Benjamin W L Margolis

NASA NTRS2023

Another Geometric Interpretation of Cramer’s Rule

We develop a geometric interpretation of Cramer’s rule as a generalization of projection onto orthogonal basis vectors using the rows of the adjugate. This interpretation makes connections between elementary linear algebra concepts like the solution to linear equations, inner products, and projections. Such connections are useful for introducing broader concepts related to Hilbert spaces and geometric algebras like Grassman algebra. Such connections were essential for the author’s mathematical education as an engineer.

linear algebra↗

NASA NTRSDate not supplied

Pterodactyl: Guidance and Control of a Symmetric Deployable Entry Vehicle using an Aerodynamic Control System

The NASA-funded Pterodactyl project seeks to advance the current state-of-the-art for entry vehicles by developing novel guidance and control technologies for Deployable Entry Vehicles (DEVs). This paper presents the guidance and control design and analysis for a mechanically-deployed DEV with a symmetric aeroshell and aerodynamic control surfaces. We present guidance tuning using both bank angle modulation with the Fully-Numerical Predictor Corrector Entry Guidance technique (FNPEG) and angle of attack and sideslip modulation with FNPEG with uncoupled range control (FNPEG URC). We show the control system design and simulation results for tracking both types of guidance commands.

Benjamin W L Margolis↗

NASA NTRSDate not supplied

Analysis and Optimization of Baseline Single Aisle Aircraft for Future Electrified Powertrain Flight Demonstrator Comparisons

The purpose of this study is to provide baseline single-aisle vehicles for future comparisons NASA’s Electrified Powertrain Flight Demonstrator (EPFD) turbofan powered Vision Systems. Both a large single-aisle (≈150 passenger) and a small single-aisle (≈100 passenger) vehicle will be analyzed using NASA’s General Aviation Synthesis Program and a modernized Python-based version of this program that enables efficient gradient-based optimization of both the airframe and propulsion that currently is being referred to as GASPy. A technology build-up will be conducted to bring the current State-of-the-art vehicles to a projected 2035 technology level by incorporating estimations for improvements in aerodynamics, structures, and propulsions. These vehicles can be used in NASA’s future EPFD project as baselines to measure the benefits of future hybrid and fully electric aircraft against. The advanced, large single-aisle will then be used to demonstrate the benefits of a coupled engine-airframe optimization for fuel burn reduction.

Carl J Recine↗

NASA NTRSDate not supplied

Pterodactyl: Coupled 6-Dof Integration of Guidance and Control Algorithms in Genesis

The NASA-funded Pterodactyl project seeks to advance the current state-of-the-art for entry vehicles by developing novel guidance and control technologies for Deployable Entry Vehicles (DEVs). This paper builds upon the Pterodactyl architecture that employed eight individually articulating flaps with two options for guidance, bank angle modulation with the Fully Numerical Predictor Corrector Entry Guidance technique (FNPEG) and angle of attack and sideslip modulation with FNPEG uncoupled range control (FNPEG URC). These, with a linear quadratic regulator (LQR) controller, had previously been presented in uncoupled 3-DOF trajectories. This work will show results from fully coupled 6-DOF simulations, leveraging recent advancements in trajectory simulation software, namely the Julia-based Genesis package. Preliminary results show good performance for angle of attack and sideslip modulation when using a controller designed at high dynamic pressure conditions.

range targeting↗

NASA NTRSDate not supplied

GASP Advancements With Symbolic Computations, Optimization, and Decoupled Numerical Methods

NASA is exploring advancements in hybrid-electric propulsion concepts for aircraft design. A new analysis capability has been deployed at NASA’s Ames Research Center using a new mathematical modeling framework in Python that leverages symbolic representation of mathematical expressions, optimization-based problem formulations, and standalone numerical methods. This capability, called Gascon, has been verified against NASA’s General Aviation Synthesis Program (GASP) results for several vehicles that exercise the analysis capability for a variety of aircraft classes and engine models, including both turbofans and turboprops. We believe this capability will set the stage for more rapid development of novel aircraft models with more flexible design assessments using optimization, and more traceable analysis for reproducibility. Additionally, a novel Pareto optimization-based design space exploration that shows the trade between range flown and fuel burn by manipulating the thrust split during cruise for a true parallel hybrid aircraft was developed by leveraging the unique features of Gascon.

aircraft design↗

NASA NTRSDate not supplied

Robust Trajectory Optimization Techniques Using a Sweeping Gradient Method and Linear Covariance Analysis

We present robust trajectory optimization techniques using a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov). SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve robust optimal trajectory design problems. We describe the individual methods and some details on how they can be combined. Then we apply the combined techniques to a variety of orbital trajectory design problems to demonstrate its use, including minimum fuel transfer and mid-course correction burn scheduling.

Benjamin W L Margolis↗

NASA NTRSDate not supplied

Co-Optimization of Navigation System Requirements and Trajectory Design Using a Sweeping Gradient Method and Linear Covariance Analysis

We describe the application of a sweeping gradient method for ordinary differential equations with events (SGM) and linear covariance analysis (LinCov) to the co-optimization of navigation system requirement generation and robust trajectory design. SGM is a method for computing the gradient of trajectory analyses defined by performance indices over initial value problems with events with respect to static parameters. LinCov is an analytic technique for predicting stochastic behavior of dynamical systems. By combining SGM and LinCov, it is possible use efficient, off-the-shelf, gradient-based optimizers to solve a combined robust optimal trajectory and navigation system design problem. In this paper, we formulate the required models to apply the combined SGM and LinCov techniques to a Near-Rectilinear Halo Orbit rendezvous approach scenario and show results for several intermediate problems.

Benjamin W L Margolis↗

NASA NTRSDate not supplied

Pterodactyl: 6-DOF Integration of Guidance and Control Algorithms in Genesis

The NASA-funded Pterodactyl project seeks to advance the current state-of-the-art for entry vehicles by developing novel guidance and control technologies for Deployable Entry Vehicles. This paper builds upon the Pterodactyl architecture that employed eight individually articulating flaps with two options for guidance, bank angle modulation with the Fully Numerical Predictor Corrector Entry Guidance (FNPEG) technique and angle of attack and sideslip modulation with FNPEG uncoupled range control. These, with a linear quadratic regulator controller, have previously been presented in separate 3-DOF trajectory simulations, one for translational motion and another for rotational dynamics. This work will show results for integrated 6-DOF simulations, leveraging recent advancements in trajectory simulation tools, namely the Julia-based Genesis package. Results show similar performance for both schemes when compared to the previously presented 3-DOF results once the controllers were adequately tuned. Angle of attack and sideslip modulation necessitated a controller designed at high dynamic pressure conditions, and bank angle modulation necessitated a controller designed at lower dynamic pressure conditions. Notably, angle of attack and sideslip modulation could not achieve the parachute deploy point target Mach number of 2, when only tuning the controller gains, thus future work will be needed to tune guidance specific parameters to achieve acceptable range targeting and guidance command tracking.

DEV↗