SEARCH · Engineering Papers
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Switching times updated to minimize errors in final positions. Algorithm computes "bang-bang" control laws for single- or multiple-input systems, both those describable by linear dynamical equations and those describable by nonlinear dynamical equations that are linear in control vectors. Algorithm needed because analytical solutions of "bang-bang" control problems intractable for all but simplest systems.
The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.
This paper considers the problem of the stabilization and control of distributed systems with time-dependent spatial domains. The evolution of the spatial domains with time is described by a finite-dimensional system of ordinary differential equations, while the distributed systems are described by first-order or second-order linear evolution equations defined on appropriate Hilbert spaces. First, results pertaining to the existence and uniqueness of solutions of the system equations are presented. Then, various optimal control and stabilization problems are considered. The paper concludes with some examples which illustrate the application of the main results.
Interaction between the large-scale circulation and the convective pattern is investigated in a coupled system governed by the linearized primitive equations. Convection is represented in terms of two components of heating: A 'climatological component' is prescribed stochastically to represent convection that is maintained by fixed distributions of land and sea and sea surface temperature (SST). An 'induced component' is defined in terms of the column-integrated moisture flux convergence to represent convection that is produced through feedback with the circulation. Each component describes the envelope organizing mesoscale convective activity. As SST on the equator is increased, induced heating amplifies in the gravest zonal wavenumbers at eastward frequencies, where positive feedback offsets dissipation. Under barotropic stratification, a critical SST of 29.5 C results in positive feedback exactly cancelling dissipation in wavenumber 1 for an eastward phase speed of 6 m/s. Sympathetic interaction between the circulation and the induced heating is the basis for 'frictional wave-Conditional Instability of the Second Kind (CISK)', which is distinguished from classical wave-CISK by rendering the gravest zonal dimensions most unstable. Under baroclinic stratification, the coupled system exhibits similar behavior. The critical SST is only 26.5 C for conditions representative of equinox, but in excess of 30 C for conditions representative of solstice. Having the form of an unsteady Walker circulation, the disturbance produced by frictional wave-CISK compares favorably with the observed life cycle of the Madden-Julian oscillation (MJO). SST above the critical value produces an amplifying disturbance in which enhanced convection coincides with upper-tropospheric westerlies and is positively correlated with temperature and surface convergence. Conversely, SST below the critical value produces a decaying disturbance in which enhanced convection coincides with upper-tropospheric easterlies and is nearly in quadrature with temperature and surface convergence. While sharing essential features with the MJO in the Eastern Hemisphere, frictional wave-CISK does not explain observed behavior in the Western Hemisphere, where the convective signal is largely absent. Comprised of Kelvin structure with the same frequency, observed behavior in the Western Hemisphere can be understood as a propagating response that is excited in and radiates away from the fluctuation of convection in the Eastern Hemisphere.
A full set of equations of motion for the twin lift system, linearized about a hover trim condition were derived and presented. It is shown that this full set of equations of motion decouples into simpler sets of equations of motion if the aerodynamic coupling derivatives of the helicopters are neglected. One of these decoupled sets of equations of motion (referred to as the planar set) was studied at length. The other decoupled set (referred to as the nonplanar set) is examined here. It is shown that when the geometric configuration of the twin-lift is symmetric that a further decoupling is possible into antisymmetric and symmetric sets of equations. One set of these reduced equations of motion referred to as the antisymmetric set is directly equivalent to the longitudinal motion of a single helicopeter with a sling load. The second set, referred to as the symmetric set corresponds to the rotation of the entire system without load motion. As in the case of the planar symmetric motion, the location of the tether attachment point influences the stability of the nonplanar symmetric mode. The trend is opposite however in the nonplanar case in that an attachment point below the helicopter center of gravity gives a favorable effect on the stability. The effect is not as strong however as the unfavorable effect on the planar symmetric mode.
Systems described by partial differential equations have an infinite-dimensional state space. Feedback control of such distributed parameter systems must be accomplished by finite-dimensional controllers to be implemented by on-line digital computers. A further practical constraint is that the controller must operate in discrete (rather than continuous) time. This paper investigates the stability of such distributed parameter feedback controllers in closed-loop with the actual system.
Computer experiments are described which used transient responses in flap-bending and torsion of a rotor blade at high advance ratio. It was found that a simple system identification method applying a linear sequential estimator also called equation of motion estimator, is suitable for this periodic system and can be used directly, if only the acceleration data are noise-polluted. In the case where noise is also present in the state-variable data, the direct application of the estimator gave poor results. However after prefiltering the data with a digital Graham filter having a cutoff frequency above the natural blade torsion frequency, the linear sequential estimator successfully recovered the parameters of the periodic coefficient analytical model.
Motion and stability of spinning spring-mass system in orbital plane with equation linearization
Linear and nonlinear systems, and differential equations for control and stability theory
Optimal control and filtering problem for stochastic linear dynamic system reduced to independent equations
Algorithms for linear system of first order differential equations, emphasizing equations associated with computer oriented circuit design
Evaluation of routines for numerical solution of matrix equation for time-invariant linear systems
Smoothing equations for a linear continuous dynamic system with linear discrete measurements, derived from the discrete results of Rauch, Tung, and Striebel (1965), (R-T-S), are used to extend, through recursive updating, the previously published results of Bryson and Frazier (1963), (B-F), and yield a modified Bryson and Frazier, (M-B-F), algorithm. A comparison of the (M-B-F) and (R-T-S) algorithms leads to the conclusion that the former is to be preferred because it entails less computation, less storage, and less instability. It is felt that the presented (M-B-F) smoothing algorithm is a practical mechanization and should be of value in smoothing discretely observed dynamic linear systems.
Major results from the frequency analysis of system program (FASP) are reported. The FASP procedure was designed to analyze or design linear dynamic systems, but can be used to solve any problem that can be described by a system of linear time invariant differential equations. The program also shows plots of performance changes as design parameters are adjusted. Experimental results on narrowband FM distortion are also reported.
A numerical generalized-capacity-matrix technique is developed for application to aerodynamic flow computations. This technique allows the very fast direct (noniterative) numerical elliptic solvers to be used in problems with arbitrary internal boundaries and with a wide class of boundary conditions, including numerical application of the Kutta condition on an airfoil without iteration. Accuracy, speed, and usefulness of the technique are demonstrated with linear problems for potential flows over airfoil shapes. The method's main advantages, however, can be exploited within iterative procedures for a variety of complex flow problems governed by systems of equations not necessarily elliptic or linear.
Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.
This paper deals with the stability of limit cycles (Steady-State Oscillations) associated with the multi-degree-of-freedom model of a frictionally damped and aerodynamically unstable rotor stage. By using the first order averaging technique, a generalized criterion has been established to sort out those unstable limit cycles which govern the maximum transient amplitude beyond which the rotor stage becomes unstable.The stability of the remaining steady-state solutions is analyzed by linearizing the averaged system of differential equations. Numerical results are discussed for three-, four- and five-bladed disks.
The flow of a fluid between concentric rotating cylinders (the Taylor problem) is studied by exploiting the symmetries of the system. The Navier-Stokes equations, linearized about Couette flow, possess two zero and four purely imaginary eigenvalues at a suitable value of the speed of rotation of the outer cylinder. There is thus a reduced bifurcation equation on a six-dimensonal space which can be shown to commute with an action of the symmetry group 0(2) x S0(2). The group structure is used to analyze this bifurcation equation in the simplest (nondegenerate) case, and to compute the stabilities of solutions. In particular, when the outer cylinder is counterrotated, transitions which seem to agree with recent experiments of Andereck, Liu, and Swinney (1984) are obtained. It is also possible to obtain the 'main sequence' in this model. This sequence is normally observed in experiments when the outer cylinder is held fixed.