SEARCH · Engineering Papers

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21

All sources NASA NTRS DOE OSTI

NASA NTRS1971

Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

Childs, A. G.↗

NASA NTRS1985

Optimization of Controlled Structures

A formulation is presented for the coupled optimal design of a structural system and its control by defining a composite objective function as a linear combination of two components: a structural objective and a control objective. For the case when the structural objective is a function of the structural design variables only, and when the control objective is represented by the quadratic functional of the response and control energy, one can analytically express the optimal control in terms of any set of admissible structural design variables. The expression for the optimal control is used recursively in an iterative Newton-Raphson search scheme, the goal of which is to determine a corresponding optimal set of structural design variables that minimize the composite objective function. A numerical example is given to illustrate the computational procedure.

Salama, M.↗

NASA NTRS1984

Modal insensitivity with optimality

This paper deals with the design of a constant gain, feedback controller which results in selected modal insensitivity, and at the same time optimizes a quadratic performance index representative of desired system performance for nominal plant parameter values. Both full state and output feedback control are considered. A constraint is established for the feedback gain matrix that results in modal insensitivity, and necessary conditions for optimality subject to this constraint are given. This forms the basis for a numerical algorithm to compute the optimal feedback gain. To illustrate the procedure, a design is carried out using the lateral dynamics of an L-1011 aircraft.

Calise, A. J.↗

NASA NTRS1988

Minimum-time pointing control of a two-link manipulator

Minimum-time pointing control for the end-effector of a planar, two-link manipulator is developed. Minimum-time pointing control is a new area of research for multilink manipulators, which can be applied to rapid retargeting control of a multibody spacecraft. The minimum-time control problem of aligning the second link of the two-link manipulator with a given target point is considered. A numerical method called the minimizing-boundary-condition method is used to determine optimal solutions for the two-point boundary-value problem associated with first-order necessary conditions. Minimum-time solutions for different models of pointing systems are compared. The results of the comparison show that a two-link manipulator with two degree-of-freedom performs better than a conventional one-link system for minimum-time pointing.

Wie, Bong↗

NASA NTRS1991

Integrated controls-structures design - A practical design tool for modern spacecraft

An integrated controls-structures design approach is developed for a class of flexible spacecraft. The integrated design problem is posed in the form of simultaneous optimization of both the structural and the control design variables. The approach is demonstrated by application to the integrated design of a geostationary platform and to a ground-based flexible structure experiment. The numerical results obtained indicate that the integrated design approach can yield spacecraft designs that have substantially superior performance over the conventional design approach wherein the structural design and control design are performed sequentially.

Maghami, P. G.↗

NASA NTRS1980

Global optimality of extremals: An example

The question of the existence and location of Darboux points is crucial for minimally sufficient conditions for global optimality and for computation of optimal trajectories. A numerical investigation is presented of the Darboux points and their relationship with conjugate points for a problem of minimum fuel, constant velocity, and horizontal aircraft turns to capture a line. This simple second order optimal control problem shows that ignoring the possible existence of Darboux points may play havoc with the computation of optimal trajectories.

Kreindler, E.↗

NASA NTRS1985

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Gibson, J. S.↗

NASA NTRS1987

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

Gibson, J. S.↗

NASA NTRS1993

An optimization-based integrated controls-structures design methodology for flexible space structures

An approach for an optimization-based integrated controls-structures design is presented for a class of flexible spacecraft that require fine attitude pointing and vibration suppression. The integrated design problem is posed in the form of simultaneous optimization of both structural and control design variables. The approach is demonstrated by application to the integrated design of a generic space platform and to a model of a ground-based flexible structure. The numerical results obtained indicate that the integrated design approach can yield spacecraft designs that have substantially superior performance over a conventional design wherein the structural and control designs are performed sequentially. For example, a 40-percent reduction in the pointing error is observed along with a slight reduction in mass, or an almost twofold increase in the controlled performance is indicated with more than a 5-percent reduction in the overall mass of the spacecraft (a reduction of hundreds of kilograms).

Maghami, Peiman G.↗

NASA NTRS1974

Optimum propellant usage for reaction jet systems of space vehicles

The on-off type control for reaction jet systems is proven to be the optimal fuel scheme. However, due to the nonlinear characteristics of this type control, no direct method of solution is known for this optimal process being applied to the attitude control of space vehicles. This paper will discuss the optimization of fuel usage for an attitude control of space vehicles. A computation technique is developed for the calculation of optimal control law. The method of calculus of variations is applied to the estimation of the changes of performance index as well as terminal constraints. Thus an algorithm is obtained by the steepest descent method. A numerical example is given in the paper.

Liu, T. C.↗

NASA NTRS1975

Sikorsky interactive graphics surface design/manufacturing system

An interactive graphics system conceived to be used in the design, analysis, and manufacturing of aircraft components with free form surfaces was described. In addition to the basic surface definition and viewing capabilities inherent in such a system, numerous other features are present: surface editing, automated smoothing of control curves, variable milling patch boundary definitions, surface intersection definition and viewing, automatic creation of true offset surfaces, digitizer and drafting machine interfaces, and cutter path optimization. Documented costs and time savings of better than six to one are being realized with this system. The system was written in FORTRAN and GSP for use on IBM 2250 CRT's in conjunction with an IBM 370/158 computer.

Robbins, R.↗

NASA NTRS1985

An Integrated Control and Minimum Mass Structural Optimization Algorithm for Large Space Structures

A new approach is discussed for solving dual structural control optimization problems for high-order flexible space structures, where reduced-order structural models are employed and minimum mass designs are sought. For a given initial structural design, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the structural design variables is then determined and used to obtain successive structural redesigns, using a constrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. The minimum mass design is obtained by solving a sequence of neighboring optimal constant mass designs, where the sequence of optimal performance indices has a minimum at the optimal minimum mass design. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.

Messac, A.↗

NASA NTRS1985

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Noor, A. K.↗

NASA NTRS1991

Discrete-time model reduction in limited frequency ranges

A mathematical formulation for model reduction of discrete time systems such that the reduced order model represents the system in a particular frequency range is discussed. The algorithm transforms the full order system into balanced coordinates using frequency weighted discrete controllability and observability grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of interest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency weighted grammians. Close form solutions for the computation of frequency weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.

Horta, Lucas G.↗

NASA NTRS1989

Modeling and control of flexible space platforms with articulated payloads

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Graves, Philip C.↗

NASA NTRS1986

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Banks, H. T.↗

NASA NTRS1991

A numerical algorithm for optimal feedback gains in high dimensional linear quadratic regulator problems

A hybrid method for computing the feedback gains in linear quadratic regulator problem is proposed. The method, which combines use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite-dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantages of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed, and numerical evidence of the efficacy of these ideas is presented.

Banks, H. T.↗

NASA NTRS1996

Finite Element Simulation of Smart Structures

Finite element equations representing the behavior of piezoelectric materials when bounded to a typical structure and used as sensors and actuators were developed. Emphasis was placed on generating sensor output equations of piezoelectric sensors and responses of a typical structure bonded with piezoelectric sensors and actuators on the basis of finite element formulation. The model can predict not only structural responses due to both mechanical and electrical loading but also electrical potential due to mechanical or thermal effects. The resulted finite element equations were then used for simple control design and performance evaluation. In the control algorithm, voltages coming out from piezoelectric sensors, which are proportional to strains at sensing locations, are taken as input. The voltages applied to the piezoelectric actuators are used as output. The feasibility of integrating control algorithm with the element routine developed herein and FEAP was demonstrated. In particular, optimal independent modal space control was implemented in a software package on the basis of finite element formulation. A rudimentary finite element-control algorithm package was also developed to evaluate the performance of candidate control laws. A few numerical simulations using the software package developed herein were given. The integrated software package will provide a design tool to address issues such as how adaptive smart systems will scale to a full size aircraft, the amount of piezoelectric materials and the powers needed to actuate it for desired performance. It will also provide a viable new structural control design concept for practical applications in large flexible structures such as aerospace vehicles and aircraft.

Cui, Y. Lawrence↗