Engineering topics

Hunt, L. R.

Publications and source records attributed to Hunt, L. R..

At least 37 records · Page 2

NASA NTRS1986

Output time response approximation

The approximation of the output response of a nonlinear system by the output response of a linear system to a desired order irrespective of the admissible input applied should prove useful for purposes of control generation and simulation. Given a nonlinear system, an integer k, and an open subset of state space, sufficient conditions are stated that such a linear approximation exists to order k for every point in the set. In addition, a method for finding the approximating linear systems is presented.

Hunt, L. R.↗

NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

NASA NTRS1985

A canonical form for nonlinear systems

The conceptions of transformation and canonical form have been much used to analyze the structure of linear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form.

Su, R.↗

NASA NTRS1985

Approximations of nonlinear systems having outputs

For a nonlinear system with output derivative x = f(x) and y = h(x), two types of linearizations about a point x(0) in state space are considered. One is the usual Taylor series approximation, and the other is defined by linearizing the appropriate Lie derivatives of the output with respect to f about x(0). The latter is called the obvservation model and appears to be quite natural for observation. It is noted that there is a coordinate system in which these two kinds of linearizations agree. In this coordinate system, a technique to construct an observer is introduced.

Hunt, L. R.↗

NASA NTRS1984

Application of nonlinear transformations to automatic flight control

The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.

Meyer, G.↗

NASA NTRS1984

Aerothermal tests of a 12.5 percent cone at Mach 6.7 for various Reynolds numbers, angles of attack and nose shapes

The effects of free-stream unit Reynolds number, angle of attack, and nose shape on the aerothermal environment of a 3-ft basediameter, 12.5 deg half-angle cone were investigated in the Langley 8-foot high temperature tunnel at Mach 6.7. The average total temperature was 3300 R, the freestream unit Reynolds number ranged from 400,000 to 1,400,000 per foot, and the angle of attack ranged from 0 deg to 10 deg. Three nose configurations were tested on the cone: a 3-in-radius tip, a 1-in-radius tip on an ogive frustum, and a sharp tip on an ogive frustum. Surface-pressure and cold-wall heating-rate distributions were obtained for laminar, transitional temperature in the shock layer were obtained. The location of the start of transition moved forward both on windward and leeward sides with increasing free-stream Reynolds numbers, increasing angle of attack, and decreasing nose bluntness.

Nowak, R. J.↗

NASA NTRS1984

Nonlinear control of aircraft

Transformations of nonlinear systems were used to design automatic flight controllers for vertical and short takeoff aircraft. Under the assumption that a nonlinear system can be mapped to a controllable linear system, a method using partial differential equations was constructed to approximate transformations in cases where exact ones cannot be found. An application of the design theory to a rotorcraft, the UH-1H helicopter, was presented.

Hunt, L. R.↗

NASA NTRS1984

Observability for two-dimensional systems

Sufficient conditions that a two-dimensinal system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no information is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problems, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability.

Hunt, L. R.↗

NASA NTRS1983

Canonical forms for nonlinear systems

Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.

Su, R.↗

NASA NTRS1983

Linear approximations of nonlinear systems

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.

Hunt, L. R.↗

NASA NTRS1983

Global transformations of nonlinear systems

Necessary and sufficient conditions for a nonlinear system of equations to be locally equivalent, in a neighborhood of the origin in the real number system, to a controllable linear system are combined with several versions of the global inverse function theorem to define sufficient conditions for transforming the nonlinear system into a linear system. Additionally, a technique is introduced for developing a transformation under the assumptions that the columns of a controllability matrix span an n-dimensional space. Finally, the n-l form of the controllability matrix columns is demonstrated to be involutive

Hunt, L. R.↗

NASA NTRS1983

Nonlinear transformat

A technique for designing automatic flight controllers for aircraft which utilizes the transformation theory of nonlinear systems to linear systems is presently being developed at NASA Ames Research Center. A method is considered in which a given nonlinear is transformed to a controllable linear system in Brunovsky canonical form. A linear approximation is introduced to the nonlinear system called the modified tangent model. This model is easily computed. Constructing the transformation for this model enables the designer to find an approximate transformation for the nonlinear system.

Ford, H.↗

NASA NTRS1983

Linear approximations of nonlinear systems

A method for designing an automatic flight controller for short and vertical takeoff aircraft is presently being developed at NASA Ames Research Center. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system, called the modified tangent model, was recently introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this an approximation of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x(0) yields the same modified tangent model.

Hunt, L. R.↗

NASA NTRS1983

A natural coordinate system for nonlinear systems

A natural coordinate system for nonlinear systems of the form x = f(x) + g(x)u is discussed where x is a element of R(N), u is an element of R, and f and g are analytic, vector-valued functions on R(N). It is shown that in these coordinates the equation becomes a system with only feedback paths (no feedforwards), if feedback linearizability conditions are satisfied.

Su, R.↗

NASA NTRS1982

Applications to aeronautics of the theory of transformations of nonlinear systems

The development of the transformation theory is discussed. Results and applications concerning the use of this design technique for automatic flight control of aircraft are presented. The theory examines the transformation of nonlinear systems to linear systems. The tracking of linear models by nonlinear plants is discussed. Results of manned simulation are also presented.

Meyer, G.↗

NASA NTRS1982

Theory of design using nonlinear transformations

This paper is presenting an overview of the theory of transformations from nonlinear systems to linear systems. Topics covered include (1) necessary and sufficient conditions for transformations to exist, (2) a method of constructing transformations (3) robustness in design (based on transformations theory) and Liapunov functions, (4) estimation theory, and (5) the relationship between transformation theory and 'nonlinear zeros'. Application of these results to automatic flight control is presented in another paper at this session.

Su, R.↗

NASA NTRS1981

Aerodynamic heating on the corrugated surface of a 10.2 deg half-angle blunted cone at Mach 6.7

A 10.2 deg half-angle blunted cone with corrugated surfaces was tested in the Langley 8-foot high-temperature structures tunnel to measure the aerodynamic heating of its surfaces. The tests were made in a turbulent boundary layer at angles of attack of 0 deg, 5 deg, and 10 deg. Heating of the windward side was in reasonable agreement with theoretical turbulent predictions for a smooth cone, while heating on the leeward side was between laminar and turbulent predictions as a result of local transitional flow or flow separation produced by high lee-side pressures. Localized heating measurements indicated a significant increase in heating at large cross-flow angles, with the maximum heating rates occurring where the flow reattaches on the upstream side of the corrugation crest and the minimum occurring on the downstream side where the flow is separated.

Weinstein, I.↗

NASA NTRS1981

Local transformations for multi-input nonlinear systems

In this paper Brockett's feedback invariants of nonlinear systems are generalized to a larger class of transformations. In terms of these invariants, the recent results on linear equivalents of nonlinear systems to the multiple-input case have also been extended.

Hunt, L. R.↗