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NASA NTRS1989

Flutter suppression control law synthesis for the Active Flexible Wing model

The Active Flexible Wing Project is a collaborative effort between the NASA Langley Research Center and Rockwell International. The objectives are the validation of methodologies associated with mathematical modeling, flutter suppression control law development and digital implementation of the control system for application to flexible aircraft. A flutter suppression control law synthesis for this project is described. The state-space mathematical model used for the synthesis included ten flexible modes, four control surface modes and rational function approximation of the doublet-lattice unsteady aerodynamics. The design steps involved developing the full-order optimal control laws, reducing the order of the control law, and optimizing the reduced-order control law in both the continuous and the discrete domains to minimize stochastic response. System robustness was improved using singular value constraints. An 8th order robust control law was designed to increase the symmetric flutter dynamic pressure by 100 percent. Preliminary results are provided and experiences gained are discussed.

Mukhopadhyay, Vivek↗

NASA NTRS1989

Aeroservoelastic modeling and applications using minimum-state approximations of the unsteady aerodynamics

The theoretical basis of flexible-aircraft modeling techniques encompassing aerodynamic, control, and elastic-structure effects is investigated analytically, with a focus on methods which employ minimum-state approximations for the unsteady aerodynamics. Rational-function approximations to generalized aerodynamic forces are reviewed; constraints and lag-coefficient optimization are explained; the problem of physical weighting in the minimum-state equations of motion is examined; and results of typical analyses from the NASA Active Flexible Wing project (Perry et al., 1988) are presented in extensive tables and graphs and discussed in detail. The minimum-state approach is shown to produce accurate models at significantly reduced computation costs.

Tiffany, Sherwood H.↗

NASA NTRS1989

Flutter suppression control law synthesis for the active flexible wing model

Mukhopadhyay, Vivek↗

NASA NTRS1990

The Bode integrals and wave front tilt control

This paper reviews four of Bode's (1940) integrals and what those integrals tell about feedback design in the frequency domain. The resulting design paradigm is known as the Bode ideal cutoff. The Bode ideal cutoff design can be done with pencil and paper and without requiring that the compensator be of a certain fixed order or even a rational function of frequency. The Bode ideal cutoff is applied to the preliminary feedback design of wave front tilt control by two mirrors on a space based interferometer. The design example illustrates how the Bode ideal cutoff takes into account bandwidth, sensor noise constraints, and uncertainties via stability margins, and then maximizes the feedback (loop gain or disturbance rejection) over a prescribed frequency band.

Kissel, Glen J.↗

NASA NTRS1991

Flexible body dynamic stability for high performance aircraft

Dynamic equations which include the effects of unsteady aerodynamic forces and a flexible body structure were developed for a free flying high performance fighter aircraft. The linear and angular deformations are assumed to be small in the body reference frame, allowing the equations to be linearized in the deformation variables. Equations for total body dynamics and flexible body dynamics are formulated using the hybrid coordinate method and integrated in a state space format. A detailed finite element model of a generic high performance fighter aircraft is used to generate the mass and stiffness matrices. Unsteady aerodynamics are represented by a rational function approximation of the doublet lattice matrices. The equations simplify for the case of constant angular rate of the body reference frame, allowing the effect of roll rate to be studied by computing the eigenvalues of the system. It is found that the rigid body modes of the aircraft are greatly affected by introducing a constant roll rate, while the effect on the flexible modes is minimal for this configuration.

Goforth, E. A.↗

NASA NTRS1992

Distributed digital signal processors for multi-body flexible structures

Multi-body flexible structures, such as those currently under investigation in spacecraft design, are large scale (high-order) dimensional systems. Controlling and filtering such structures is a computationally complex problem. This is particularly important when many sensors and actuators are located along the structure and need to be processed in real time. This report summarizes research activity focused on solving the signal processing (that is, information processing) issues of multi-body structures. A distributed architecture is developed in which single loop processors are employed for local filtering and control. By implementing such a philosophy with an embedded controller configuration, a supervising controller may be used to process global data and make global decisions as the local devices are processing local information. A hardware testbed, a position controller system for a servo motor, is employed to illustrate the capabilities of the embedded controller structure. Several filtering and control structures which can be modeled as rational functions can be implemented on the system developed in this research effort. Thus the results of the study provide a support tool for many Control/Structure Interaction (CSI) NASA testbeds such as the Evolutionary model and the nine-bay truss structure.

Lee, Gordon K. F.↗

NASA NTRS1993

ISAC - A tool for aeroservoelastic modeling and analysis

This paper discusses the capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrate some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

NASA NTRS1993

A hybrid Pade-Galerkin technique for differential equations

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Geer, James F.↗

NASA NTRS1993

ISAC: A tool for aeroservoelastic modeling and analysis

The capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules is discussed. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrates some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

NASA NTRS1993

Aeroservoelasticity

An overview of some research activities being conducted on aeroservoelasticity (ASE) in flight vehicles is given. Modeling procedures involving rational functions for approximating unsteady aerodynamics are briefly examined along with analysis methods using the ISAC and ADAM codes. The use of ASE in integrated structure/control law design methodology, control design using constrained optimization/singular value constraints, and adaptive structures is addressed. Test demonstrations of aeroelastic wind-tunnel models or full-scale flight vehicles with active control concepts are described which have significantly enhanced the state of the art in active control technology. The Active Flexible Wing wind-tunnel test project is discussed in detail to emphasize today's activities and accomplishments. Finally, recent activities illustrating the state of the art of ASE in high-speed aircraft are examined.

Noll, Thomas E.↗

NASA NTRS1992

Size-reduction techniques for the determination of efficient aeroservoelastic models

Size-reduction techniques for determining efficient time-domain state-space aeroservoelastic models are presented. Various rational function approximation methods of the unsteady aerodynamic force coefficients are brought to a common motion, emphasizing their differences. Among these, the classic Roger's method is the easier to apply but its resulting number of aerodynamic states is typically equal to or larger than the number of structural states. On the other hand, the minimum-state (MS) method, which typically reduces the number of aerodynamic states by 70 percent or more, requires the solution of an iterative nonlinear least-square solution. The MS computational efforts are reduced significantly when three approximation constraints are applied.

Karpel, Mordechay↗

NASA NTRS1995

A test of a vortex method for the computation of flap side edge noise

Upon approach to landing, a major source location of airframe noise occurs at the side edges of the part span, trailing edge flaps. In the vicinity of these flaps, a complex arrangement of spanwise flow with primary and secondary tip vortices may form. Each of these vortices is observed to become fully three-dimensional. In the present study, a numerical model is developed to investigate the noise radiated from the side edge of a flap. The inherent three-dimensionality of this flow forces us to carefully consider a numerical scheme which will be both accurate in its prediction of the flow acoustics and also computationally efficient. Vortex methods have offered a fast and efficient means of simulating many two and three-dimensional, vortex dominated flows. In vortex methods, the time development of the flow is tracked by following exclusively the vorticity containing regions. Through the Biot-Savart law, knowledge of the vorticity field enables one to obtain flow quantities at any desired location during the flow evolution. In the present study, a numerical procedure has been developed which incorporates the Lagrangian approach of vortex methods into a calculation for the noise radiated by a flow-surface interaction. In particular, the noise generated by a vortex in the presence of a flat half plane is considered. This problem serves as a basic model of flap edge flow. It also permits the direct comparison between our computed results and previous acoustic analyses performed for this problem. In our numerical simulations, the mean flow is represented by the complex potential W(z) = Aiz(exp l/2), which is obtained through conformal mapping techniques. The magnitude of the mean flow is controlled by the parameter A. This mean flow has been used in the acoustic analysis by Hardin and is considered a reasonable model of the flow field in the vicinity of the edge and away from the leading and trailing edges of the flap. To represent the primary vortex which occurs near the flap, a point vortex is introduced just below the flat half plane. Using a technique from panel methods, boundary conditions on the flap surface are satisfied by the introduction of a row of stationary point vortices along the extent of the flap. At each time step in the calculation, the strength of these vortices is chosen to eliminate the normal velocity at intermediary collocation points. The time development of the overall flow field is then tracked using standard techniques from vortex methods. Vortex trajectories obtained through this computation are in good agreement with those predicted by the analytical solution given by Hardin, thus verifying the viability of this procedure for more complex flow arrangements. For the flow acoustics, the Ffowcs Williams-Hawkings equation is numerically integrated. This equation supplies the far field acoustic pressure based upon pressures occurring along the flap surface. With our vortex method solution, surface pressures may be obtained with exceptional resolution. The Ffowcs Williams-Hawkings equation is integrated using a spatially fourth order accurate Simpson's rule. Rational function interpolation is used to obtain the surface pressures at the appropriate retarded times. Comparisons between our numerical results for the acoustic pressure and those predicted by the Hardin analysis have been made. Preliminary results indicate the need for an improved integration technique. In the future, the numerical procedure developed in this study will be applied to the case of a rectangular flap of finite thickness and ultimately modified for application to the fully three-dimensional problem.

Martin, James E.↗

NASA NTRS1995

The Third-Difference Approach to Modified Allan Variance

This study gives strategies for estimating the modified Allan variance (mvar) and formulas for computing the equivalent degrees of freedom (edf) of the estimators. A third-difference formulation of mvar leads to a tractable formula for edf in the presence of power-law phase noise. The effect of estimation stride on edf is tabulated. First-degree rational-function approximations for edf are derived.

Allan variance frequency instability statistical m↗

NASA NTRS2009

Application of Reduced Order Transonic Aerodynamic Influence Coefficient Matrix for Design Optimization

Supporting the Aeronautics Research Mission Directorate guidelines, the National Aeronautics and Space Administration [NASA] Dryden Flight Research Center is developing a multidisciplinary design, analysis, and optimization [MDAO] tool. This tool will leverage existing tools and practices, and allow the easy integration and adoption of new state-of-the-art software. Today s modern aircraft designs in transonic speed are a challenging task due to the computation time required for the unsteady aeroelastic analysis using a Computational Fluid Dynamics [CFD] code. Design approaches in this speed regime are mainly based on the manual trial and error. Because of the time required for unsteady CFD computations in time-domain, this will considerably slow down the whole design process. These analyses are usually performed repeatedly to optimize the final design. As a result, there is considerable motivation to be able to perform aeroelastic calculations more quickly and inexpensively. This paper will describe the development of unsteady transonic aeroelastic design methodology for design optimization using reduced modeling method and unsteady aerodynamic approximation. The method requires the unsteady transonic aerodynamics be represented in the frequency or Laplace domain. Dynamically linear assumption is used for creating Aerodynamic Influence Coefficient [AIC] matrices in transonic speed regime. Unsteady CFD computations are needed for the important columns of an AIC matrix which corresponded to the primary modes for the flutter. Order reduction techniques, such as Guyan reduction and improved reduction system, are used to reduce the size of problem transonic flutter can be found by the classic methods, such as Rational function approximation, p-k, p, root-locus etc. Such a methodology could be incorporated into MDAO tool for design optimization at a reasonable computational cost. The proposed technique is verified using the Aerostructures Test Wing 2 actually designed, built, and tested at NASA Dryden Flight Research Center. The results from the full order model and the approximate reduced order model are analyzed and compared.

Pak, Chan-gi↗

NASA NTRS2001

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function - i.e. a ratio of two polynomials - of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGSs performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa.

Mengshoel, Ole J.↗

NASA NTRS2015

Kodiak: An Implementation Framework for Branch and Bound Algorithms

Recursive branch and bound algorithms are often used to refine and isolate solutions to several classes of global optimization problems. A rigorous computation framework for the solution of systems of equations and inequalities involving nonlinear real arithmetic over hyper-rectangular variable and parameter domains is presented. It is derived from a generic branch and bound algorithm that has been formally verified, and utilizes self-validating enclosure methods, namely interval arithmetic and, for polynomials and rational functions, Bernstein expansion. Since bounds computed by these enclosure methods are sound, this approach may be used reliably in software verification tools. Advantage is taken of the partial derivatives of the constraint functions involved in the system, firstly to reduce the branching factor by the use of bisection heuristics and secondly to permit the computation of bifurcation sets for systems of ordinary differential equations. The associated software development, Kodiak, is presented, along with examples of three different branch and bound problem types it implements.

Smith, Andrew P.↗

NASA NTRS2016

Unsteady Aerodynamic Force Sensing from Measured Strain

A simple approach for computing unsteady aerodynamic forces from simulated measured strain data is proposed in this study. First, the deflection and slope of the structure are computed from the unsteady strain using the two-step approach. Velocities and accelerations of the structure are computed using the autoregressive moving average model, on-line parameter estimator, low-pass filter, and a least-squares curve fitting method together with analytical derivatives with respect to time. Finally, aerodynamic forces over the wing are computed using modal aerodynamic influence coefficient matrices, a rational function approximation, and a time-marching algorithm. A cantilevered rectangular wing built and tested at the NASA Langley Research Center (Hampton, Virginia, USA) in 1959 is used to validate the simple approach. Unsteady aerodynamic forces as well as wing deflections, velocities, accelerations, and strains are computed using the CFL3D computational fluid dynamics (CFD) code and an MSC/NASTRAN code (MSC Software Corporation, Newport Beach, California, USA), and these CFL3D-based results are assumed as measured quantities. Based on the measured strains, wing deflections, velocities, accelerations, and aerodynamic forces are computed using the proposed approach. These computed deflections, velocities, accelerations, and unsteady aerodynamic forces are compared with the CFL3D/NASTRAN-based results. In general, computed aerodynamic forces based on the lifting surface theory in subsonic speeds are in good agreement with the target aerodynamic forces generated using CFL3D code with the Euler equation. Excellent aeroelastic responses are obtained even with unsteady strain data under the signal to noise ratio of -9.8dB. The deflections, velocities, and accelerations at each sensor location are independent of structural and aerodynamic models. Therefore, the distributed strain data together with the current proposed approaches can be used as distributed deflection, velocity, and acceleration sensors. This research demonstrates the feasibility of obtaining induced drag and lift forces through the use of distributed sensor technology with measured strain data. An active induced drag control system thus can be designed using the two computed aerodynamic forces, induced drag and lift, to improve the fuel efficiency of an aircraft. Interpolation elements between structural finite element grids and the CFD grids and centroids are successfully incorporated with the unsteady aeroelastic computation scheme. The most critical technology for the success of the proposed approach is the robust on-line parameter estimator, since the least-squares curve fitting method depends heavily on aeroelastic system frequencies and damping factors.

shape sensing↗

NASA NTRS2017

Aeroservoelastic Modeling of Body Freedom Flutter for Control System Design

One of the most severe forms of coupling between aeroelasticity and flight dynamics is an instability called freedom flutter. The existing tools often assume relatively weak coupling, and are therefore unable to accurately model body freedom flutter. Because the existing tools were developed from traditional flutter analysis models, inconsistencies in the final models are not compatible with control system design tools. To resolve these issues, a number of small, but significant changes have been made to the existing approaches. A frequency domain transformation is used with the unsteady aerodynamics to ensure a more physically consistent stability axis rational function approximation of the unsteady aerodynamic model. The aerodynamic model is augmented with additional terms to account for limitations of the baseline unsteady aerodynamic model and to account for the gravity forces. An assumed modes method is used for the structural model to ensure a consistent definition of the aircraft states across the flight envelope. The X-56A stiff wing flight-test data were used to validate the current modeling approach. The flight-test data does not show body-freedom flutter, but does show coupling between the flight dynamics and the aeroelastic dynamics and the effects of the fuel weight.

aeroservoelastic↗