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NASA NTRS1989

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed.

Noll, Thomas E.↗

NASA NTRS1989

Recent activities within the aeroservoelasticity branch at the NASA Langley Research Center

Noll, Thomas↗

NASA NTRS1991

A methodology for using nonlinear aerodynamics in aeroservoelastic analysis and design

A methodology is presented for using the Volterra-Wiener theory of nonlinear systems in aeroservoelastic (ASE) analyses and design. The theory is applied to the development of nonlinear aerodynamic response models that can be defined in state-space form and are, therefore, appropriate for use in modern control theory. The theory relies on the identification of nonlinear kernels that can be used to predict the response of a nonlinear system due to an arbitrary input. A numerical kernel identification technique, based on unit impulse responses, is presented and applied to a simple bilinear, single-input single-output (SISO) system. The linear kernel (unit impulse response) and the nonlinear second-order kernel of the system are numerically-identified and compared with the exact, analytically-defined and linear and second-order kernels. This kernel identification technique is then applied to the CAP-TSD (Computational Aeroelasticity Program-Transonic Small Disturbance) code for identification of the linear and second-order kernels of a NACA64A010 rectangular wing undergoing pitch at M = 0.5, M = 8.5 (transonic), and M = 0.93 (transonic). Results presented demonstrate the feasibility of this approach for use with nonlinear, unsteady aerodynamic responses.

Silva, Walter A.↗

NASA NTRS1975

Adaptive spacecraft attitude control utilizing eigenaxis rotations

Conventional and adaptive attitude control of spacecraft which use control moment gyros (CMG's) as torque sources are discussed. Control laws predicated on the assumption of a linear system are used since the spacecraft equations of motion are formulated in an 'eigenaxis system' so that they are essentially linear during 'slow' maneuvers even if large angles are involved. The overall control schemes are 'optimal' in several senses. Eigenaxis rotations and a weighted pseudo-inverse CMG steering law are used and, in the adaptive case, a Model Reference Adaptive System (MRAS) controller based on Liapunov's Second Method is adopted. To substantiate the theory, digital simulation results obtained using physical parameters of a Large Space Telescope type spacecraft are presented. These results indicate that an adaptive control law is often desirable.

Cochran, J. E., Jr.↗

NASA NTRS1993

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Burns, John A.↗

NASA NTRS2004

Fleet Assignment Using Collective Intelligence

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

Antoine, Nicolas E.↗

NASA NTRS2012

Adaptive Control of Linear Modal Systems Using Residual Mode Filters and a Simple Disturbance Estimator

Flexible structures containing a large number of modes can benefit from adaptive control techniques which are well suited to applications that have unknown modeling parameters and poorly known operating conditions. In this paper, we focus on a direct adaptive control approach that has been extended to handle adaptive rejection of persistent disturbances. We extend our adaptive control theory to accommodate troublesome modal subsystems of a plant that might inhibit the adaptive controller. In some cases the plant does not satisfy the requirements of Almost Strict Positive Realness. Instead, there maybe be a modal subsystem that inhibits this property. This section will present new results for our adaptive control theory. We will modify the adaptive controller with a Residual Mode Filter (RMF) to compensate for the troublesome modal subsystem, or the Q modes. Here we present the theory for adaptive controllers modified by RMFs, with attention to the issue of disturbances propagating through the Q modes. We apply the theoretical results to a flexible structure example to illustrate the behavior with and without the residual mode filter.

Balas, Mark↗

NASA NTRS1983

Vibration control of large linear quadratic symmetric systems

Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.

Jeon, G. J.↗

NASA NTRS1976

On the use of Pade approximants to represent unsteady aerodynamic loads for arbitrarily small motions of wings

The general behavior of unsteady airloads in the frequency domain is explained. Based on this, a systematic procedure is described whereby the airloads, produced by completely arbitrary, small, time-dependent motions of a thin lifting surface in an airstream, can be predicted. This scheme employs as raw materials any of the unsteady linearized theories that have been mechanized for simple harmonic oscillations. Each desired aerodynamic transfer function is approximated by means of an appropriate Pade approximant, that is, a rational function of finite degree polynomials in the Laplace transform variable. Although these approximations have many uses, they are proving especially valuable in the design of automatic control systems intended to modify aeroelastic behavior.

Vepa, R.↗

NASA NTRS1982

An approximation theory for nonlinear partial differential equations with applications to identification and control

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Banks, H. T.↗

NASA NTRS1987

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗

NASA NTRS1988

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one-dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗

NASA NTRS1971

A control-theory model for human decision-making

A model for human decision making is an adaptation of an optimal control model for pilot/vehicle systems. The models for decision and control both contain concepts of time delay, observation noise, optimal prediction, and optimal estimation. The decision making model was intended for situations in which the human bases his decision on his estimate of the state of a linear plant. Experiments are described for the following task situations: (a) single decision tasks, (b) two-decision tasks, and (c) simultaneous manual control and decision making. Using fixed values for model parameters, single-task and two-task decision performance can be predicted to within an accuracy of 10 percent. Agreement is less good for the simultaneous decision and control situation.

Levison, W. H.↗

NASA NTRS1981

Fixed-trim re-entry guidance analysis

The terminal guidance problem for a fixed-trim re-entry body is formulated with the objective of synthesizing a closed-loop steering law. A transformation of variables and subsequent linearization of the motion, with the sight-line to the target as a reference, reduces the order of the state system for the guidance problem. The reduced order system, although nonlinear and time-varying, is simple enough to lend itself to synthesis of a class of guidance laws. A generalization of the feedforward device of classical control theory is successfully employed for compensation of roll autopilot lags. The proposed steering law exhibits superior miss-distance performance in a computational comparison with existing fixed-trim guidance laws.

Gracey, C.↗

NASA NTRS1994

Hierarchical Control and Trajectory Planning

Most of the time on this project was spent on the trajectory planning problem. The construction is equivalent to the classical spline construction in the case that the system matrix is nilpotent. If the dimension of the system is n then the spline of degree 2n-1 is constructed. This gives a new approach to the construction of splines that is more efficient than the usual construction and at the same time allows the construction of a much larger class of splines. All known classes of splines are reconstructed using the approach of linear control theory. As a numerical analysis tool control theory gives a very good tool for constructing splines. However, for the purposes of trajectory planning it is quite another story. Enclosed in this document are four reports done under this grant.

Martin, Clyde F.↗

NASA NTRS1996

Experimental and Theoretical Results in Output-Trajectory Redesign for Flexible Structures

In this paper we study the optimal redesign of output trajectory for linear invertible systems. This is particularly important for tracking control of flexible structures because the input-state trajectories that achieve the required output may cause excessive vibrations in the structure. A trade-off is then required between tracking and vibrations reduction. We pose and solve this problem as the minimization of a quadratic cost function. The theory is developed and applied to the output tracking of a flexible structure and experimental results are presented.

Dewey, J. S.↗

NASA NTRS1974

An experimental study of a hybrid adaptive control system

A Liapunov type model reference adaptive control system with five adjustable gains is implemented using a PDP-11 digital computer and an EAI 380 analog computer. The plant controlled is a laboratory type dc servo system. It is made to follow closely a second order linear model. The experimental results demonstrate the feasibility of implementing this rather complex design using only a minicomputer and a reasonable number of operational amplifiers. Also, it points out that satisfactory performance can be achieved even when certain assumptions necessary for the theory are not satisfied.

Lizewski, E. F.↗

NASA NTRS1984

Chemoviscosity modeling for thermosetting resins - I

A new analytical model for chemoviscosity variation during cure of thermosetting resins was developed. This model is derived by modifying the widely used WLF (Williams-Landel-Ferry) Theory in polymer rheology. Major assumptions involved are that the rate of reaction is diffusion controlled and is linearly inversely proportional to the viscosity of the medium over the entire cure cycle. The resultant first order nonlinear differential equation is solved numerically, and the model predictions compare favorably with experimental data of EPON 828/Agent U obtained on a Rheometrics System 4 Rheometer. The model describes chemoviscosity up to a range of six orders of magnitude under isothermal curing conditions. The extremely non-linear chemoviscosity profile for a dynamic heating cure cycle is predicted as well. The model is also shown to predict changes of glass transition temperature for the thermosetting resin during cure. The physical significance of this prediction is unclear at the present time, however, and further research is required. From the chemoviscosity simulation point of view, the technique of establishing an analytical model as described here is easily applied to any thermosetting resin. The model thus obtained is used in real-time process controls for fabricating composite materials.

Hou, T. H.↗