Optimal post-experiment estimation of poorly modeled dynamic systems

Recently, a novel strategy for post-experiment state estimation of discretely-measured dynamic systems has been developed. The method accounts for errors in the system dynamic model equations in a more general and rigorous manner than do filter-smoother algorithms. The dynamic model error terms do not require the usual process noise assumptions of zero-mean, symmetrically distributed random disturbances. Instead, the model error terms require no prior assumptions other than piecewise continuity. The resulting state estimates are more accurate than filters for applications in which the dynamic model error clearly violates the typical process noise assumptions, and the available measurements are sparse and/or noisy. Estimates of the dynamic model error, in addition to the states, are obtained as part of the solution of a two-point boundary value problem, and may be exploited for numerous reasons. In this paper, the basic technique is explained, and several example applications are given. Included among the examples are both state estimation and exploitation of the model error estimates

Time domain modal identification/estimation of the mini-mast testbed

The Mini-Mast is a 20 meter long 3-dimensional, deployable/retractable truss structure designed to imitate future trusses in space. Presented here are results from a robust (with respect to measurement noise sensitivity), time domain, modal identification technique for identifying the modal properties of the Mini-Mast structure even in the face of noisy environments. Three testing/analysis procedures are considered: sinusoidal excitation near resonant frequencies of the Mini-Mast, frequency response function averaging of several modal tests, and random input excitation with a free response period

Theoretical constraints in the design of multivariable control systems

The theoretical constraints inherent in the design of multivariable control systems were defined and investigated. These constraints are manifested by the system transmission zeros that limit or bound the areas in which closed loop poles and individual transfer function zeros may be placed. These constraints were investigated primarily in the context of system decoupling or non-interaction. It was proven that decoupling requires the placement of closed loop poles at the system transmission zeros. Therefore, the system transmission zeros must be minimum phase to guarantee a stable decoupled system. Once decoupling has been accomplished, the remaining part of the system exhibits transmission zeros at infinity, so nearly complete design freedom is possible in terms of placing both poles and zeros of individual closed loop transfer functions. A general, dynamic inversion model following system architecture was developed that encompasses both the implicit and explicit configuration. Robustness properties are developed along with other attributes of this type of system. Finally, a direct design is developed for the longitudinal-vertical degrees of freedom of aircraft motion to show how a direct lift flap can be used to improve the pitch-heave maneuvering coordination for enhanced flying qualities

Correlation techniques to determine model form in robust nonlinear system realization/identification

The fundamental challenge in identification of nonlinear dynamic systems is determining the appropriate form of the model. A robust technique is presented which essentially eliminates this problem for many applications. The technique is based on the Minimum Model Error (MME) optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature is the ability to identify nonlinear dynamic systems without prior assumption regarding the form of the nonlinearities, in contrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. Model form is determined via statistical correlation of the MME optimal state estimates with the MME optimal model error estimates. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length

An experimental study of nonlinear dynamic system identification

A technique based on the Minimum Model Error optimal estimation approach is employed for robust identification of a nonlinear dynamic system. A simple harmonic oscillator with quadratic position feedback was simulated on an analog computer. With the aid of analog measurements and an assumed linear model, the Minimum Model Error Algorithm accurately identifies the quadratic nonlinearity. The tests demonstrate that the method is robust with respect to prior ignorance of the nonlinear system model and with respect to measurement record length, regardless of initial conditions

An experimental study of nonlinear dynamic system identification

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length

Scalar gain interpretation of large order filters

A technique is developed which demonstrates how to interpret a large fully-populated filter gain matrix as a set of scalar gains. The inverse problem is also solved, namely, how to develop a large-order filter gain matrix from a specified set of scalar gains. Examples are given to illustrate the method

Theoretical constraints in the design of multivariable control systems

The research being performed under NASA Grant NAG1-1361 involves a more clear understanding and definition of the constraints involved in the pole-zero placement or assignment process for multiple input, multiple output systems. Complete state feedback to more than a single controller under conditions of complete controllability and observability is redundant if pole placement alone is the design objective. The additional feedback gains, above and beyond those required for pole placement can be used for eignevalue assignment or zero placement of individual closed loop transfer functions. Because both poles and zeros of individual closed loop transfer functions strongly affect the dynamic response to a pilot command input, the pole-zero placement problem is important. When fewer controllers than degrees of freedom of motion are available, complete design freedom is not possible, the transmission zeros constrain the regions of possible pole-zero placement. The effect of transmission zero constraints on the design possibilities, selection of transmission zeros and the avoidance of producing non-minimum phase transfer functions is the subject of the research being performed under this grant

I Hope It Rains So My Corn and Your Okra Grows: A Case Study of A Kindergarten Teacher\u27S Language Use In Expanding Children\u27s Language Repetoires

The continuing disparity of academic success, commonly referred to as the achievement gap, the gap between economically disadvantaged subgroups and their more economically advantaged peers, is the greatest problem we face in the United States today (Slavin & Madden, 2006). In this dissertation, I studied in-depth the complexity of a quality teacher and her program at the kindergarten level, I focused my study on three areas, realizing that each of these areas is very complex. Although they overlap, they also have their own unique subtopics within the larger topic. The three areas of study are: oral language development, teacher/child interactions, and teacher quality. This teacher\u27s success in closing or narrowing the achievement gap was a phenomenon worth studying. For one year, I studied a kindergarten teacher and seven of her students who exhibited the lowest language and literacy repertoires in her class. She taught in a school with a 99% poverty index. In the analysis of the data, there appears to be a thread that ran or perhaps intertwined throughout the day in Mrs. Lucas\u27 kindergarten class. It emerged as a critical tool in this teacher\u27s ability to scaffold even the lowest performing students. The thread that intertwined throughout the day was the prevalence of talk used to foster language development and the prevalence of opportunities Mrs. Lucas set up for her kindergarten students to engage in talk. When a student\u27s oral language is not yet where it should be, instruction needs to occur so the students\u27 foundation will be sturdy. The results of this study will be beneficial to Head Start programs, Preschool programs and kindergarten teachers in public school settings and private school settings

Are food exposures obtained through commercial market panels representative of the general population? Implications for outbreak investigations

Current methods of control recruitment for case-control studies can be slow (a particular issue for outbreak investigations), resource-intensive and subject to a range of biases. Commercial market panels are a potential source of rapidly recruited controls. Our study evaluated food exposure data from these panel controls, compared with an established reference dataset. Market panel data were collected from two companies using retrospective internet-based surveys; these were compared with reference data from the National Diet and Nutrition Survey (NDNS). We used logistic regression to calculate adjusted odds ratios to compare exposure to each of the 71 food items between the market panel and NDNS participants. We compared 2103 panel controls with 2696 reference participants. Adjusted for socio-demographic factors, exposure to 90% of foods was statistically different between both panels and the reference data. However, these differences were likely to be of limited practical importance for 89% of Panel A foods and 79% of Panel B foods. Market panel food exposures were comparable with reference data for common food exposures but more likely to be different for uncommon exposures. This approach should be considered for outbreak investigation, in conjunction with other considerations such as population at risk, timeliness of response and study resources