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A new inverse method for the aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed as a function of the arclength of the still unknown body. It is shown that this inverse problem is mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary.
A numerical method to solve the inverse problem for airfoil cascades is described. The case of compressible, inviscid flow is considered. The proposed method is based on the finite difference approximation of the time-dependent Euler equations. Numerical examples show the capability of the method to design subsonic or transonic shockless blades.
Dynamic inversion is a technique for control law design in which feedback is used to simultaneously cancel system dynamics and achieve desired dynamic response characteristics. However, dynamic inversion control laws lack robustness to modeling errors if improperly designed. This paper examines a simple linear example, control of roll rate about the body axis of high performance aircraft, to illustrate some robustness problems which may occur with a simple dynamic inversion control law. The paper demonstrates how structured singular value synthesis techniques can be used to enhance the robustness properties of the dynamic inversion controller.
Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.
During this year, we concentrated our efforts on the design of controllers for lateral/directional control using mu synthesis. This proved to be a more difficult task than we anticipated and we are still working on the designs. In the lateral-directional control problem, the inputs are pilot lateral stick and pedal commands and the outputs are roll rate about the velocity vector and side slip angle. The control effectors are ailerons, rudder deflection, and directional thrust vectoring vane deflection which produces a yawing moment about the body axis. Our math model does not contain any provision for thrust vectoring of rolling moment. This has resulted in limitations of performance at high angles of attack. During 1994-95, the following tasks for the lateral-directional controllers were accomplished: (1) Designed both inner and outer loop dynamic inversion controllers. These controllers are implemented using accelerometer outputs rather than an a priori model of the vehicle aerodynamics; (2) Used classical techniques to design controllers for the system linearized by dynamics inversion. These controllers acted to control roll rate and Dutch roll response; (3) Implemented the inner loop dynamic inversion and classical controllers on the six DOF simulation; (4) Developed a lateral-directional control allocation scheme based on minimizing required control effort among the ailerons, rudder, and directional thrust vectoring; and (5) Developed mu outer loop controllers combined with classical inner loop controllers.
Independent Modal Space Control (IMSC) method avoids control spillover generated by conventional control schemes such as Coupled Modal Control by decoupling the large flexible space structure into independent subsystems of second order and controlling each mode independently. The IMSC implementation requires that the number of actuators be equal to that of modeled modes, which is in general very huge. Consequently the number of required actuators is unrealizable. Two methods are proposed for the implementation of IMSC with reduced number of actuators. In the first method, the first m modes are optimized, leaving the last (n-m) modes unchanged. In the second method, generalized inverse matrices are employed to design the feedback controller so that the control scheme is suboptimal with respect to IMSC. The performance of the proposed methods is tested by performing computer simulation on a simply support beam. Simulation results are presented and discussed.
Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome 0 "would have been right if the outcome had been the desired one." The algorithm then proceeds as follows: (1) store the action that produced the wrong outcome as a "target" (2) redefine the wrong outcome as a desired goal (3) submit the new desired goal to the system (4) compare the new action with the target action and modify the system by using a suitable algorithm for credit assignment (Back propagation in our example) (5) resubmit the original goal. Prior publications by our group in this area focused on demonstrating empirical results based on the inverse kinematic problem for a simulated robotic arm. In this paper we apply the inversion process to much simpler analytic functions in order to elucidate the dynamic behavior of the system and to determine the sensitivity of the learning process to various parameters. This understanding will be necessary for the acceptance of GDMI as a practical tool.
Orbital rendezvous involves execution of a sequence of maneuvers by a chaser vehicle to bring the chaser to a desired state relative to a target vehicle while meeting intermediate and final relative constraints. Intermediate and final relative constraints are necessary to meet a multitude of requirements such as to control approach direction, ensure relative position is adequate for operation of space-to-space communication systems and relative sensors, provide fail-safe trajectory features, and provide contingency hold points. The effect of maneuvers on constraints is often coupled, so the maneuvers must be solved for as a set. For example, maneuvers that affect orbital energy change both the chaser's height and downrange position relative to the target vehicle. Rendezvous designers use experience and rules-of-thumb to design a sequence of maneuvers and constraints. A non-iterative method is presented for targeting a rendezvous scenario that includes a sequence of maneuvers and relative constraints. This method is referred to as Multi-Maneuver Clohessy-Wiltshire Targeting (MM_CW_TGT). When a single maneuver is targeted to a single relative position, the classic CW targeting solution is obtained. The MM_CW_TGT method involves manipulation of the CW state transition matrix to form a linear system. As a starting point for forming the algorithm, the effects of a series of impulsive maneuvers on the state are derived. Simple and moderately complex examples are used to demonstrate the pattern of the resulting linear system. The general form of the pattern results in an algorithm for formation of the linear system. The resulting linear system relates the effect of maneuver components and initial conditions on relative constraints specified by the rendezvous designer. Solution of the linear system includes the straight-forward inverse of a square matrix. Inversion of the square matrix is assured if the designer poses a controllable scenario - a scenario where the the constraints can be met by the sequence of maneuvers. Matrices in the linear system are dependent on selection of maneuvers and constraints by the designer, but the matrices are independent of the chaser's initial conditions. For scenarios where the sequence of maneuvers and constraints are fixed, the linear system can be formed and the square matrix inverted prior to real-time operations. Example solutions are presented for several rendezvous scenarios to illustrate the utility of the method. The MM_CW_TGT method has been used during the preliminary design of rendezvous scenarios and is expected to be useful for iterative methods in the generation of an initial guess and corrections.
PROFILE program solves diverse and inverse airfoil-flow problems. It combines conformational mapping method for design of airfoils with prescribed velocity-distribution characteristics, panel method for potential-flow analysis, and boundary-layer method. PROFILE is written in FORTRAN IV for implementation on CDC 6000-series computer.
Climate changes traditionally have been detected from long series of observations and long after they happened. The 'inverse sequential' monitoring procedure is designed to detect changes as soon as they occur. Frequency distribution parameters are estimated both from the most recent existing set of observations and from the same set augmented by 1,2,...j new observations. Individual-value probability products ('likelihoods') are then calculated which yield probabilities for erroneously accepting the existing parameter(s) as valid for the augmented data set and vice versa. A parameter change is signaled when these probabilities (or a more convenient and robust compound 'no change' probability) show a progressive decrease. New parameters are then estimated from the new observations alone to restart the procedure. The detailed algebra is developed and tested for Gaussian means and variances, Poisson and chi-square means, and linear or exponential trends; a comprehensive and interactive Fortran program is provided in the appendix.
This paper addresses the modeling of nonlinear constitutive relations and hysteresis inherent to piezoceramic materials at moderate to high drive levels. Such models are, necessary to realize the, full potential of the materials in high performance control applications, and a necessary prerequisite is the development of techniques which permit control implementation. The approach employed here is based on the qualification of reversible and irreversible domain wall motion in response to applied electric fields. A comparison with experimental data illustrates that because the resulting ODE model is physics-based, it can be employed for both characterization and prediction of polarization levels throughout the range of actuator operation. Finally, the ODE formulation is amenable to inversion which facilitates the development of an inverse compensator for linear control design.
Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome "would have been right if the outcome had been the desired one." The algorithm makes use of these intermediate "successes" to achieve the final goal. A unique and potentially very important feature of this algorithm is the ability to modify the output of the learning module to force upon it a desired syntactic structure. This differs from ordinary supervised learning in the following way: in supervised learning the exact desired output pattern must be provided. In GDMI instead, it is possible to require simply that the output obey certain rules, i.e., that it "make sense" in some way determined by the knowledge domain. The exact pattern that will achieve the desired outcome is then found by the system. The ability to impose rules while allowing the system to search for its own answers in the context of neural networks is potentially a major breakthrough in two ways: 1) it may allow the construction of networks that can incorporate immediately some important knowledge, i.e. would not need to learn everything from scratch as normally required at present, and 2) learning and searching would be limited to the areas where it is necessary, thus facilitating and speeding up the process. These points are illustrated with examples from robotic path planning and parametric design.
Goal Directed Model Inversion (GDMI) is an algorithm designed to generalize supervised learning to the case where target outputs are not available to the learning system. The output of the learning system becomes the input to some external device or transformation, and only the output of this device or transformation can be compared to a desired target. The fundamental driving mechanism of GDMI is to learn from success. Given that a wrong outcome is achieved, one notes that the action that produced that outcome "would have been right if the outcome had been the desired one." The algorithm makes use of these intermediate "successes" to achieve the final goal. A unique and potentially very important feature of this algorithm is the ability to modify the output of the learning module to force upon it a desired syntactic structure. This differs from ordinary supervised learning in the following way: in supervised learning the exact desired output pattern must be provided. In GDMI instead, it is possible to require simply that the output obey certain rules, i.e., that it "make sense" in some way determined by the knowledge domain. The exact pattern that will achieve the desired outcome is then found by the system. The ability to impose rules while allowing the system to search for its own answers in the context of neural networks is potentially a major breakthrough in two ways: (1) it may allow the construction of networks that can incorporate immediately some important knowledge, i.e., would not need to learn everything from scratch as normally required at present; and (2) learning and searching would be limited to the areas where it is necessary, thus facilitating and speeding up the process. These points are illustrated with examples from robotic path planning and parametric design.
This study presents a detailed theoretical assessment of the information content of passive polarimetric observations over snow scenes, using a global sensitivity analysis (GSA) method. Conventional sensitivity studies focus on varying a single parameter while keeping all other parameters fixed. In contrast, the GSA correctly addresses the covariance of state parameters across their entire parameter space, hence favoring a more correct interpretation of inversion algorithms and the optimal design of their state vectors. The forward simulations exploit a vector radiative transfer model to obtain the Stokes vector emerging at the top of the atmosphere for different solar zenith angles, when the bottom boundary consists of a vertically resolved snowpack of non-spherical grains. The presence of light-absorbing particulates (LAPs), either embedded in the snow or aloft in the atmosphere above in the form of aerosols, is also considered. The results are presented for a set of wavelengths spanning the visible (VIS), near-infrared (NIR), and shortwave infrared (SWIR) region of the spectrum. The GSA correctly captures the expected, high sensitivity of the reflectance to LAPs in the VIS–NIR and to grain size at different depths in the snowpack in the NIR–SWIR. With adequate viewing geometries, mono-angle measurements of total reflectance in the VIS–SWIR (akin to those of the Moderate Resolution Imaging Spectroradiometer, MODIS) resolve grain size in the top layer of the snowpack sufficiently well. The addition of multi-angle polarimetric observations in the VIS–NIR provides information on grain shape and microscale roughness. The simultaneous sensitivity in the VIS–NIR to both aerosols and snow-embedded impurities can be disentangled by extending the spectral range to the SWIR, which contains information on aerosol optical depth while remaining essentially unaffected when the same particulates are mixed with the snow. Multi-angle polarimetric observations can therefore (i) effectively partition LAPs between the atmosphere and the surface, which represents a notorious challenge for snow remote sensing based on measurements of total reflectance only and (ii) lead to better estimates of grain shape and roughness and, in turn, the asymmetry parameter, which is critical for the determination of albedo. The retrieval uncertainties are minimized when the degree of linear polarization is used in place of the polarized reflectance. The Sobol indices, which are the main metric for the GSA, were used to select the state parameters in retrievals performed on data simulated for multiple instrument configurations. Improvements in retrieval quality with the addition of measurements of polarization, multi-angle views, and different spectral channels reflect the information content, identified by the Sobol indices, relative to each configuration. The results encourage the development of new remote sensing algorithms that fully leverage multi-angle and polarimetric capabilities of modern remote sensors. They can also aid flight planning activities, since the optimal exploitation of the information content of multi-angle measurements depends on the viewing geometry. The better characterization of surface and atmospheric parameters in snow-covered regions advances research opportunities for scientists of the cryosphere and ultimately benefits albedo estimates in climate models.
Theoretical methods (computer programs) which are available for analyzing reflector performance are of the 'forward' type. Performance parameters can be calculated after the configuration of the reflector is given. In many practical applications, however, the problem is often of the 'inverse' type. The reflector has to be designed on the basis of a given set of performance parameters. Attention is given to a systematic procedure based on simple formulas for solving such an inverse problem. Because of the simplicity of the formulas, the final results obtained from the procedure do not have great accuracy. Thus, they represent only a preliminary design, which can be refined by repeatedly using the forward-type programs.
Two issues that are fundamental to developing autonomous intelligent robots, namely, rudimentary learning capability and dexterous manipulation, are examined. A powerful neural learning formalism is introduced for addressing a large class of nonlinear mapping problems, including redundant manipulator inverse kinematics, commonly encountered during the design of real-time adaptive control mechanisms. Artificial neural networks with terminal attractor dynamics are used. The rapid network convergence resulting from the infinite local stability of these attractors allows the development of fast neural learning algorithms. Approaches to manipulator inverse kinematics are reviewed, the neurodynamics model is discussed, and the neural learning algorithm is presented.
Some new developments relevant to the design of single-element airfoils using potential flow methods are presented. In particular, the ramifications of the unbounded trailing edge pressure gradients generally present in the potential flow solution for the flow over an airfoil are examined, and the conditions necessary to obtain a class of airfoils having finite trailing edge pressure gradients developed. The incorporation of these conditions into the inverse method of Eppler for the design of low-speed airfoils is discussed, and designs generated using the modified scheme are presented for consideration. A detailed viscous analysis of one of these airfoils demonstrates a significant reduction in the strong inviscid-viscid interactions generally present near the trailing edge. These reductions offer the possibility of improved airfoil performance, as well as the possibility of improved accuracy in the methods of airfoil design and analysis.
The first generation of remote power controllers (RPC) developed included: a 5-ampere design (Type 1), capable of limiting maximum overload current to 15 amperes for .1 sec; and 5-ampere noncurrent (Type 2) and 30-ampere noncurrent (Type 3) limiting designs, both with selectable instant trip levels for high-current overload. Each design provides overcurrent protection through an inverse I squared T trip-out function with an automatic reset option and demonstrates step-applied fault capability with a 4000-ampere surge, fast-risetime (low-inductance) power source. They also meet MIL - STD - 461A specification for electromagnetic interference. The second generation RPCs traded off specification compliance for reduction in cost and complexity for the Type 1 and 2 designs and give comparable or improved performance in most areas. The noncurrent limiting RPC proved to be a more economical and feasible method of overload protection for certain load types.