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Control of the NASA Langley 16-Foot Transonic Tunnel with the Self-Organizing Feature Map
A predictive, multiple model control strategy is developed based on an ensemble of local linear models of the nonlinear system dynamics for a transonic wind tunnel. The local linear models are estimated directly from the weights of a Self Organizing Feature Map (SOFM). Local linear modeling of nonlinear autonomous systems with the SOFM is extended to a control framework where the modeled system is nonautonomous, driven by an exogenous input. This extension to a control framework is based on the consideration of a finite number of subregions in the control space. Multiple self organizing feature maps collectively model the global response of the wind tunnel to a finite set of representative prototype controls. These prototype controls partition the control space and incorporate experimental knowledge gained from decades of operation. Each SOFM models the combination of the tunnel with one of the representative controls, over the entire range of operation. The SOFM based linear models are used to predict the tunnel response to a larger family of control sequences which are clustered on the representative prototypes. The control sequence which corresponds to the prediction that best satisfies the requirements on the system output is applied as the external driving signal. Each SOFM provides a codebook representation of the tunnel dynamics corresponding to a prototype control. Different dynamic regimes are organized into topological neighborhoods where the adjacent entries in the codebook represent the minimization of a similarity metric which is the essence of the self organizing feature of the map. Thus, the SOFM is additionally employed to identify the local dynamical regime, and consequently implements a switching scheme than selects the best available model for the applied control. Experimental results of controlling the wind tunnel, with the proposed method, during operational runs where strict research requirements on the control of the Mach number were met, are presented. Comparison to similar runs under the same conditions with the tunnel controlled by either the existing controller or an expert operator indicate the superiority of the method.
SDR Input Power Estimation Algorithms
The General Dynamics (GD) S-Band software defined radio (SDR) in the Space Communications and Navigation (SCAN) Testbed on the International Space Station (ISS) provides experimenters an opportunity to develop and demonstrate experimental waveforms in space. The SDR has an analog and a digital automatic gain control (AGC) and the response of the AGCs to changes in SDR input power and temperature was characterized prior to the launch and installation of the SCAN Testbed on the ISS. The AGCs were used to estimate the SDR input power and SNR of the received signal and the characterization results showed a nonlinear response to SDR input power and temperature. In order to estimate the SDR input from the AGCs, three algorithms were developed and implemented on the ground software of the SCAN Testbed. The algorithms include a linear straight line estimator, which used the digital AGC and the temperature to estimate the SDR input power over a narrower section of the SDR input power range. There is a linear adaptive filter algorithm that uses both AGCs and the temperature to estimate the SDR input power over a wide input power range. Finally, an algorithm that uses neural networks was designed to estimate the input power over a wide range. This paper describes the algorithms in detail and their associated performance in estimating the SDR input power.
Structural Properties and Estimation of Delay Systems
Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.
An Innovative Method for Low Cost, Autonomous Navigation for Low Earth Orbit Satellites
An innovative approach to autonomous attitude, trajectory, and rate estimation is presented for low earth orbit (LEO) satellites which relies on magnetometers and sun sensors. These two sensors are reliable, inexpensive, and are used routinely in LEO missions for attitude determination and control. An extended Kalman filter (EKF) is developed from two existing systems, one which uses an EKF to estimate attitude and trajectory using magnetometer and gyro data and a second pseudo-linear filter which estimates rotation rate using magnetometer and sun sensor data. The theoretical background of the combined system is presented along with test results from noisy, simulated sensor data.
Multicollinearity in simultaneous equations system: evaluation of estimation performance of two-parameter estimator
In simultaneous equations model, two-stage least squares estimator is easy to apply and commonly preferred. When multicollinearity exists, two-stage least squares estimator has some drawbacks and it is no longer favorable. In this context, biased estimation methods are recommended. Two-parameter estimator of Özkale and Kaçıranlar (Commun Stat Theory Methods 36(15):2707–2725, 2007) had been established to be superior to the ordinary least squares estimator under some conditions in linear regression model suffering from multicollinearity. In this paper, the idea of two-parameter estimation in linear regression model is carried out to the simultaneous equations model. For this model, two-stage two-parameter estimator is proposed to remedy the problem of multicollinearity. Estimation performance of this new estimator is evaluated by means of two real-life data analyses. In addition to the numerical example, an extensive Monte Carlo experiment is conducted.
Stochastic Satbility and Performance Robustness of Linear Multivariable Systems
Stochastic robustness, a simple technique used to estimate the robustness of linear, time invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters are discussed. The application of stochastic performance robustness, and the relationship between performance objectives and design parameters are demonstrated by means of example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
Stochastic stability and performance robustness of linear multivariable systems
Stochastic robustness, a simple technique used to estimate the robustness of linear, time-invariant systems, is applied to a single-link robot arm control system. Concepts behind stochastic stability robustness are extended to systems with estimators and to stochastic performance robustness. Stochastic performance robustness measures based on classical design specifications are introduced, and the relationship between stochastic robustness measures and control system design parameters is discussed. The application of stochastic performance robustness and the relationship between performance objectives and design parameters are demonstrated by means of the example. The results prove stochastic robustness to be a good overall robustness analysis method that can relate robustness characteristics to control system design parameters.
An analysis of the 7-year record of SBUV satellite ozone data - Global profile features and trends in total ozone
Results are presented from an analysis of Nimbus 7 SBUV monthly-average total ozone data for the November 1978 - September 1985 period. Linear drifts are estimated for the differences between SBUV and Dobson ground station total ozone data. The results show an average negative linear drift in SBUV data relative to Dobson data of about -0.4 percent per year. The global estimate of the relation between total ozone and solar flux variations is 0.97 + or - 0.61/100 solar flux units, representing a change of total ozone over the 7-year period associated with solar flux variations of about -0.20 + or - 0.13 percent per year.
Modeling the vestibulo-ocular reflex of the squirrel monkey during eccentric rotation and roll tilt
Model simulations of the squirrel monkey vestibulo-ocular reflex (VOR) are presented for two motion paradigms: constant velocity eccentric rotation and roll tilt about a naso-occipital axis. The model represents the implementation of three hypotheses: the "internal model" hypothesis, the "gravito-inertial force (GIF) resolution" hypothesis, and the "compensatory VOR" hypothesis. The internal model hypothesis is based on the idea that the nervous system knows the dynamics of the sensory systems and implements this knowledge as an internal dynamic model. The GIF resolution hypothesis is based on the idea that the nervous system knows that gravity minus linear acceleration equals GIF and implements this knowledge by resolving the otolith measurement of GIF into central estimates of gravity and linear acceleration, such that the central estimate of gravity minus the central estimate of acceleration equals the otolith measurement of GIF. The compensatory VOR hypothesis is based on the idea that the VOR compensates for the central estimates of angular velocity and linear velocity, which sum in a near-linear manner. During constant velocity eccentric rotation, the model correctly predicts that: (1) the peak horizontal response is greater while "facing-motion" than with "back-to-motion"; (2) the axis of eye rotation shifts toward alignment with GIF; and (3) a continuous vertical response, slow phase downward, exists prior to deceleration. The model also correctly predicts that a torsional response during the roll rotation is the only velocity response observed during roll rotations about a naso-occipital axis. The success of this model in predicting the observed experimental responses suggests that the model captures the essence of the complex sensory interactions engendered by eccentric rotation and roll tilt.
An identification algorithm which is insensitive to initial parameter estimates
Identification algorithm for estimating parameters in constant coefficient linear system independent of prior estimates
An identification algorithm that is insensitive to initial parameter estimates
Identification algorithm for estimating parameters in constant coefficient linear system independent of prior estimates
On resolving 2M - 1 narrow-band signals with an M sensor uniform linear array
Length 2M real signal vectors are used to address the problem of determining the maximum number of narrow-band signals whose parameters can be estimated with a linear array of M equally spaced sensors. It is shown that 2M of these real vectors are linearly independent with probability one, and, thus in the presence of additive white noise, the parameters of 2M - 1 signals can be estimated. An algorithm for determining directions and amplitudes is presented.
The application of parameter estimation to flight measurements to obtain lateral-directional stability derivatives of an augmented jet-flap STOL airplane
Flight experiments with an augmented jet flap STOL aircraft provided data from which the lateral directional stability and control derivatives were calculated by applying a linear regression parameter estimation procedure. The tests, which were conducted with the jet flaps set at a 65 deg deflection, covered a large range of angles of attack and engine power settings. The effect of changing the angle of the jet thrust vector was also investigated. Test results are compared with stability derivatives that had been predicted. The roll damping derived from the tests was significantly larger than had been predicted, whereas the other derivatives were generally in agreement with the predictions. Results obtained using a maximum likelihood estimation procedure are compared with those from the linear regression solutions.
Minimum entropy filtering for a single output non-Gaussian stochastic system using state transformation
This paper presents a novel filter design for the single-output stochastic non-linear systems subjected to non-Gaussian noises and the proposed assumptions. Based on a state transformation, the unmeasurable states of the systems can be estimated where non-linear terms in the systems have been eliminated. It has been shown that the estimation error is linearly dynamical regarding to the presented vector-valued filter gain which can be optimised by minimising the entropy-based performance criterion. In addition, the convergence of the presented algorithm is analysed in mean-square sense and a numerical example is given to verify the effectiveness of the presented filtering algorithm. Meanwhile, the extended Kalman filter, unscented particle filter and minimum entropy filter are given for the comparisons of the filtering performance. Following the presented framework, some extensions of the presented filtering algorithm are discussed to indicate the flexibility of the filter design. The contribution of this paper can be summarised as establishing a novel minimum entropy filtering framework which consists of model transformation, entropy optimisation and convergence analysis.
Turbulent Reconnection Rates from Cluster Observations in the Magneto sheath
The role of turbulence in producing fast reconnection rates is an important unresolved question. Scant in situ analyses exist. We apply multiple spacecraft techniques to a case of nonlinear turbulent reconnection in the magnetosheath to test various theoretical results for turbulent reconnection rates. To date, in situ estimates of the contribution of turbulence to reconnection rates have been calculated from an effective electric field derived through linear wave theory. However, estimates of reconnection rates based on fully nonlinear turbulence theories and simulations exist that are amenable to multiple spacecraft analyses. Here we present the linear and nonlinear theories and apply some of the nonlinear rates to Cluster observations of reconnecting, turbulent current sheets in the magnetos heath. We compare the results to the net reconnection rate found from the inflow speed. Ultimately, we intend to test and compare linear and nonlinear estimates of the turbulent contribution to reconnection rates and to measure the relative contributions of turbulence and the Hall effect.
Turbulent Reconnection Rates from Cluster Observations in the Magnetosheath
The role of turbulence in producing fast reconnection rates is an important unresolved question. Scant in situ analyses exist. We apply multiple spacecraft techniques to a case of nonlinear turbulent reconnection in the magnetosheath to test various theoretical results for turbulent reconnection rates. To date, in situ estimates of the contribution of turbulence to reconnection rates have been calculated from an effective electric field derived through linear wave theory. However, estimates of reconnection rates based on fully nonlinear turbulence theories and simulations exist that are amenable to multiple spacecraft analyses. Here we present the linear and nonlinear theories and apply some of the nonlinear rates to Cluster observations of reconnecting, turbulent current sheets in the magnetosheath. We compare the results to the net reconnection rate found from the inflow speed. Ultimately, we intend to test and compare linear and nonlinear estimates of the turbulent contribution to reconnection rates and to measure the relative contributions of turbulence and the Hall effect.
On the time growth of the error of the DG method for advective problems
Abstract In this paper we derive a priori $L^{\infty }(L^{2})$ and L2(L2) error estimates for a linear advection–reaction equation with inlet and outlet boundary conditions. The goal is to derive error estimates for the discontinuous Galerkin method that do not blow up exponentially with respect to time, unlike the usual case when Gronwall’s inequality is used. While this is possible in special cases, such as divergence-free advection fields, we take a more general approach using exponential scaling of the exact and discrete solutions. Here we use a special scaling function, which corresponds to time taken along individual pathlines of the flow. For advection fields, where the time that massless particles carried by the flow spend inside the spatial domain is uniformly bounded from above by some $\widehat{T}$, we derive $\mathcal{O}$(hp+1/2) error estimates where the constant factor depends only on $\widehat{T}$, but not on the final time T. This can be interpreted as applying Gronwall’s inequality in the error analysis along individual pathlines (Lagrangian setting), instead of physical time (Eulerian setting).