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At least 613 records · Page 34
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

A method for linearizing a nonlinear system with six state variables and three control variables

A nonlinear system governed by x = f(x,u) with six state variables and three control variables is considered in this project. A set of transformations from (x,u) - space to (z,v) - space is defined such that the linear tangent model is independent of the operating point in the z-space. Therefore, it is possible to design a control law satisfying all operating points in the transformed space. An algorithm to construct the above transformations and to obtain the associated linearized system is described in this report. This method is applied to a rigid body using pole placement for the control law. Results are verified by numerical simulation. Closed loop poles in x-space using traditional local linearization are compared with those pole placements in the z-space.

Hsia, W. S.↗
NASA NTRS1988

Analysis of limit cycles in control systems for joint dominated structures

An approach to the modeling of limit cycles due to joint nonlinearities in large joint dominated space structures is presented which makes it possible to predict limit cycles and determine their stability. An actively controlled truss structure with nonlinear joints is modeled as a linear system with nonlinear feedback by separating the joint load-displacement characteristics into a linear part, which prevails at large displacements, and a nonlinear part. By replacing the joints by their linear parts, it is possible to perform a standard model decomposition which yields a reduced order linear model. Linear control laws can be easily included into the linear part of the system; nonlinear control laws can be implemented but they must be fed back to the linear model. The modeling approach described here allows straightforward limit cycle analysis.

Mercadal, M.↗
NASA NTRS1976

Control by model error estimation

Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST).

Likins, P. W.↗
NASA NTRS1993

Active control of acoustic pressure fields using smart material technologies

An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanism. Interior sound pressure levels are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Well-posedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using linear quadratic regulator (LQR) optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example.

Banks, H. T.↗
NASA NTRS1998

Stable Inversion for Nonlinear Nonminimum-Phase Time Varying Systems

In this paper, we extend stable inversion to nonlinear time-varying systems and study computational issues; the technique is applicable to minimum-phase as well as nonminimum-phase systems. The inversion technique is new, even in the linear time-varying case, and relies on partitioning (the dichotomic split of) the linearized system dynamics into time-varying, stable, and unstable, submanifolds. This dichotomic split is used to build time-varying filters which are, in turn, the basis of a contraction used to find a bounded inverse input-state trajectory. Finding the inverse input-state trajectory allows the development or exact-output tracking controllers. The method is local to the time-varying trajectory and requires that the internal dynamics vary slowly; however, the method represents a significant advance relative to presently available tracking controllers. Present techniques are restricted to time-invariant nonlinear systems and, in the general case, track only asymptotically.

Devasia, S.↗
NASA NTRS1977

New frequency domain methods for system identification

This paper presents two new techniques for frequency domain identification of linear system parameters. The first technique uses the instrumental variables approach. The frequency domain formulation is shown to give a considerable insight into the selection of efficient and convergent instrumental variables. The new maximum likelihood formulation affords simplier numerical solution and provides a way to select parameter starting values in the gradient based optimization method.

Gupta, N. K.↗
NASA NTRS1986

A canonical form for nonlinear systems

The concepts of transformation and canonical form have been used in analyzing linear systems. These ideas are extended to nonlinear 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. For control design involving a nonlinear system, one approach is to put the system in its canonical form and approximate by that part having only feedback paths.

Su, R.↗
NASA NTRS1992

Balanced systems and structures - Reduction, assignment, and perturbations

New results on properties of balanced linear systems and structures are presented. Balanced representation is defined for systems with poles at an imaginary axis or at the origin. Grammians do not exist in this case, but antigrammians are introduced which make balanced reduction possible. System grammians of specified properties are obtained by assigning the sensor and actuator configuration. The latter is determined using input-output assignment procedures introduced for general systems and specified to structures. A system is said to be uniformly balanced if all its Hankel singular values are equal.

Gawronski, Wodek↗
NASA NTRS1997

Assessing Aircraft Susceptibility to Nonlinear Aircraft-Pilot Coupling/Pilot-Induced Oscillations

A unified approach for assessing aircraft susceptibility to aircraft-pilot coupling (or pilot-induced oscillations) which was previously reported in the literature and applied to linear systems is extended to nonlinear systems, with emphasis upon vehicles with actuator rate saturation. The linear methodology provided a tool for predicting: (1) handling qualities levels, (2) pilot-induced oscillation rating levels and (3) a frequency range in which pilot-induced oscillations are likely to occur. The extension to nonlinear systems provides a methodology for predicting the latter two quantities. Eight examples are presented to illustrate the use of the technique. The dearth of experimental flight-test data involving systematic variation and assessment of the effects of actuator rate limits presently prevents a more thorough evaluation of the methodology.

Hess, R.A.↗
NASA NTRS1992

A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

Yedavalli, R. K.↗
NASA NTRS1988

A methodology based on reduced complexity algorithm for system applications using microprocessors

The paper considers a methodology on the analysis and design of a minimum mean-square error criterion linear system incorporating a tapped delay line (TDL) where all the full-precision multiplications in the TDL are constrained to be powers of two. A linear equalizer based on the dispersive and additive noise channel is presented. This microprocessor implementation with optimized power of two TDL coefficients achieves a system performance comparable to the optimum linear equalization with full-precision multiplications for an input data rate of 300 baud.

Yan, T. Y.↗
NASA NTRS1992

Frequency domain state-space system identification

An algorithm for identifying state-space models from frequency response data of linear systems is presented. A matrix-fraction description of the transfer function is employed to curve-fit the frequency response data, using the least-squares method. The parameters of the matrix-fraction representation are then used to construct the Markov parameters of the system. Finally, state-space models are obtained through the Eigensystem Realization Algorithm using Markov parameters. The main advantage of this approach is that the curve-fitting and the Markov parameter construction are linear problems which avoid the difficulties of nonlinear optimization of other approaches. Another advantage is that it avoids windowing distortions associated with other frequency domain methods.

Chen, Chung-Wen↗
NASA NTRS1984

Two time scale stabilization of systems with output feedback

The problem of constant gain output feedback regulator design for linear systems with ill-conditioned dynamics is considered in the context of singular perturbation theory. A design approach is developed in which gains can be separately calculated to stabilize reduced-order slow and fast subsystem models. By employing the notion of combined control and observation spillover suppression, conditions are derived assuring that these gains will stabilize the full-order system, assuming sufficient frequency separation between the slow and fast subsystems. An LQ design procedure is described in which the spillover suppression conditions are satisfied by adjoining penalty functions to the subsystem performance indices. The theory is demonstrated in a controller design for a flexible space structure.

Moerder, D. D.↗
NASA NTRS1989

Recursive form of the eigensystem realization algorithm for system identification

An algorithm is developed for recursively calculating the minimum realization of a linear system from sampled impulse response data. The Gram-Schmidt orthonormalization technique is used to generate an orthonormal basis for factorization of the data matrix. The system matrix thus identified is in upper Hessenberg form, which has advantages for the identification of modal parameters including damping coefficients, frequencies, mode shapes, and modal participation factors. It also has the property that once an element of the system matrix is computed, it is never altered as the dimension of the model is increased in the recursive process. Numerical examples are presented for comparison of the recursive and nonrecursive forms of the eigensystem realization algorithm.

Longman, Richard W.↗