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The underlying mathematical formulation and issues associated with integrated control, structure, and optical design are discussed. Topics addressed include the development of cost functionals, optimization in the vector objective setting, and computational aspects of the optimization problem with special emphasis on model reduction strategies. Results on simple design problems are presented.
The objective of this research is to develop optimization procedures to provide design trends in high speed prop-rotors. The necessary disciplinary couplings are all considered within a closed loop optimization process. The procedures involve the consideration of blade aeroelastic, aerodynamic performance, structural and dynamic design requirements. Further, since the design involves consideration of several different objectives, multiobjective function formulation techniques are developed.
A higher-order theory is developed to model composite box beams with arbitrary wall thicknesses. The theory, based on a refined displacement field, represents a three-dimensional model which approximates the elasticity solution. Therefore, the cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are automatically included in the formulation. The model accurately captures the transverse shear stresses through the thickness of each wall while satisfying all stress-free boundary conditions. Several numerical results are presented to validate the present theory. The developed theory is then used to model the load carrying member of a tilt-rotor blade which has thick-walled sections. The composite structural analysis is coupled with an aerodynamic analysis to compute the aeroelastic stability of the blade. Finally, a multidisciplinary optimization procedure is developed to improve the aerodynamic, structural and aeroelastic performance of the tilt-rotor aircraft. The Kreisselmeier-Steinhauser function is used to formulate the multiobjective function problem and a hybrid approximate analysis is used to reduce the computational effort. The optimum results are compared with the baseline values and show significant improvements in the overall performance of the tilt-rotor blade.
The objective of this research is to develop optimization procedures to provide design trends in high speed prop-rotors. The necessary disciplinary couplings are all considered within a closed loop multilevel decomposition optimization process. The procedures involve the consideration of blade-aeroelastic aerodynamic performance, structural-dynamic design requirements, and acoustics. Further, since the design involves consideration of several different objective functions, multiobjective function formulation techniques are developed.
The use of multidimensional optimization methods in solving power plant siting problems, which are characterized by several conflicting, noncommensurable objectives is addressed. After a discussion of data requirements and exclusionary site screening methods for bounding the decision space, classes of multiobjective and goal programming models are discussed in the context of finite site selection. Advantages and limitations of these approaches are highlighted and the linkage of multidimensional methods with the subjective, behavioral components of the power plant siting process is emphasized.
An optimization procedure is developed for addressing the design of composite tilt rotor blades. A comprehensive technique, based on a higher-order laminate theory, is developed for the analysis of the thick composite load-carrying sections, modeled as box beams, in the blade. The theory, which is based on a refined displacement field, is a three-dimensional model which approximates the elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the transverse shear stresses through the thickness of each wall while satisfying stress free boundary conditions on the inner and outer surfaces of the beam. The aerodynamic loads on the blade are calculated using the classical blade element momentum theory. Analytical expressions for the lift and drag are obtained based on the blade planform with corrections for the high lift capability of rotor blades. The aerodynamic analysis is coupled with the structural model to formulate the complete coupled equations of motion for aeroelastic analyses. Finally, a multidisciplinary optimization procedure is developed to improve the aerodynamic, structural and aeroelastic performance of the tilt rotor aircraft. The objective functions include the figure of merit in hover and the high speed cruise propulsive efficiency. Structural, aerodynamic and aeroelastic stability criteria are imposed as constraints on the problem. The Kreisselmeier-Steinhauser function is used to formulate the multiobjective function problem. The search direction is determined by the Broyden-Fletcher-Goldfarb-Shanno algorithm. The optimum results are compared with the baseline values and show significant improvements in the overall performance of the tilt rotor blade.
The latest results of an ongoing study of computer-aided design of airplane control systems are given. Constrained minimization algorithms are used, with the design objectives in the constraint vector. The concept of Pareto optimiality is briefly reviewed. It is shown how an experienced designer can use it to find designs which are well-balanced in all objectives. Then the problem of finding designs which are insensitive to uncertainty in system parameters are discussed, introducing a probabilistic vector definition of sensitivity which is consistent with the deterministic Pareto optimal problem. Insensitivity is important in any practical design, but it is particularly important in the design of feedback control systems, since it is considered to be the most important distinctive property of feedback control. Methods of tradeoff between deterministic and stochastic-insensitive (SI) design are described, and tradeoff design results are presented for the example of the a Shuttle lateral stability augmentation system. This example is used because careful studies have been made of the uncertainty in Shuttle aerodynamics. Finally, since accurate statistics of uncertain parameters are usually not available, the effects of crude statistical models on SI designs are examined.
We are developing a programmable multiobject field selector for the NGST NIRSpec. This device is a microshutter array, a close-packed 2000 x 2000 array of 100 micrometer x 100 micrometer shutters fabricated with Micro-ElectroMechanical Systems (MEMS) technologies. The shutters are opened using a magnet scanned over the array. The shutters are held open by electrostatic potentials on adjacent vertical electrodes. Modeling of the magnetic actuation of the microshutters allowed optimization of the magnetic field configuration, the distance between magnet and shutters, and the force and torque produced by the magnet. The results of laboratory tests are consistent with our modeling. We have demonstrated actuation, latching and addressing. We are able to rotate shutters out of the plane up to 90 degree and more, to latch them electrostatically to the walls and release them selectively. During the last six month all critical elements of the array have been demonstrated. Fabrication processes were developed to deposit vertical electrodes on support grid side walls and insulated light-shields that block the gaps between shutters and the support grid. Physical optics analysis was performed to assess the expected optical performance of the microshutters. A preliminary Fourier optics analysis on the microshutter array performance has been carried out. More detailed analysis of wave propagation through 3D structures is a next step. An optical test station for verifying optical parameters of the shutter array at room temperature has been developed. It allows to measure parameters, such as transmission, scattering, contrast ratio, and diffraction of the array structure. Initial data have been acquired and are being analyzed and compared to theoretical predictions.
A multiobjective computer-aided design algorithm has been developed which minimizes the sensitivity of the design objectives to uncertainties in system parameters. The more important uncertain parameters are described by a gaussian random vector with known covariance matrix, and a vector sensitivity objective function is defined as the probabilities that the design objectives will violate specified requirements constraints. Control system parameters are found which minimize the sensitivity vector in a Pareto-optimal sense, using constrained minimization algorithms. Example results are shown for lateral stability augmentation system (SAS) design for three Shuttle flight conditions.
A multiobjective cost function that includes a form of the standard LQR regulator cost and its partial variation with respect to the additional design parameters is presented in connection with the design of an orbiting control/structural system. Simple models of uniform solid and tubular beams are demonstrated with two typical additional payload masses, i.e., symmetrically distributed and asymmetrically distributed, with respect to the center of the beam. By regarding the transient response of pitch angle and free-free beam deformations in the orbital plane, the optimal outer diameter of the beam and all feedback control can be determined by numerical analysis with this multicriterial approach. It is concluded that the multicriteria design approach should give better results from both the structural designer's and the control designer's standpoints.
The chief goals of the summer project have been twofold - first, for my host group and myself to learn as much of the working details of Taguchi analysis as possible in the time allotted, and, secondly, to apply the methodology to a design problem with the intention of establishing a preliminary set of near-optimal (in the sense of producing a desired response) design parameter values from among a large number of candidate factor combinations. The selected problem is concerned with determining design factor settings for an automated approach program which is to have the capability of guiding the Shuttle into the docking port of the Space Station under controlled conditions so as to meet and/or optimize certain target criteria. The candidate design parameters under study were glide path (i.e., approach) angle, path intercept and approach gains, and minimum impulse bit mode (a parameter which defines how Shuttle jets shall be fired). Several performance criteria were of concern: terminal relative velocity at the instant the two spacecraft are mated; docking offset; number of Shuttle jet firings in certain specified directions (of interest due to possible plume impingement on the Station's solar arrays), and total RCS (a measure of the energy expended in performing the approach/docking maneuver). In the material discussed here, we have focused on single performance criteria - total RCS. An analysis of the possibility of employing a multiobjective function composed of a weighted sum of the various individual criteria has been undertaken, but is, at this writing, incomplete. Results from the Taguchi statistical analysis indicate that only three of the original four posited factors are significant in affecting RCS response. A comparison of model simulation output (via Monte Carlo) with predictions based on estimated factor effects inferred through the Taguchi experiment array data suggested acceptable or close agreement between the two except at the predicted optimum point, where a difference outside a rule-of-thumb bound was observed. We have concluded that there is most likely an interaction effect not provided for in the original orthogonal array selected as the basis for our experimental design. However, we feel that the data indicates that this interaction is a mild one and that inclusion of its effect will not alter the location of the optimum.
The Cosmic Evolution Through UV Spectroscopy (CETUS) concept enables parallel observations by the UV multiobject spectrometer (MOS) and near-UV/far-UV camera which operate simultaneously but independently with their separate field of views. The near-UV MOS can target up to 100 objects at a time without confusion with nearby sources or background zodiacal light. This multiplexing will allow over 100,000 galaxies to be observed over a typical mission lifetime. The MOS includes a next-generation micro-shutter array (NGMSA), an efficient aspheric Offner-like spectrometer design with a convex grating, and nanotube light traps for suppressing unwanted wavelengths. The NUV/FUV Camera has the capability to image in a range of sub-bands from 115-400 nm at the same time the MOS is operating at 180-350 nm. The UV camera has a similar Offner-like relay, selectable filters, and two separate detectors to optimize observing in either the far-UV (115-175 nm) or the near-UV (180-400 nm) utilizing a CsI Micro-Channel Plate detector (MCP) and a CCD respectively.
Active structural acoustic control is a method in which the control inputs (used to reduce interior noise) are applied directly to a vibrating structural acoustic system. The control concept modeled in this work is the application of in-plane force inputs to piezoceramic patches bonded to the wall of a vibrating cylinder. The cylinder is excited by an exterior noise source -- an acoustic monopole -- located near the outside of the cylinder wall. The goal is to determine the force inputs and sites for the piezoelectric actuators so that (1) the interior noise is effectively damped; (2) the level of vibration of the cylinder shell is not increased; and (3) the power requirements needed to drive the actuators are not excessive. We studied external monopole excitations at two frequencies. A cylinder resonance of 100 Hz, where the interior acoustic field is driven in multiple, off-resonance cylinder cavity modes, and a cylinder resonance of 200 Hz are characterized by both near and off-resonance cylinder vibration modes which couple effectively with a single, dominant, low-order acoustic cavity mode at resonance. Previous work has focused almost exclusively on meeting objective (1) and solving a complex least-squares problem to arrive at an optimal force vector for a given set of actuator sites. In addition, it has been noted that when the cavity mode couples with cylinder vibration modes (our 200 Hz case) control spillover may occur in higher order cylinder shell vibrational modes. How to determine the best set of actuator sites to meet objectives (1)-(3) is the main contribution of our research effort. The selection of the best set of actuator sites from a set of potential sites is done via two metaheuristics -- simulated annealing and tabu search. Each of these metaheuristics partitions the set of potential actuator sites into two disjoint sets: those that are selected to control the noise (on) and those that are not (off). Next, each metaheuristic attempts to improve this initial solution by calculating the change in the objective value when one selected actuator site is turned off and one actuator site that previously was not selected is turned on. All such pairwise exchanges are performed and the exchange that improves the objective the most is made. Eventually the search is unable to improve the objective value and a local optimum (with respect to pairwise exchanges) is reached. Both simulated annealing and tabu search provide mechanisms to escape local optima and allow the search to continue until (hopefully) a global optimum is found. Our experiments with the 100 Hz and 200 Hz cases confirm that both metaheuristics are able to uncover better solutions than those selected based upon engineering judgement alone. In addition, the high quality solutions generated by these metaheuristics, when minimizing interior noise, do not further excite the cylinder shell. Thus, we are able to meet objective (2) without imposing an additional constraint or forming a multiobjective performance measure. An additional observation is that in many cases the amplitude and phase values for several chosen actuator sites were nearly identical. This natural grouping means that fewer control channels are needed and the resulting control system is simpler. Currently no power requirements have been set, so objective (3) cannot be addressed. A set of experiments is planned with a laboratory test article (a cylinder). For these experiments the transfer matrices will be generated experimentally. It is hoped that the predicted performance of the best actuator sites found by our metaheuristics will correlate well with the measured performance.