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NASA NTRS2017

LMI-Based Fuzzy Optimal Variance Control of Airfoil Model Subject to Input Constraints

This paper presents a study of fuzzy optimal variance control problem for dynamical systems subject to actuator amplitude and rate constraints. Using Takagi-Sugeno fuzzy modeling and dynamic Parallel Distributed Compensation technique, the stability and the constraints can be cast as a multi-objective optimization problem in the form of Linear Matrix Inequalities. By utilizing the formulations and solutions for the input and output variance constraint problems, we develop a fuzzy full-state feedback controller. The stability and performance of the proposed controller is demonstrated through its application to the airfoil flutter suppression.

optimal variance control↗

NASA NTRS1987

Physiographic constraints on the origin of lunar wrinkle ridges

Wrinkle ridges are linear asymmetric topographic highs with considerable morphologic complexity that are commonly found on the lunar maria and the smooth plains of Mars and Mercury. The origin of planetary wrinkle ridges has been a much argued and debated topic. Early ideas suggested that wrinkle ridges resulted from volcanic intrusion and extrusion of high viscosity lavas; these early ideas were countered with suggestions that wrinkle ridges formed from tectonic processes involving folding and faulting. Combined volcanic and tectonic mechanisms have also been suggested. The identification and analysis of a number of morphologically similar structures on the earth has helped in the recent interpretation of wrinkle ridges as thrust faults that deform surface rocks. Nevertheless, there remains the uncertainty of the dominant role of thrusting versus folding in the formation of planetary wrinkle ridges. Presented is a detailed physiographic analysis of lunar wrinkle ridges in an effort to help distinguish the dominant deformation mechanism. Results agree with the findings of the earth analog study and support the hypothesis that wrinkle ridges form from thrust faults that deform surface rocks.

Golombek, M. P.↗

NASA NTRS1988

Recursive dynamics of topological trees of rigid bodies via Kalman filtering and Bryson-Frazier smoothing

The inverse and forward dynamics problems for a set of rigid bodies connected by hinges to form a topological tree are solved by using recursive techniques from linear filtering and smoothing theory. An inward filtering sequence computes a set of constraint moments and forces. This is followed by an outward sequence to determine a corresponding set of angular and linear accelerations. An inward sequence begins at the tips of all of the terminal bodies of the tree and proceeds inwardly through all of the branches until it reaches the root. Similarly, an outward sequence begins at the root and propagates to all of the tree branches until it reaches the tips of the terminal bodies. The paper also provides an approach to evaluate recursively the composite multibody system inertia matrix and its inverse.

Rodriguez, G.↗

NASA NTRS1991

Linearizing feedforward/feedback attitude control

An approach to attitude control theory is introduced in which a linear form is postulated for the closed-loop rotation error dynamics, then the exact control law required to realize it is derived. The nonminimal (four-component) quaternion form is used to attitude because it is globally nonsingular, but the minimal (three-component) quaternion form is used for attitude error because it has no nonlinear constraints to prevent the rotational error dynamics from being linearized, and the definition of the attitude error is based on quaternion algebra. This approach produces an attitude control law that linearizes the closed-loop rotational error dynamics exactly, without any attitude singularities, even if the control errors become large.

Paielli, Russell A.↗

NASA NTRS1973

A model of the human in a cognitive prediction task.

The human decision maker's behavior when predicting future states of discrete linear dynamic systems driven by zero-mean Gaussian processes is modeled. The task is on a slow enough time scale that physiological constraints are insignificant compared with cognitive limitations. The model is basically a linear regression system identifier with a limited memory and noisy observations. Experimental data are presented and compared to the model.

Rouse, W. B.↗

NASA NTRS1991

Stacking-sequence optimization for buckling of laminated plates by integer programming

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for given total thickness, and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily aviable software. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Haftka, Raphael T.↗

NASA NTRS1973

Synthesis of oscillating adaptive feedback systems

A synthesis theory is developed which allows system design to proceed from practical specifications on system command and/or disturbance response to a design which is very nearly optimal in terms of feedback sensor noise effects. The approach taken is to replace the nonlinear element by a mean square error minimizing approximation (dual-input describing function), and then use linear frequency domain synthesis techniques subject to additional constraints imposed by the limit cycle and the approximator. Synthesis techniques are also developed for a similar system using an externally excited oscillating signal with the above approach. The results remove the design of the systems considered from the realm of simulation and experimentation, permitting true synthesis and the optimization that accompanies it.

Smay, J. W.↗

NASA NTRS1973

The Lyapunov stabilization of satellite equations of motion using integrals

A method is introduced that weakens the Lyapunov or in track instability of satellite equations of motion. The method utilizes a linearized energy integral of satellite motion as a constraint on solutions obtained by numerical integration. The procedure prevents local numerical error from altering the frequency associated with the fast angular variable and thereby reduces the Lyapunov instability and the global numerical error. Applications of the method to satellite motion show accuracy improvements of two to three orders of magnitude in position and velocity after 50 revolutions. A modification of the method is presented that allows the use of slowly varying integrals of motion.

Nacozy, P. E.↗

NASA NTRS1975

A transformation method for constrained-function minimization

A direct method for constrained-function minimization is discussed. The method involves the construction of an appropriate function mapping all of one finite dimensional space onto the region defined by the constraints. Functions which produce such a transformation are constructed for a variety of constraint regions including, for example, those arising from linear and quadratic inequalities and equalities. In addition, the computational performance of this method is studied in the situation where the Davidon-Fletcher-Powell algorithm is used to solve the resulting unconstrained problem. Good performance is demonstrated for 19 test problems by achieving rapid convergence to a solution from several widely separated starting points.

Park, S. K.↗

NASA NTRS1975

A variable-metric algorithm employing linear and quadratic penalties

A variable-metric algorithm is described that uses both linear and quadratic penalty terms for handling nonlinear constraints. Quadratic penalty coefficients are adjusted in a process which maintains a positive-definite matrix of second partial derivatives of the function without generating the large positive eigenvalues which cause zigzagging and slow convergence. The schemes suggested use inferred second-order properties not only in terms of the variable metric of the Davidson-Fletcher-Powell algorithm (or its relatives) but by estimating of second directional derivatives by fitting cubics to various functions along search directions.

Kelley, H. J.↗

NASA NTRS1978

Optimal analytic rendezvous using Clohessy-Wiltshire equations

The optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous is obtained analytically for the Clohessy-Wiltshire equations with a linear gravity model assumption. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.

Jezewski, D. J.↗

NASA NTRS1979

Linearized unsteady jet analysis

The introduction of a time dependency into a jet flow to change the rate at which it mixes with a coflowing stream or ambient condition is investigated. The advantages and disadvantages of the unsteady flow are discussed in terms of steady state mass and momentum transfer. A linear system which is not limited by frequency constraints and evolves through a simplification of the equations of motion is presented for the analysis of the unsteady flow field generated by the time dependent jet.

Viets, H.↗

NASA NTRS1980

Thermal structure of Jupiter's atmosphere obtained by inversion of Voyager 1 infrared measurements

Data from the Voyager 1 infrared spectroscopy investigation have been used to retrieve temperature profiles in the atmosphere of Jupiter. An analysis of information content indicates good vertical resolution with low measurement noise propagation in the Jovian troposphere and reduced resolution in the stratosphere. Among the problems found in common with the sounding of the terrestrial atmosphere are limited tropopause definition and dependence on upper boundary constraints. Preliminary results obtained by using a constrained linear algorithm and a filtered Chahine approach are presented.

Conrath, B. J.↗

NASA NTRS1984

Fitting aerodynamic forces in the Laplace domain: An application of a nonlinear nongradient technique to multilevel constrained optimization

A technique which employs both linear and nonlinear methods in a multilevel optimization structure to best approximate generalized unsteady aerodynamic forces for arbitrary motion is described. Optimum selection of free parameters is made in a rational function approximation of the aerodynamic forces in the Laplace domain such that a best fit is obtained, in a least squares sense, to tabular data for purely oscillatory motion. The multilevel structure and the corresponding formulation of the objective models are presented which separate the reduction of the fit error into linear and nonlinear problems, thus enabling the use of linear methods where practical. Certain equality and inequality constraints that may be imposed are identified; a brief description of the nongradient, nonlinear optimizer which is used is given; and results which illustrate application of the method are presented.

Tiffany, S. H.↗

NASA NTRS1985

Single step optimization of feedback-decoupled spacecraft attitude maneuvers

A next-state optimization technique for monitoring spacecraft maneuvers is examined. The optimization technique permits simultaneous trajectory planning and tracking, incorporates actuator saturation and attitude constraints, and prevents overshoot and undershoot. The global linearization of the dynamics and kinematics for a spacecraft driven by reaction wheels is considered. The equations utilized to derive the spacecraft trajectories are presented. The applications of the next-state optimization procedure to a spacecraft maneuvered by momentum transfer devices and the tracking of the nominal trajectory of a critically damped harmonic oscillator response are described.

Dwyer, T. A. W., III↗

NASA NTRS1993

Forcing function modeling for flow induced vibration

The fundamental forcing function unsteady aerodynamics for application to turbomachine blade row forced response are considered, accomplished through a series of experiments performed in a rotating annular cascade and a research axial flow turbine. In particular, the unsteady periodic flowfields downstream of rotating rows of perforated plates, airfoils and turbine blade rows are measured with a cross hot-wire and an unsteady total pressure probe. The unsteady velocity and static pressure fields were then analyzed harmonically and split into vortical and potential gusts, accomplished by developing a gust splitting analysis which includes both gust unsteady static pressure and velocity data. The perforated plate gusts closely were found to be linear theory vortical gusts, satisfying the vortical gust constraints. The airfoil and turbine blade row generated velocity perturbations did not satisfy the vortical gust constraints. However, the decomposition of the unsteady flow field separated the data into a propagating vortical component which satisfied these vortical gust constraints and a decaying potential component.

Fleeter, Sanford↗

NASA NTRS1993

Simplified, inverse, ejector design tool

A simple lumped parameter based inverse design tool has been developed which provides flow path geometry and entrainment estimates subject to operational, acoustic, and design constraints. These constraints are manifested through specification of primary mass flow rate or ejector thrust, fully-mixed exit velocity, and static pressure matching. Fundamentally, integral forms of the conservation equations coupled with the specified design constraints are combined to yield an easily invertible linear system in terms of the flow path cross-sectional areas. Entrainment is computed by back substitution. Initial comparison with experimental and analogous one-dimensional methods show good agreement. Thus, this simple inverse design code provides an analytically based, preliminary design tool with direct application to High Speed Civil Transport (HSCT) design studies.

Dechant, Lawrence J.↗

NASA NTRS1997

Optimal Trajectories for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

This paper presents a summary of a series of recent analytical studies conducted to investigate one-engine-inoperative (OEI) optimal control strategies and the associated optimal trajectories for a twin engine helicopter in Category-A terminal-area operations. These studies also examine the associated heliport size requirements and the maximum gross weight capability of the helicopter. Using an eight states, two controls, augmented point-mass model representative of the study helicopter, continued takeoff (CTO), rejected takeoff (RTO), balked landing (BL), and continued landing (CL) are investigated for both vertical-takeoff-and-landing (VTOL) and short-takeoff-and-landing (STOL) terminal-area operations. The formulation of the non-linear optimal control problems with considerations for realistic constraints, solution methods for the two-point boundary-value problem, a new real-time generation method for the optimal OEI trajectories, and the main results of this series of trajector optimization studies are presented. In particular, a new balanced-weight concept for determining the takeoff decision point for VTOL Category-A operations is proposed, extending the balanced-field length concept used for STOL operations.

Chen, Robert T. N.↗