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NASA NTRS1993

Mapping robust parallel multigrid algorithms to scalable memory architectures

The convergence rate of standard multigrid algorithms degenerates on problems with stretched grids or anisotropic operators. The usual cure for this is the use of line or plane relaxation. However, multigrid algorithms based on line and plane relaxation have limited and awkward parallelism and are quite difficult to map effectively to highly parallel architectures. Newer multigrid algorithms that overcome anisotropy through the use of multiple coarse grids rather than relaxation are better suited to massively parallel architectures because they require only simple point-relaxation smoothers. In this paper, we look at the parallel implementation of a V-cycle multiple semicoarsened grid (MSG) algorithm on distributed-memory architectures such as the Intel iPSC/860 and Paragon computers. The MSG algorithms provide two levels of parallelism: parallelism within the relaxation or interpolation on each grid and across the grids on each multigrid level. Both levels of parallelism must be exploited to map these algorithms effectively to parallel architectures. This paper describes a mapping of an MSG algorithm to distributed-memory architectures that demonstrates how both levels of parallelism can be exploited. The result is a robust and effective multigrid algorithm for distributed-memory machines.

Overman, Andrea↗

NASA NTRS1993

Robust unstructured grid generation with VGRID

The objective of this work is to develop a robust, user-oriented, unstructured grid-generation technique for fast generation of Euler/viscous grids around complex 2D and 3D configurations. To do this, two different approaches are employed: the advancing-front method for generation of Euler grids; and the advancing-layers method for generation of viscous grids. A discussion of these topics is presented in viewgraph form.

Shahyar Pirzadeh↗

NASA NTRS1994

Robust stability of second-order systems

Nonlinear control using feedback linearization or inverse dynamics for robotic manipulators yields good results in the absence of modeling uncertainty. However, modeling uncertainties due to unknown joint friction coefficients and payload variations can give rise to undesirable characteristics when these control systems are implemented. It is shown how passivity concepts can be used to supplement the feedback linearization control design technique, in order to make it robust with respect to the uncertain effects mentioned above. Results are obtained for space manipulators with freely floating base; however, they are applicable to fixed base manipulators as well. The controller guarantees asymptotic tracking of the joint variables. Closed-loop simulation results are illustrated for planar space manipulators for cases where uncertainty exists in friction modeling and payload inertial parameters.

Chuang, C.-H.↗

NASA NTRS1994

Research in robust control for hypersonic aircraft

The research during the third reporting period focused on fixed order robust control design for hypersonic vehicles. A new technique was developed to synthesize fixed order H(sub infinity) controllers. A controller canonical form is imposed on the compensator structure and a homotopy algorithm is employed to perform the controller design. Various reduced order controllers are designed for a simplified version of the hypersonic vehicle model used in our previous studies to demonstrate the capabilities of the code. However, further work is needed to investigate the issue of numerical ill-conditioning for large order systems and to make the numerical approach more reliable.

Calise, A. J.↗

NASA NTRS1994

Parametric robust control and system identification: Unified approach

Despite significant advancement in the area of robust parametric control, the problem of synthesizing such a controller is still a wide open problem. Thus, we attempt to give a solution to this important problem. Our approach captures the parametric uncertainty as an H(sub infinity) unstructured uncertainty so that H(sub infinity) synthesis techniques are applicable. Although the techniques cannot cope with the exact parametric uncertainty, they give a reasonable guideline to model the unstructured uncertainty that contains the parametric uncertainty. An additional loop shaping technique is also introduced to relax its conservatism.

Keel, Leehyun↗

NASA NTRS1994

Robust control design techniques for active flutter suppression

In this paper, an active flutter suppression problem is studied for a thin airfoil in unsteady aerodynamics. The mathematical model of this system is infinite dimensional because of Theodorsen's function which is irrational. Several second order approximations of Theodorsen's function are compared. A finite dimensional model is obtained from such an approximation. We use H infinity control techniques to find a robustly stabilizing controller for active flutter suppression.

Ozbay, Hitay↗

NASA NTRS1994

Robustness properties of LQG optimized compensators for collocated rate sensors

In this paper we study the robustness with respect to stability of the closed-loop system with collocated rate sensor using LQG (mean square rate) optimized compensators. Our main result is that the transmission zeros of the compensator are precisely the structure modes when the actuator/sensor locations are 'pinned' and/or 'clamped': i.e., motion in the direction sensed is not allowed. We have stability even under parameter mismatch, except in the unlikely situation where such a mode frequency of the assumed system coincides with an undamped mode frequency of the real system and the corresponding mode shape is an eigenvector of the compensator transfer function matrix at that frequency. For a truncated modal model - such as that of the NASA LaRC Phase Zero Evolutionary model - the transmission zeros of the corresponding compensator transfer function can be interpreted as the structure modes when motion in the directions sensed is prohibited.

Balakrishnan, A. V.↗

NASA NTRS1994

A flux splitting scheme with high-resolution and robustness for discontinuities

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

Wada, Yasuhiro↗

NASA NTRS1994

Robust stability of second-order systems

This progress report gives current progress of the research in nonlinear robust control using positive real concept. The progress is documented in a draft paper. In the paper, the manipulator dynamics is reformulated differently from the existing equations of motion for free base robots. This new formulation gives a compact form of the dynamic equations for easy computation. The nonlinear terms are now considered. The results show that for an additional nonlinear friction term, the feedback controller designed using passivity concept works quite well. Although design of such a controller requires simulation of the dynamics for the example shown in the following draft, this design procedure is feasible.

Chuang, C.-H.↗

NASA NTRS1993

Flight control application of new stability robustness bounds for linear uncertain systems

This paper addresses the issue of obtaining bounds on the real parameter perturbations of a linear state-space model for robust stability. Based on Kronecker algebra, new, easily computable sufficient bounds are derived that are much less conservative than the existing bounds since the technique is meant for only real parameter perturbations (in contrast to specializing complex variation case to real parameter case). The proposed theory is illustrated with application to several flight control examples.

Yedavalli, Rama K.↗

NASA NTRS1994

Robust inverse kinematics using damped least squares with dynamic weighting

This paper presents a general method for calculating the inverse kinematics with singularity and joint limit robustness for both redundant and non-redundant serial-link manipulators. Damped least squares inverse of the Jacobian is used with dynamic weighting matrices in approximating the solution. This reduces specific joint differential vectors. The algorithm gives an exact solution away from the singularities and joint limits, and an approximate solution at or near the singularities and/or joint limits. The procedure is here implemented for a six d.o.f. teleoperator and a well behaved slave manipulator resulted under teleoperational control.

Schinstock, D. E.↗

NASA NTRS1994

Matlab as a robust control design tool

This presentation introduces Matlab as a tool used in flight control research. The example used to illustrate some of the capabilities of this software is a robust controller designed for a single stage to orbit air breathing vehicles's ascent to orbit. The global requirements of the controller are to stabilize the vehicle and follow a trajectory in the presence of atmospheric disturbances and strong dynamic coupling between airframe and propulsion.

Gregory, Irene M.↗

NASA NTRS1994

Robust telescope scheduling

This paper presents a technique for building robust telescope schedules that tend not to break. The technique is called Just-In-Case (JIC) scheduling and it implements the common sense idea of being prepared for likely errors, just in case they should occur. The JIC algorithm analyzes a given schedule, determines where it is likely to break, reinvokes a scheduler to generate a contingent schedule for each highly probable break case, and produces a 'multiply contingent' schedule. The technique was developed for an automatic telescope scheduling problem, and the paper presents empirical results showing that Just-In-Case scheduling performs extremely well for this problem.

Swanson, Keith↗

NASA NTRS1995

Robust Rocket Engine Concept

The potential for a revolutionary step in the durability of reusable rocket engines is made possible by the combination of several emerging technologies. The recent creation and analytical demonstration of life extending (or damage mitigating) control technology enables rapid rocket engine transients with minimum fatigue and creep damage. This technology has been further enhanced by the formulation of very simple but conservative continuum damage models. These new ideas when combined with recent advances in multidisciplinary optimization provide the potential for a large (revolutionary) step in reusable rocket engine durability. This concept has been named the robust rocket engine concept (RREC) and is the basic contribution of this paper. The concept also includes consideration of design innovations to minimize critical point damage.

Lorenzo, Carl F.↗

NASA NTRS1995

Robust Quantitative Measurement of Flows and Transparent or Highly Reflective Objects

The liquid crystal point diffraction interferometer (LCPDI) is a new instrument that has been developed for the measurement of phase objects. The LCPDI uses the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave-fronts. A solid state camera provides very high data density and automated data reduction. The instrument can measure either transparent objects like fluids and lenses, or highly reflective opaque objects like mirrors. In the former case, the refractive index distribution is measured and then related to various properties like temperature, density, chemical composition, or thickness. In the latter case, the measured phase distribution is related to the object shape. The objects measured must be stationary or quasisteady state because the measurement requires the acquisition of several frames of image data during which time the object's properties must not have changed. The data acquisition time depends on the speed of the frame grabber and the required number of data frames. Typically, three to five frames taking 1 to 2 seconds are required. The potential for faster data acquisition exists.

Mercer, Carolyn R.↗

NASA NTRS1994

Robustness of reduced-order multivariable state-space self-tuning controller

In this paper, we present a quantitative analysis of the robustness of a reduced-order pole-assignment state-space self-tuning controller for a multivariable adaptive control system whose order of the real process is higher than that of the model used in the controller design. The result of stability analysis shows that, under a specific bounded modelling error, the adaptively controlled closed-loop real system via the reduced-order state-space self-tuner is BIBO stable in the presence of unmodelled dynamics.

Yuan, Zhuzhi↗

NASA NTRS1996

An efficient and robust method for predicting helicopter rotor high-speed impulsive noise

A new formulation for the Ffowcs Williams-Hawkings quadrupole source, which is valid for a far-field in-plane observer, is presented. The far-field approximation is new and unique in that no further approximation of the quadrupole source strength is made and integrands with r(exp -2) and r(exp -3) dependence are retained. This paper focuses on the development of a retarded-time formulation in which time derivatives are analytically taken inside the integrals to avoid unnecessary computational work when the observer moves with the rotor. The new quadrupole formulation is similar to Farassat's thickness and loading formulation 1A. Quadrupole noise prediction is carried out in two parts: a preprocessing stage in which the previously computed flow field is integrated in the direction normal to the rotor disk, and a noise computation stage in which quadrupole surface integrals are evaluated for a particular observer position. Preliminary predictions for hover and forward flight agree well with experimental data. The method is robust and requires computer resources comparable to thickness and loading noise prediction.

Brentner, Kenneth S.↗

NASA NTRS1996

Processing and Properties of Fiber Reinforced Polymeric Matrix Composites: Processing Robustness of IM7/PETI Polyimide Composites - Part 2

The processability of a phenylethynyl terminated imide (PETI) resin matrix composite was investigated. Unidirectional prepregs were made by coating an N-methylpyrrolidone solution of the amide acid oligomer onto unsized IM7. Two batches of prepregs were used: one was made by NASA in-house, and the other was from an industrial source. The composite processing robustness was investigated with respect to the effect of B-staging conditions, the prepreg shelf life, and the optimal processing window. Rheological measurements indicated that PETI's processability was only slightly affected over a wide range of B-staging temperatures (from 250 C to 300 C). The open hole compression (OHC) strength values were statistically indistinguishable among specimens consolidated using various B-staging conditions. Prepreg rheology and OHC strengths were also found not to be affected by prolonged (i.e., up to 60 days) ambient storage. An optimal processing window was established using response surface methodology. It was found that IM7/PETI composite is more sensitive to the consolidation temperature than to the consolidation pressure. A good consolidation was achievable at 371 C/100 Psi, which yielded an OHC strength of 62 Ksi at room temperature. However, processability declined dramatically at temperatures below 350 C.

Hou, Tan-Hung↗