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Results for “numerical optimal control”

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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Development of an hp-version finite element method for computational optimal control

The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version finite elements in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element.

Hodges, Dewey H.↗
NASA NTRS1973

Computer simulation for time optimal or energy optimal attitude control of spin-stabilized spacecraft.

An original technique for determining the optimal magnetic torque strategy for control of the attitude of spin stabilized spacecraft is presented. By employing Lagrange multipliers and the Calculus of Variations, optimal control equations are derived which define minimum time and minimum energy attitude maneuvers. Computer program algorithms to numerically solve these optimal control equations are also described. The performance of this technique is compared with a commonly employed planning method.

Woolley, R. D.↗
NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗
NASA NTRSDate not supplied

Wind-Optimal Trajectories for Multirotor eVTOL Aircraft on UAM Missions

Distributed electric propulsion powered electric vertical takeoff and landing aircraft are expected to enable urban air mobility. Low specific energy of onboard lithium-ion polymer batteries and wind conditions impose constraints on flight endurance. Therefore, from the safety and efficiency perspective, planning and flying minimum energy trajectories are important.The primary motivation for this paper is to determine if there is an operational benefit to flying wind-optimal trajectories for short flights (less than 60 miles) in the urban environment. This study employs wind-optimal trajectories for a NASA-proposed conceptual multirotor aircraft flight in the urban environment. The optimal control model presented includes a wind model for quantifying the effect of wind on the trajectory. The optimal control problem is numerically solved using the direct method. Energy consumption and flight duration flying wind-optimal trajectories between origins and destinations in a metropolitan area are compared with energy consumption and flight duration flying on the great-circle paths between the same origin and destination pairs to determine the operational benefit of wind-optimal routing for short flights.The flight duration results for different scenarios are validated using a simulation tool designed and developed by NASA for exploring advanced air traffic management concepts. In summary,this research study suggests that for short flights in an urban environment, the wind-optimal trajectories have a very slight (insignificant) operational advantage over the great-circle trajectories in terms of energy consumption and flight duration. As expected, headwinds and tailwinds along the route of flight have a significant impact on energy consumption and flight duration.

Urban Air Mobility↗
NASA NTRS2022

Wind-Optimal Lateral Trajectories for a Multirotor Aircraft in Urban Air Mobility

The primary motivation for this paper is to quantify the operational benefits (energy consumption and flight duration) of flying wind-optimal lateral trajectories for short flights (less than 60 miles) anticipated in the urban environment. The optimal control model presented includes a wind model for quantifying the effect of wind on the lateral trajectory. The optimal control problem is numerically solved using the direct collocation method. Energy consumption and flight duration flying wind-optimal lateral trajectories are compared with corresponding values obtained flying great-circle paths between the same origin and destination pairs to determine the operational benefits of wind-optimal routing for short flights. The flight duration results for different scenarios are validated using a simulation tool designed and developed at NASA for exploring advanced air traffic management concepts. This research study suggests that for short flights in an urban environment, operational benefits of the wind-optimal lateral trajectories over the corresponding great-circle trajectories in terms of energy consumption and flight duration per flight are dependent on: i) wind field’s spatial variability, ii) wind magnitude, iii) the direction of route relative to the wind field, and iv) cruise segment length. The operational benefits observed in realistic flyable wind scenarios are less than 2.5%; these could be translated to an equivalent of a maximum of 2 min of cruise flight duration savings in the urban air mobility environment. As expected, headwinds and tailwinds along the flight route most significantly impact energy consumption and flight duration.

Wind-Optimal Trajectory, Lateral Path, Urban Air M↗
NASA NTRS1991

Progress in multirate digital control system design

A new methodology for multirate sampled-data control design based on a new generalized control law structure, two new parameter-optimization-based control law synthesis methods, and a new singular-value-based robustness analysis method are described. The control law structure can represent multirate sampled-data control laws of arbitrary structure and dynamic order, with arbitrarily prescribed sampling rates for all sensors and update rates for all processor states and actuators. The two control law synthesis methods employ numerical optimization to determine values for the control law parameters. The robustness analysis method is based on the multivariable Nyquist criterion applied to the loop transfer function for the sampling period equal to the period of repetition of the system's complete sampling/update schedule. The complete methodology is demonstrated by application to the design of a combination yaw damper and modal suppression system for a commercial aircraft.

Berg, Martin C.↗
DOE OSTI2025

Powering the Woods Hole X-Spar Buoy with Ocean Wave Energy—A Control Co-Design Feasibility Study

Despite its success in measuring air–sea exchange, the Woods Hole Oceanographic Institution’s (WHOI) X-Spar Buoy faces operational limitations due to energy constraints, motivating the integration of an energy harvesting apparatus to improve its deployment duration and capabilities. This work explores the feasibility of an augmented, self-powered system in two parts. Part 1 presents the collaborative design between X-Spar developers and wave energy researchers translating user needs into specific functional requirements. Based on requirements like desired power levels, deployability, survivability, and minimal interference with environmental data collection, unsuitable concepts are pre-eliminated from further feasibility study consideration. In part 2, we focus on one of the promising concepts: an internal rigid body wave energy converter. We apply control co-design methods to consider commercial of the shelf hardware components in the dynamic models and investigate the concept’s power conversion capabilities using linear 2-port wave-to-wire models with concurrently optimized control algorithms that are distinct for every considered hardware configuration. During this feasibility study we utilize two different control algorithms, the numerically optimal (but acausal) benchmark and the optimized damping feedback. We assess the sensitivity of average power to variations in drive-train friction, a parameter with high uncertainty, and analyze stroke limitations to ensure operational constraints are met. Our results indicate that a well-designed power take-off (PTO) system could significantly extend the WEC-Spar’s mission by providing additional electrical power without compromising data quality.

autonomous systems↗
DOE OSTI2023

Selective and Scalable Control of Spin Quantum Memories in a Photonic Circuit

A central goal in many quantum information processing applications is a network of quantum memories that can be entangled with each other while being individually controlled and measured with high fidelity. This goal has motivated the development of programmable photonic integrated circuits (PICs) with integrated spin quantum memories using diamond color center spin-photon interfaces. However, this approach introduces a challenge into the microwave control of individual spins within closely packed registers. Here, we present a quantum memory-integrated photonics platform capable of (i) the integration of multiple diamond color center spins into a cryogenically compatible, high-speed programmable PIC platform, (ii) selective manipulation of individual spin qubits addressed via tunable magnetic field gradients, and (iii) simultaneous control of qubits using numerically optimized microwave pulse shaping. The combination of localized optical control, enabled by the PIC platform, together with selective spin manipulation opens the path to scalable quantum networks on intrachip and interchip platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

Parallel and vector computation for stochastic optimal control applications

A general method for parallel and vector numerical solutions of stochastic dynamic programming problems is described for optimal control of general nonlinear, continuous time, multibody dynamical systems, perturbed by Poisson as well as Gaussian random white noise. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random atmospheric fluctuations. The numerical formulation is highly suitable for a vector multiprocessor or vectorizing supercomputer, and results exhibit high processor efficiency and numerical stability. Advanced computing techniques, data structures, and hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations.

Hanson, F. B.↗
NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗
NASA NTRS1977

A piecewise linear approximation scheme for hereditary optimal control problems

An approximation scheme based on 'piecewise linear' approximations of L2 spaces is employed to formulate a numerical method for solving quadratic optimal control problems governed by linear retarded functional differential equations. This piecewise linear method is an extension of the so called averaging technique. It is shown that the Riccati equation for the linear approximation is solved by simple transformation of the averaging solution. Thus, the computational requirements are essentially the same. Numerical results are given.

Cliff, E. M.↗
NASA NTRS1973

Constrained low-thrust guidance.

Constrained low thrust guidance algorithms for three axis and spin-stabilized, constant power, solar electric propelled spacecraft on fixed time rendezvous missions are developed. A 'bang-bang' type of minimum-propellant thrust program is used. Control constraints arise from the specification that the thrust vector must remain fixed relative to the solar panels. The guidance law is derived from deterministic linear perturbation theory and is controllable to first order on trajectories containing at least two thrust arcs. The number and timing of guidance updates and the effectiveness of the guidance law in compensating for state and control estimation biases and uncertainties are discussed. Numerical comparisons between the optimal control and the restricted control case are presented on a Encke comet rendezvous.

Ungs, M. J.↗
NASA NTRS1987

Guidance and control strategies for aerospace vehicles

A simplified method of matched asymptotic expansions was developed where the common part in composite solution is generated as a polynomial in stretched variable instead of actually evaluating the same from the outer solution. This methodology was applied to the solution of the exact equations for three dimensional atmospheric entry problems. Compared to previous works, the present simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods. The optimal control problem arising in the noncoplanar orbital transfer employing aeroassist was also addressed.

Hibey, Joseph L.↗
NASA NTRS1982

The use of optimization techniques to design controlled diffusion compressor blading

A method for automating compressor blade design using numerical optimization, and applied to the design of a controlled diffusion stator blade row is presented. A general purpose optimization procedure is employed, based on conjugate directions for locally unconstrained problems and on feasible directions for locally constrained problems. Coupled to the optimizer is an analysis package consisting of three analysis programs which calculate blade geometry, inviscid flow, and blade surface boundary layers. The optimizing concepts and selection of design objective and constraints are described. The procedure for automating the design of a two dimensional blade section is discussed, and design results are presented.

Sanger, N. L.↗
NASA NTRS1992

A reliable algorithm for optimal control synthesis

In recent years, powerful design tools for linear time-invariant multivariable control systems have been developed based on direct parameter optimization. In this report, an algorithm for reliable optimal control synthesis using parameter optimization is presented. Specifically, a robust numerical algorithm is developed for the evaluation of the H(sup 2)-like cost functional and its gradients with respect to the controller design parameters. The method is specifically designed to handle defective degenerate systems and is based on the well-known Pade series approximation of the matrix exponential. Numerical test problems in control synthesis for simple mechanical systems and for a flexible structure with densely packed modes illustrate positively the reliability of this method when compared to a method based on diagonalization. Several types of cost functions have been considered: a cost function for robust control consisting of a linear combination of quadratic objectives for deterministic and random disturbances, and one representing an upper bound on the quadratic objective for worst case initial conditions. Finally, a framework for multivariable control synthesis has been developed combining the concept of closed-loop transfer recovery with numerical parameter optimization. The procedure enables designers to synthesize not only observer-based controllers but also controllers of arbitrary order and structure. Numerical design solutions rely heavily on the robust algorithm due to the high order of the synthesis model and the presence of near-overlapping modes. The design approach is successfully applied to the design of a high-bandwidth control system for a rotorcraft.

Vansteenwyk, Brett↗
DOE OSTI2023

Dynamic modeling and simulation of pressure swing adsorption processes using toPSAil

Pressure swing adsorption (PSA) has attracted significant recent interest for chemical process intensification due to its potential for high energy efficiency and amenability to small, modular designs. However, the lack of simulation tools that are readily available, transparent, and trusted, has been identified as a serious impediment to widespread adoption of PSA, as well as to further research on PSA modeling, numerical solution, optimization, and control. This paper presents a complete framework for dynamic modeling and simulation of PSA processes and its implementation in an open-source simulator called toPSAil. Further, the presentation is tutorial and includes many modeling and implementation details often overlooked in existing literature. Novel methods are presented for handling flow reversals and implementing various pressure–flow relationships, along with controlled boundary conditions. Finally, the code contains several innovations designed to improve efficiency and reduce the extensive trial-and-error tuning often required to produce a working PSA cycle.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗