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Identification of Systems
Quasilinearization for system identification and programming strategies
Identification of a linear system from sampled noisy data, part C Final project report
Step input linear system modeling from nonlinear system sampled noisy data based on method of perturbation or quasilinearization of automatic control system data
Determination of stability derivatives from flight data using a Newton-Raphson minimization technique
A modified Newton-Raphson or quasilinearization minimization technique for determining stability derivatives from flight data was developed and compared with simple-equations, analog-matching, least-squares, and Shinbrot methods of analysis. For the data analyzed, the solutions computed by using the estimates obtained from the Newton-Raphson technique fit the data and determined coefficients adequately. A further modification to include a priori information was found to be useful. A model statistically similar to the flight data was analyzed using the same methods (excluding analog matching), and the Newton-Raphson technique was found to yield superior estimates. An approximate Cramer-Rao bound was compared with the error covariance matrix of the model and was found to provide information about the reliability of the individual estimates obtained. The technique was successfully applied to data obtained from a light airplane, a large supersonic airplane, and a lifting body vehicle. It was shown that the reliability of the estimates of a given coefficient obtained from these vehicles depends upon the data analyzed.
Systems identification using a modified Newton-Raphson method: A FORTRAN program
A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.
Performance Analysis and Design Synthesis (PADS) computer program. Volume 1: Formulation
The program formulation for PADS computer program is presented. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module.
Human control capabilities
The capabilities and limitations of man as an element in a closed loop control system under normal environmental conditions are described. Controller characteristics are enumerated, using manual control, quasilinear models, pilot opinion and ratings, compensatory tracking, optimum control models, motion cues, multiple input tracking, multiple loop tracking, transmission delays, and adaptive manual control. Various controls, manipulators, and displays are also considered.
Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 1
The Performance Analysis and Design Synthesis (PADS) computer program has a two-fold purpose. It can size launch vehicles in conjunction with calculus-of-variations optimal trajectories and can also be used as a general-purpose branched trajectory optimization program. In the former use, it has the Space Shuttle Synthesis Program as well as a simplified stage weight module for optimally sizing manned recoverable launch vehicles. For trajectory optimization alone or with sizing, PADS has two trajectory modules. The first trajectory module uses the method of steepest descent; the second employs the method of quasilinearization, which requires a starting solution from the first trajectory module. For Volume 1 see N73-13199.
Finite deformation of elasto-plastic solids
A theoretical basis is established for analysis of finite deformation of metals. The observation that finite deformation of such elastoplastic materials may be viewed as a process rather than an event leads to derivation of a complete initial and boundary value problem distinguished by its quasilinear nature. This feature of the formulation motivates adoption of an incremental approach to numerical problem solving. Numerical solution capability is established for problems of plane stress and plane strain. The validity of the theory and numerical analysis is demonstrated by consideration of a number of problems of homogeneous finite deformation for which analytic solutions are available. Subsequently the analysis is employed for the investigation of necking in flat metal tensile bars. The results of this investigation provide the first full numerical solutions for tensile necking in plane stress and plane strain. In addition a basis is provided for assessment of the validity of stress-strain relations inferred from tensile test data.
New approach to cosmic-ray diffusion theory.
We have investigated a new approach to deriving a diffusion equation for charged particles in a static, random magnetic field. Our method incorporates essential effects of the magnetic fluctuations in the lowest order particle orbits. Significant corrections to the usual quasilinear diffusion coefficient for cosmic rays with pitch angles near 90 deg are a consequence. Monte Carlo results bear out the validity of our theory.
A comparison of two methods of extracting stability derivatives from flight test data
Two methods for extracting stability derivatives from flight data are compared. A modified Newton-Raphson quasilinearization minimization technique and a digital-analog (hybrid) matching technique were used to analyze the same data maneuvers obtained from two aircraft. About 70 maneuvers from an F-111E aircraft were analyzed over a Mach number range of 0.3 to 2.0 and an angle of attack range of 3 to 19 degrees. About 20 maneuvers were analyzed for the X-24A lifting body at Mach numbers of 0.5, 0.8, and 0.9, and an angle of attack range of 4 to 13 degrees. Stability derivatives were extracted from these maneuvers and the results from the two techniques, along with wind tunnel results, were compared.
Estimation of longitudinal aerodynamic coefficients and comparison with wind-tunnel values
Some recent experience at Ames Research Center in the estimation of aerodynamic coefficients for the Lear-Jet and the Augmentor Wing Jet STOL Research Aircraft is reviewed. The coefficients estimated from flight data are compared with values based on large-scale wind-tunnel tests. The results obtained by the regression and quasilinearization identification techniques are also compared. The regression method generally provides the lower standard deviation in the coefficient estimates and provides the better fit to the wind-tunnel values. The addition of nonlinear terms in the aerodynamic equations decreases the difference between the estimated and measured time histories but also increases the standard deviation in the estimated coefficient values.
A macroscopic plasma Lagrangian and its application to wave interactions and resonances
The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction.
Users manual: Dynamics of two bodies connected by an elastic tether, six degrees of freedom forebody and five degrees of freedom decelerator
The equations of motion and a computer program for the dynamics of a six degree of freedom body joined to a five degree of freedom body by a quasilinear elastic tether are presented. The forebody is assumed to be a completely general rigid body with six degrees of freedom; the decelerator is also assumed to be rigid, but with only five degrees of freedom (symmetric about its longitudinal axis). The tether is represented by a spring and dashpot in parallel, where the spring constant is a function of tether elongation. Lagrange's equation is used to derive the equations of motion with the Lagrange multiplier technique used to express the constraint provided by the tether. A computer program is included which provides a time history of the dynamics of both bodies and the tension in the tether.
Parameter estimation of powered-lift STOL aircraft characteristics including turbulence and ground effects
The estimation of longitudinal aerodynamic coefficients from data recorded during flight tests of a powered-lift STOL aircraft is considered. First, a comparison is made between the coefficient values determined by the regression and quasilinearization identification techniques from records taken during elevator pulse maneuvers. The results show that for these tests the regression method provides less scatter in coefficient estimates and provides better correlation with the predicted values. Special techniques are then developed which allow identification of the coefficients from records taken during landing maneuvers in which the aircraft encounters turbulence while flying in ground effect. Flight test results are presented to illustrate the effects of air turbulence and ground proximity on the estimated coefficient values.
On the improper neglect of certain terms in random function theory
This paper presents some exact solutions of problems in random function theory for the purpose of testing the validity of an approximate method known variously in the many different fields of its application as first order smoothing theory, first order cumulant discard, quasilinear theory, or the adiabatic approximation. The hydromagnetic dynamo equations are used here, as particularly appropriate for such an investigation. The calculations show that in one case the exact and approximate solutions agree. In the other case the approximate solution is wrong. Hence, in the absence of a general criterion for validity, a result based on first order smoothing theory is a conjecture rather than a fact. This impacts strongly on much of the recent work on hydromagnetic dynamos.
Parameter estimation of powered-lift STOL aircraft characteristics including turbulence and ground effects
Longitudinal aerodynamic coefficients are estimated from data recorded during flight tests of a powered-lift STOL aircraft. A comparison is made between the coefficient values determined by the regression and quasilinearization identification techniques from records taken during elevator pulse maneuvers. The results show that for these tests the regression method provides less scatter in coefficient estimates and provides better correlation with the predicted values. Special techniques are developed which allow identification of the coefficients from records taken during landing maneuvers in which the aircraft encounters turbulence while flying in ground effect. Flight test results are presented to illustrate the effects of air turbulence and ground proximity on the estimated coefficient values.
Effect of nonsymmetrical flow resistance upon orifice impedance
Previous laboratory work has indicated that an orifice in a thin sheet behaves in a quasisteady manner under acoustical excitation. Also, it has been found that the steady flow resistance of an orifice may be dependent upon the direction of flow, especially in the presence of a crossflow on one side of the hole. An analytical study is presented which assumes a nonreactive orifice in an infinite baffle. The pressure difference across the orifice varies sinusoidally with amplitude 1.0 and average value -P. The orifice resistance is discontinuous at zero velocity and exhibits the constant values when the velocity is nonzero. The resultant velocity has power in all harmonics of the excitation frequency, providing an explanation of the even harmonic excitation observed by other investigators, but not predicted by symmetric nonlinearity. A quasilinear resistance is defined and found to be relatively insensitive to the presence or absence of a resonant backing cavity.