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Results for “Optimal Control Problem”

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 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

bound tightening↗
NASA NTRS1973

Optimality of incompletely measurable active and passive attitude control systems

Passive attitude control systems and active systems with incomplete state measurements are only suboptimal systems in the sense of optimal control theory, since optimal systems require complete state measurements or state estimations. An optimal system, then, requires additional hardware (especially in the case of flexible spacecraft) which results in higher costs. Therefore, it is a real engineering problem to determine how much an optimal system exceeds the suboptimal system, or in other words, what is the suboptimal system's degree of optimality. The problem will be treated in three steps: (1) definition of the degree of optimality for linear, time-invariant systems; (2) a computation method using the quadratic cost functional; (3) application to a gravity-gradient stabilized three-body satellite and a spinning flexible satellite.

Schiehlen, W.↗
NASA NTRS1975

ORACLS - A modern control theory design package

A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.

Armstrong, E. S.↗
NASA NTRS1985

Relative control effectiveness technique with application to airplane control coordination

A method to select optimal combinations of the control variables of a linear system is reported. The combinations are chosen so that the control channels have their principal influences on selected fundamental modes of the system. A series of algebraic maximization problems is used to maximize the effects of the control channels on selected modes while simultaneously minimizing the effects on the remaining modes. The method is applied to the lateral and directional control of a linearized airplane model having ailerons, a rudder, and differential tail surfaces. Integration of these control eliminates oscillations present in the roll rate for a step lateral-control input and improves the sideslip response with reduced rolling motions for a step directional-control input. Inclusion of thrust-vectoring engine nozzles improves the roll rate capability of the airplane.

Lallman, F. J.↗
NASA NTRS1985

Optimal flight paths through microburst wind profiles

The problem of safe microburst wind shear encounter during the approach and climb-out flight phases is addressed using flight path optimization. The purpose was to investigate the physical limits of safe penetration and to determine control strategies that take full advantage of those limits. Optimal trajectories for both jet transport and general aviation aircraft were computed for encounters with idealized and actual microburst profiles. The results demonstrate that limits to control system design rather than to the aircraft's physical performance may be the deciding factor in an aircraft's capability for safe passage through a wide class of microbursts. The best control strategies responded to airspeed loss in an unconventional manner: by raising the nose to maintain lift.

Psiaki, M. L.↗
NASA NTRS1988

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Rosen, I. G.↗
NASA NTRS1996

Theory and Computation of Optimal Low- and Medium- Thrust Orbit Transfers

This report presents new theoretical results which lead to new algorithms for the computation of fuel-optimal multiple-burn orbit transfers of low and medium thrust. Theoretical results introduced herein show how to add burns to an optimal trajectory and show that the traditional set of necessary conditions may be replaced with a much simpler set of equations. Numerical results are presented to demonstrate the utility of the theoretical results and the new algorithms. Two indirect methods from the literature are shown to be effective for the optimal orbit transfer problem with relatively small numbers of burns. These methods are the Minimizing Boundary Condition Method (MBCM) and BOUNDSCO. Both of these methods make use of the first-order necessary conditions exactly as derived by optimal control theory. Perturbations due to Earth's oblateness and atmospheric drag are considered. These perturbations are of greatest interest for transfers that take place between low Earth orbit altitudes and geosynchronous orbit altitudes. Example extremal solutions including these effects and computed by the aforementioned methods are presented. An investigation is also made into a suboptimal multiple-burn guidance scheme. The FORTRAN code developed for this study has been collected together in a package named ORBPACK. ORBPACK's user manual is provided as an appendix to this report.

Goodson, Troy D.↗
NASA NTRS2005

Quadratic Programming for Allocating Control Effort

A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

Singh, Gurkirpal↗
DOE OSTI2019

Scalable flexibility control of distributed loads in a power grid

The technology described herein is generally directed towards a distributed optimization technology for the control of aggregation of distributed flexibility resource nodes that operates iteratively until a commanded power profile is produced by aggregated loads. The technology uses a distributed iterative solution in which each node solves a local optimization problem with local constraints and states, while using a global Lagrange multiplier that is based upon information from each other node. The global Lagrange multiplier is determined at an aggregation level using load-specific information that is obtained in a condensed form (e.g., a scalar) from each node at each iteration. The global Lagrange multiplier is broadcasted to the nodes for each new iteration. The technology provides an iterative, distributed solution to the network optimization problem of power tracking of aggregated loads.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Dynamically Learning Incentives for Load Control

As electrical generation becomes more distributed and volatile, and loads become more uncertain, controllability of distributed energy resources (DERs), regardless of their ownership status, will be necessary for grid reliability. Grid operators lack direct control over end-users' grid interactions, such as energy usage, but incentives can influence behavior -- for example, an end-user that receives a grid-driven incentive may adjust their consumption or expose relevant control variables in response. A key challenge in studying such incentives is the lack of data about human behavior, which usually motivates strong assumptions, such as distributional assumptions on compliance or rational utility-maximization. In this paper, we propose a general incentive mechanism in the form of a constrained optimization problem -- our approach is distinguished from prior work by modeling human behavior (e.g., reactions to an incentive) as an arbitrary unknown function. We propose feedback-based optimization algorithms to solve this problem that each leverage different amounts of information and/or measurements. We show that each converges to an asymptotically stable incentive with (near)-optimality guarantees given mild assumptions on the problem. Finally, we evaluate our proposed techniques in voltage regulation simulations on standard test beds. We test a variety of settings, including those that break assumptions required for theoretical convergence (e.g., convexity, smoothness) to capture realistic settings. In this evaluation, our proposed algorithms are able to find near-optimal incentives even when the reaction to an incentive is modeled by a theoretically difficult (yet realistic) function.

demand response↗
DOE OSTI2020

Shape Optimization for Control and Isolation of Structural Vibrations in Aerospace and Defense Applications

Among the main challenges in shape optimization is the coupling of Finite Element Method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multi-physics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. There are two mathematically equivalent approaches to computing the shape derivative: the volume method, and the boundary method. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. Prior implementations of shape derivatives at Sandia have been based on the volume method. We introduce the strip method, which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. The development of the strip method also offers us the opportunity to share some lessons learned about implementing the volume method and boundary method, to show shape optimization results on problems of interest, and to begin addressing the other main challenges at hand: constraints on optimized shapes, and their interplay with optimization algorithms.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2024

Optimization of District Heating Network Parameters in Steady-State Operation

Here we examine the modeling, simulation, and optimization of district heating systems, which are widely used for thermal transport using steam or hot water as a carrier. We propose a generalizable framework to specify network models and scenario parameters, and develop an optimization method for evaluating system states including pressures, fluid flowrates, and temperatures throughout the network. The network modeling includes pipes, thermal plants, pumps, and passive or controllable loads as system components. We propose basic models for thermodynamic fluid transport and enforce the balance of physical quantities in steady-state flow over co-located outgoing and return networks. We formulate an optimization problem with steam and hot water as the outgoing and return carriers, as in legacy twentieth century systems. The physical laws and engineering limitations are specified for each component type, and the thermal network flow optimization problem is formulated and solved for a realistic test network under several scenarios.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

FARM supervisory capabilities for thermal energy storage

The FARM (Feasible Actuator Range Modifier) module is a component of the RAVEN-based FORCE framework for the analysis of Integrated Energy Systems (IES). FARM aids HERON in the solution of the power dispatch problem by evaluating feasible set-point signals to be issued to the control systems of the different IES unit components. Set-points need to satisfy limits on both production variables (i.e., the variables to be optimized such as the electrical power, etc.) and process variables tied to the service life of equipment (e.g., steam flowrate, vessel pressure, turbine firing temperature, etc.). To enforce all these limits, a two-stage approach is adopted. First, the power dispatcher algorithm in HERON module estimates set-points that meet the constraints on the production variables, e.g., power levels and power ramp rate limits. These constraints are called explicit constraints. Then, if necessary, FARM adjusts these set-points to ensure the respect of the limits on the process variables of interest, given the knowledge of the system dynamics acquired through machine learning algorithms. These constraints are called implicit constraints. From this standpoint, FARM constitutes a bridge between the HERON power dispatcher that adopts a simplified description of the IES unit (low-resolution physics) and the HYBRID high-fidelity models (high-resolution physics). In this report, an overview of the major capabilities of the latest release of FARM is provided, along with a summary of the tool demonstration campaign conducted at the Dynamic Energy Technology and Integration Laboratory (DETAIL) facility. These results assess the performance of the control system architecture embedding FARM both as a Validator of the HERON power dispatcher and as a real time Supervisory control scheme. Additionally, the report outlines the areas that FARM might benefit from, along with proposed solutions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1978

Combined monitoring, decision and control model for the human operator in a command and control desk

A report is given on the ongoing efforts to mode the human operator in the context of the task during the enroute/return phases in the ground based control of multiple flights of remotely piloted vehicles (RPV). The approach employed here uses models that have their analytical bases in control theory and in statistical estimation and decision theory. In particular, it draws heavily on the modes and the concepts of the optimal control model (OCM) of the human operator. The OCM is being extended into a combined monitoring, decision, and control model (DEMON) of the human operator by infusing decision theoretic notions that make it suitable for application to problems in which human control actions are infrequent and in which monitoring and decision-making are the operator's main activities. Some results obtained with a specialized version of DEMON for the RPV control problem are included.

Muralidharan, R.↗
NASA NTRS1983

Optimal symmetric flight with an intermediate vehicle model

The present investigation is concerned with an examination of optimal symmetry flight on the basis of the intermediate vehicle model. The analysis is partly based upon an exploration of Euler solutions for the path-angle-as-control model carried out by Kelley (1958). The current analysis takes into account higher-order optimality conditions and 'chattering-control' phenomena. Attention is given to details regarding the intermediate vehicle model, the Legendre-Clebsch necessary condition, the conjugate-point test, and the numerical solution of the time-range problem. It is found that the flight path angle takes on the role of control variable in the model. From physical considerations, it can be seen that when a positive margin of thrust over drag exists, the maximum-range climb trajectory without time or fuel constraints has no proper maximum nor an upper bound.

Kelley, H. J.↗