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NASA NTRSDate not supplied

System Identification for eVTOL Aircraft Using Simulated Flight Data

This paper describes a system identification method for electric vertical takeoff and landing (eVTOL) aircraft. The approach merges fixed-wing and rotary-wing modeling techniques with new strategies to develop a modeling method for eVTOL vehicles using flight test data. The eVTOL aircraft system identification approach is demonstrated through application to the NASA LA-8 tandem tilt-wing, distributed electric propulsion aircraft using a high-fidelity flight dynamics simulation. Orthogonal phase-optimized multisine inputs are applied to each control surface and propulsor at numerous flight conditions throughout the flight envelope to collect informative flight data. An aero-propulsive model is identified at each flight condition using the equation-error method in the frequency domain. The local model parameters are then blended to create a global model across the nominal flight envelope. Parameter estimation results are shown to provide a good fit to modeling data and have good prediction capability. The methodology is developed with a discussion of unique eVTOL vehicle aerodynamic characteristics and practical strategies intended to inform future flight-based system identification efforts for eVTOL aircraft.

system identification↗
NASA NTRS1984

Gain optimization with non-linear controls

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Slater, G. L.↗
NASA NTRS2007

Initial Ares I Bending Filter Design

The Ares-I launch vehicle represents a challenging flex-body structural environment for control system design. Software filtering of the inertial sensor output will be required to ensure control system stability and adequate performance. This paper presents a design methodology employing numerical optimization to develop the Ares-I bending filters. The filter design methodology was based on a numerical constrained optimization approach to maximize stability margins while meeting performance requirements. The resulting bending filter designs achieved stability by adding lag to the first structural frequency and hence phase stabilizing the first Ares-I flex mode. To minimize rigid body performance impacts, a priority was placed via constraints in the optimization algorithm to minimize bandwidth decrease with the addition of the bending filters. The bending filters provided here have been demonstrated to provide a stable first stage control system in both the frequency domain and the MSFC MAVERIC time domain simulation.

Jang, Jiann-Woei↗
NASA NTRS1991

Vortex generator design for aircraft inlet distortion as a numerical optimization problem

Aerodynamic compatibility of aircraft/inlet/engine systems is a difficult design problem for aircraft that must operate in many different flight regimes. Takeoff, subsonic cruise, supersonic cruise, transonic maneuvering, and high altitude loiter each place different constraints on inlet design. Vortex generators, small wing like sections mounted on the inside surfaces of the inlet duct, are used to control flow separation and engine face distortion. The design of vortex generator installations in an inlet is defined as a problem addressable by numerical optimization techniques. A performance parameter is suggested to account for both inlet distortion and total pressure loss at a series of design flight conditions. The resulting optimization problem is difficult since some of the design parameters take on integer values. If numerical procedures could be used to reduce multimillion dollar development test programs to a small set of verification tests, numerical optimization could have a significant impact on both cost and elapsed time to design new aircraft.

Anderson, Bernhard H.↗
NASA NTRS2019

Optimal Control within the Context of Multidisciplinary Design, Analysis, and Optimization

Multidisciplinary design, analysis and optimization involves modeling the interactions of complex systems across a variety of disciplines. The optimization of such systems can be a computationally expensive exercise with multiple levels of nested nonlinear solvers running under an optimizer.The application of optimal control in project development often involves performing trajectory optimization for fixed vehicle designs or parametric sweeps across some key vehicle properties.This information is then relayed to the subsystem design teams who update their designs and relay some bulk characteristics back to the trajectory optimization procedure.This iteration is then repeated until the design closes.However, with increasing interest in more tightly coupled systems, such as electric and hybrid-electric aircraft propulsion and boundary layer ingestion, this process is prone to ignore subtle coupling between vehicle subsystem designs and vehicle operation on a given mission.Integrating trajectory optimization into a tightly coupled multidisciplinary design procedure can be computationally prohibitive, depending on the complexity of the subsystem analyses and the optimal control technique applied.To address these issues a new optimal control software tool, Dymos, has been developed.Dymos is built upon NASA's OpenMDAO software and can leverage its capabilities to efficiently compute gradients for the optimization and optimize complex models in parallel on distributed memory systems.This report provides some explanation into the numerical methods employed in Dymos and provides several use cases that demonstrate its performance on traditional optimal control problems and improvements ino techniques have been used extensively in recent decades to solve a variety of optimal control problems, typically in the form of aerospace vehicle trajectory optimization.

pseudospectral↗
NASA NTRS2021

Recent Advancements in Modeling and Simulation of Entry Systems at NASA

This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA’s exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA’s Entry Systems Modeling (ESM) Project, which serves as the Agency’s only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specificmodels for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures. Results for both configurations have demonstrated the ability to land within the 50-meter precision requirement demanded by Mars human exploration missions, while also reducing propellant requirements by enabling more efficient control through entry and descent. Ongoing research in GN&C is developing mechanical specifications for the systems and establishing engineering feasibility.

aerothermodynamics↗
NASA NTRS2019

Recent Advancements in Modeling and Simulation of Entry Systems at NASA

This paper describes recent development of modeling and simulation technologies for entry systems in support of NASA's exploration missions. Mission-tailored research and development in modeling of entry systems occurs across the Agency (e.g., within the Orion and Mars 2020 Programs), however the aim of this paper is to discuss the broad, cross-mission research conducted by NASA's Entry Systems Modeling (ESM) Project, which serves as the Agency's only concerted effort toward advancing entry systems across a range of technical disciplines. Technology development in ESM is organized and prioritized from a system-level perspective, resulting in four broad technical areas of investment: (1) Predictive material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. Investments in thermal protection material modeling are geared toward high-fidelity, predictive models capable of handling complex structures, with an eye toward optimizing design performance and quantifying thermal protection system reliability. New computational tools have been developed to characterize material properties and behavior at the microstructural level, and experimental techniques (molecular beam scattering, micro-computed tomography, among others) have been developed to measure material kinetics, morphology, and other parameters needed to inform and validate detailed simulations. Advancements have also been made in macrostructural simulation capability to enable 3-D system-scale calculations of material response with complex topological features, including differential recession of tile gaps. Research and development in the area of shock layer kinetics has focused on air and CO2-based atmospheres. Capacity and capability of the NASA Ames Electric Arc Shock Tube (EAST) have been expanded in recent years and analysis of resulting data has led to several improvements in kinetic models, while simultaneously reducing uncertainties associated with radiative heat transfer predictions. First-principles calculations of fundamental kinetic, thermodynamic, and transport data, along with state-specific models for non-equilibrium flow regimes, have also yielded new insights and have the potential to vastly improve model fidelity. Aerosciences is a very broad area of interest in entry systems, yet a number of important challenges are being addressed: Coupled fluid-structure simulations of parachute inflation and dynamics; Experimental and computational studies of vehicle dynamics; Multi-phase flow with dust particles to simulate entry environments at Mars during dust storms; Studies of roughness-induced heating augmentation relevant to tiled and woven thermal protection systems; and Advanced numerical methods to optimize computational analyses for desired accuracy versus cost. Guidance and control in the context of entry systems has focused on development of methods for multi-axis control (i.e. pitch and yaw, rather than bank angle alone) of spacecraft during entry and descent. With precision landing requirements driven by Mars human exploration goals, recent efforts have yielded 6-DOF models of multi-axis control with propulsive descent of both inflatable and rigid ellipsled-like architectures.

Barnhardt, Michael D.↗
NASA NTRS2017

The Quantum Approximation Optimization Algorithm for MaxCut: A Fermionic View

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of steps in which a classical Hamiltonian, derived from the cost function, is applied followed by a mixing Hamiltonian. The 2p times for which these two Hamiltonians are applied are the parameters of the algorithm. As p increases, however, the parameter search space grows quickly. The success of the QAOA approach will depend, in part, on finding effective parameter-setting strategies. Here, we analytically and numerically study parameter setting for QAOA applied to MAXCUT. For level-1 QAOA, we derive an analytical expression for a general graph. In principle, expressions for higher p could be derived, but the number of terms quickly becomes prohibitive. For a special case of MAXCUT, the Ring of Disagrees, or the 1D antiferromagnetic ring, we provide an analysis for arbitrarily high level. Using a Fermionic representation, the evolution of the system under QAOA translates into quantum optimal control of an ensemble of independent spins. This treatment enables us to obtain analytical expressions for the performance of QAOA for any p. It also greatly simplifies numerical search for the optimal values of the parameters. By exploring symmetries, we identify a lower-dimensional sub-manifold of interest; the search effort can be accordingly reduced. This analysis also explains an observed symmetry in the optimal parameter values. Further, we numerically investigate the parameter landscape and show that it is a simple one in the sense of having no local optima.

quantum algorithm↗
NASA NTRS1975

Interpolation in numerical optimization

The present work discusses the generation of the cubic-spline interpolator in numerical optimization methods which use a variable-step integrator with step size control based on local relative truncation error. An algorithm for generating the cubic spline with successive over-relaxation is presented which represents an improvement over that given by Ralston and Wilf (1967). Rewriting the code reduces the number of N-vectors from eight to one. The algorithm is formulated in such a way that the solution of the linear system set up yields the first derivatives at the nodal points. This method is as accurate as other schemes but requires the minimum amount of storage.

Hall, K. R.↗
NASA NTRS1986

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Gibson, J. S.↗
NASA NTRS1987

Optimization and guidance of abort landing trajectories in a windshear

The abort landing problem for flight trajectories in the presence of windshear is considered with reference to flight in a vertical plane. The optimal trajectory (OT) problem is a minimax problem or Chebyshev problem of optimal control which can be converted into a Bolza problem through suitable transformations. Numerical results for several combinations of windshear intensities and initial altitudes are presented. A guidance trajectory (GT) law is implemented in feedback control form, subject to prescribed bounds on the angle of attack and its time derivative. Simplified guidance trajectories (SGT) are then considered, leading to a safe target altitude guidance. Conclusions derived for strong-to-severe windshear conditions include GT and SGT preserving the basic properties of OT, and the peak altitude drop of GT and SGT being less than that of the constant pitch trajectory and the maximum angle-of-attack trajectory.

Miele, A.↗
NASA NTRS1992

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Ta'asan, Shlomo↗
NASA NTRS1993

Theory and computation of optimal low- and medium-thrust transfers

This report presents the formulation of the optimal low- and medium-thrust orbit transfer control problem and methods for numerical solution of the problem. The problem formulation is for final mass maximization and allows for second-harmonic oblateness, atmospheric drag, and three-dimensional, non-coplanar, non-aligned elliptic terminal orbits. We setup some examples to demonstrate the ability of two indirect methods to solve the resulting TPBVP's. The methods demonstrated are the multiple-point shooting method as formulated in H. J. Oberle's subroutine BOUNDSCO, and the minimizing boundary-condition method (MBCM). We find that although both methods can converge solutions, there are trade-offs to using either method. BOUNDSCO has very poor convergence for guesses that do not exhibit the correct switching structure. MBCM, however, converges for a wider range of guesses. However, BOUNDSCO's multi-point structure allows more freedom in quesses by increasing the node points as opposed to only quessing the initial state in MBCM. Finally, we note an additional drawback for BOUNDSCO: the routine does not supply information to the users routines for switching function polarity but only the location of a preset number of switching points.

Chuang, C.-H.↗
NASA NTRS1993

Physical insight into the simultaneous optimization of structure and control

Recent trends in spacecraft design which yield larger structures with more stringent performance requirements place many flexible modes of the structure within the bandwidth of active controllers. The resulting complications to the spacecraft design make it highly desirable to understand the impact of structural changes on an optimally controlled structure. This work uses low structural models with optimal H(sub 2) and H(sub infinity) controllers to develop some basic insight into this problem. This insight concentrates on several basic approaches to improving controlled performance and how these approaches interact in determining the optimal designs. A numerical example is presented to demonstrate how this insight can be generalized to more complex problems.

Jacques, Robert N.↗
NASA NTRS1992

Active adhesion concepts for in-orbit structural construction

The in-orbit assembly of structural elements is presently addressed by means of a continuum-based theory of active-adhesion contact/impact which assumes the manufacturability of active adhesion elements by piezoelectric (and similarly behaving) materials. Block bonding characteristics can furnish an effective alternative to optimal control-based, impact surge force-mitigation strategies, especially in the numerous nonsmooth control problems that are difficult to synthesize and implement. Attention is given to design concepts employing combined serial/parallel-bonded active adhesion elements composed of cascaded piezoelectric devices.

Park, K. C.↗
NASA NTRS1992

Minimum-exposure near-terrain flight trajectories for rotorcraft

The paper presents methodologies for constructing optimal trajectories for rotorcraft executing nap-of-the-earth flight over known terrain. Unlike the standard techniques, the present approaches require only a one-dimensional numerical search for determining optimal trajectories. Numerical algorithms are developed using two kinematic vehicle models in conjunction with optimal control theory.

Menon, P. K. A.↗
NASA NTRS2008

Ares-I Bending Filter Design using a Constrained Optimization Approach

The Ares-I launch vehicle represents a challenging flex-body structural environment for control system design. Software filtering of the inertial sensor output is required to ensure adequate stable response to guidance commands while minimizing trajectory deviations. This paper presents a design methodology employing numerical optimization to develop the Ares-I bending filters. The design objectives include attitude tracking accuracy and robust stability with respect to rigid body dynamics, propellant slosh, and flex. Under the assumption that the Ares-I time-varying dynamics and control system can be frozen over a short period of time, the bending filters are designed to stabilize all the selected frozen-time launch control systems in the presence of parameter uncertainty. To ensure adequate response to guidance command, step response specifications are introduced as constraints in the optimization problem. Imposing these constrains minimizes performance degradation caused by the addition of the bending filters. The first stage bending filter design achieves stability by adding lag to the first structural frequency to phase stabilize the first flex mode while gain stabilizing the higher modes. The upper stage bending filter design gain stabilizes all the flex bending modes. The bending filter designs provided here have been demonstrated to provide stable first and second stage control systems in both Draper Ares Stability Analysis Tool (ASAT) and the MSFC MAVERIC 6DOF nonlinear time domain simulation.

Hall, Charles↗
NASA NTRS1990

Trajectory optimization for an asymmetric launch vehicle

A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.

Sullivan, Jeanne Marie↗