G. L. Slater

Health monitoring of flexible structures using modal filter concepts

This paper develops an approach for the health monitoring of a smart structures with multiple embedded sensing and actuation capability. For such a structure the consideration of failure consequences is an important component of any real application. The approach developed here is an integrated control and monitoring procedure whereby the sensors, which are assumed to be distributed spatially across the structure, are processed by a set of spatial modal filters which automatically track the modal coordinates of desired, specified modes, and similarly track changes in modal characteristics such as modal frequency, damping, and mode shape. The adaptive modal filter is formulated and applied to tr:a.ck the time varying behavior of specified modes, thereby indicating in some general sense, the health of the structural system. The adaptive modal filter is insensitive to failures or calibration shifts in individual sensors and will automatically ignore failed sensors. It can also be used to detect disturbances entering the system as well as to identify failed actuator locations. A modal controller based on these estimates is then able to adapt to a changing structure and in addition is insensitive to failures in the sensors and actuators. Both the tl1eory and experimental results from a test structure is discussed.

Departure Trajectory Synthesis and the Intercept Problem

Two areas of the departure problem in air traffic control are discussed. The first topic is the generation of climb-out trajectories to a fix. The trajectories would be utilized by a scheduling algorithm to allocate runways, sequence the proposed departures, and assign a departure time. The second area is concerned with finding horizontal trajectories to merge aircraft from the TRACON to an open slot in the en-route environment. Solutions are presented for the intercept problem for two cases: (1) the aircraft is traveling at the speed of the aircraft in the jetway, (2) the merging aircraft has to accelerate to reach the speed of the aircraft in the en-route stream. An algorithm is given regarding the computation of a solution for the latter case. For the former, a set of equations is given that allows us to numerically solve for the coordinate where the merge will occur.

A disturbance model for control/structure optimization with output feedback control

This paper deals with a technique for the integrated optimization of structure and control in the design of flexible systems. The current approach uses the concept of response to dynamic constraints to establish a concise variational methodology to total system optimization, and eliminates the need to specify rather arbitrary trade-offs between control energy and structural mass. Results give an explicit dependency between structural stiffness (hence mass), disturbance magnitude, available control energy, and deflection constraints. The current paper presents results for direct output feedback and dynamic filter compensation with optional positive real constraints on the filters. The key element of the design approach is to formulate a set of response constraints that bound the allowable deflections and a set of constraints that bound the allowable control energy. The results for model structures indicate the importance of the control-structure interaction in a light-weight structure and the trade-offs between controller complexity, energy and structural mass.

Practical Experience with Multivariable Positivity Controllers

This paper presents a summary of our experience with the application of positivity designed multivariable controllers for the NASA ACES flexible beam experiment at NASA Marshall Space Flight Center. Multivariable controllers were designed using sets of rotational sensors/actuators (rate gyros/torque actuators) and linear sensors/actuators (accelerometers/LMEDs). Our experience with this set of controllers demonstrated the difficulty of designing controllers with significant modal uncertainty and significant phase uncertainty. With the aid of multivariable scaling techniques these designs were able to ultimately achieve a high level of closed loop damping.

Gain Optimization with Nonlinear Controls

An algorithm has been developed for the analysis and design of controls for nonlinear systems. The technical approach is to use statistical linearization to model the nonlinear dynamics of a system. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this report is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general however and numerical omputation requires only that the specific nonlinearity be considered in the analysis.

Adaptive Eulerian Modeling for Air Traffic Flow Management

A method for deriving an Eulerian traffic flow model in real time without depending on online integration of aircraft trajectories is introduced. In this method, online model derivation starts with a baseline Eulerian airspace model, which is derived offline using historical track data. In real time, parameters of this baseline model are adapted depending on the differences in flight plans and control volume aircraft counts between the baseline model and the real world. The baseline model derivation method is based on bookkeeping of control volume aircraft counts and, hence, the model produces control decisions in terms of whole number aircraft counts, unlike the fractional counts produced by Eulerian models based on average aircraft speeds. The bookkeeping-based model indirectly retains trajectory information and aircraft identities. Hence, it serves as an excellent tradeoff between Eulerian and trajectory-based modeling approaches. Most importantly, as an improvement over previous approaches, we take into consideration the control-dependent nature of the Eulerian model while computing optimal flow-control decisions. A key feature of this model is the use of interstream jump (y) parameters. These parameters make the model easily amenable to emulate a wide variety of control actions like rerouting. As a proof of concept, we derive a baseline model for the Fort Worth center from recorded track data for a period of 1 h on 13 March 2005 and adapt it it to predict sector counts for another time period. An application of the adaptive model to optimal rerouting is also presented.