control systems of the types needed for supersonic propulsion. But the methodology is generally applicable to any classical control-system design where the transfer function of the plant is known or can be evaluated. In the case of a supersonic aerospace vehicle, a major challenge is to design the system to attenuate anticipated external and internal disturbances, using such actuators as fuel injectors and valves, bypass doors, and ramps, all of which are subject to limitations in actuator response, rates, and ranges. Also, for supersonic vehicles, with long slim type of structures, coupling between the engine and the structural dynamics can produce undesirable effects that could adversely affect vehicle stability and ride quality. In order to design distributed controls that can suppress these potential adverse effects, within the full capabilities of the actuation system, it is important to employ a systematic control design methodology such as this that can maximize the effectiveness of the control design in a methodical and quantifiable way. The emphasis is in generating simple but rather powerful design techniques that will allow even designers with a layman s knowledge in controls to develop effective feedback control designs. Unlike conventional ad hoc methodologies of feedback control design, in this approach actuator rates are incorporated into the design right from the start: The relation between actuator speeds and the desired control bandwidth of the system is established explicitly. The technique developed is demonstrated via design examples in a step-by-step tutorial way. Given the actuation system rates and range limits together with design specifications in terms of stability margins, disturbance rejection, and transient response, the procedure involves designing the feedback loop gain to meet the requirements and maximizing the control system effectiveness, without exceeding the actuation system limits and saturating the controller. Then knowing the plant transfer function, the procedure involves designing the controller so that the controller transfer function together with the plant transfer function equate to the designed loop gain. The technique also shows what the limitations of the controller design are and how to trade competing design requirements such as stability margins and disturbance rejection. Finally, the technique is contrasted against other more familiar control design techniques, like PID control, to show its advantages.

Kopasakis, George↗
NASA NTRS2003

Effects of CO2 concentration and light intensity on photosynthesis of a rootless submerged plant, Ceratophyllum demersum L., used for aquatic food production in bioregenerative life support systems

In addition to green microalgae, aquatic higher plants are likely to play an important role in aquatic food production modules in bioregenerative systems for producing feed for fish, converting CO2 to O2 and remedying water quality. In the present study, the effects of culture conditions on the net photosynthetic rate of a rootless submerged plant, Ceratophyllum demersum L., was investigated to determine the optimum culture conditions for maximal function of plants in food production modules including both aquatic plant culture and fish culture systems. The net photosynthetic rate in plants was determined by the increase in dissolved O2 concentrations in a closed vessel containing a plantlet and water. The water in the vessel was aerated sufficiently with a gas containing a known concentration of CO2 gas mixed with N2 gas before closing the vessel. The CO2 concentrations in the aerating gas ranged from 0.3 to 10 mmol mol-1. Photosynthetic photon flux density (PPFD) in the vessel ranged from 0 (dark) to 1.0 mmol m-2 s-1, which was controlled with a metal halide lamp. Temperature was kept at 28 degrees C. The net photosynthetic rate increased with increasing PPFD levels and was saturated at 0.2 and 0.5 mmol m-2 s-1 PPFD under CO2 levels of 1.0 and 3.0 mmol mol-1, respectively. The net photosynthetic rate increased with increasing CO2 levels from 0.3 to 3.0 mmol mol-1 showing the maximum value, 75 nmol O2 gDW-1 s-1, at 2-3 mmol mol-1 CO2 and gradually decreased with increasing CO2 levels from 3.0 to 10 mmol mol-1. The results demonstrate that C. demersum could be an efficient CO2 to O2 converter under a 2.0 mmol mol-1 CO2 level and relatively low PPFD levels in aquatic food production modules. c2003 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

Ecological Systems, Closed↗
NASA NTRS1979

MHD performance calculations with oxygen enrichment

The impact of oxygen enrichment of the combustion air on the generator and overall plant performance was studied for the ECAS-scale MHD/steam plants. A channel optimization technique is described and the results of generator performance calculations using this technique are presented. Performance maps were generated to assess the impact of various generator parameters. Directly and separately preheated plant performance with varying O2 enrichment was calculated. The optimal level of enrichment was a function of plant type and preheat temperature. The sensitivity of overall plant performance to critical channel assumptions and oxygen plant performance characteristics was also examined.

Pian, C. C. P.↗
NASA NTRS1989

Autonomous frequency domain identification: Theory and experiment

The analysis, design, and on-orbit tuning of robust controllers require more information about the plant than simply a nominal estimate of the plant transfer function. Information is also required concerning the uncertainty in the nominal estimate, or more generally, the identification of a model set within which the true plant is known to lie. The identification methodology that was developed and experimentally demonstrated makes use of a simple but useful characterization of the model uncertainty based on the output error. This is a characterization of the additive uncertainty in the plant model, which has found considerable use in many robust control analysis and synthesis techniques. The identification process is initiated by a stochastic input u which is applied to the plant p giving rise to the output. Spectral estimation (h = P sub uy/P sub uu) is used as an estimate of p and the model order is estimated using the produce moment matrix (PMM) method. A parametric model unit direction vector p is then determined by curve fitting the spectral estimate to a rational transfer function. The additive uncertainty delta sub m = p - unit direction vector p is then estimated by the cross spectral estimate delta = P sub ue/P sub uu where e = y - unit direction vectory y is the output error, and unit direction vector y = unit direction vector pu is the computed output of the parametric model subjected to the actual input u. The experimental results demonstrate the curve fitting algorithm produces the reduced-order plant model which minimizes the additive uncertainty. The nominal transfer function estimate unit direction vector p and the estimate delta of the additive uncertainty delta sub m are subsequently available to be used for optimization of robust controller performance and stability.

Yam, Yeung↗