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At least 307 records · Page 17

The detrimental effect of friction on space microgravity robotics

The authors present an analysis of why control systems are ineffective in compensating for acceleration disturbances due to Coulomb friction. Linear arguments indicate that the effects of Coulomb friction on a body are most difficult to reject when the control actuator is separated from the body of compliance. The linear arguments were illustrated in a nonlinear simulation of optimal linear tracking control in the presence of nonlinear friction. The results of endpoint acceleration measurements for four robot designs are presented and are compared with simulation and to equivalent measurements on a human. It is concluded that Coulomb friction in common bearings and transmission induces unacceptable levels of endpoint acceleration, that these accelerations cannot be adequately attenuated by control, and that robots for microgravity work will require special design considerations for inherently low friction.

Newman, Wyatt S.↗

Alternatives for jet engine control

Alternatives to linear quadratic regulator theory in the linear case are examined along with nonlinear modelling and optimization approaches for global control. Context for the studies has been set by the DYNGEN digital simulator and by models generated for various phases of the F100 Multivariable Control Synthesis Program. With respect to the linear alternatives, the multivariable frequency domain is stressed. Progress is reported in both the direct algebraic approach to exact model matching, by means of stimulating work on the basic computational issues, and in the indirect generalized Nyquist approach. With respect to nonlinear modelling and optimization, the emphasis is twofold: the development of analytical nonlinear models of the jet engine and the use of these models in conjunction with techniques of mathematical programming in order to study global control over nonincremental portions of the flight envelope. The possibility of using tensor methods is explored.

Sain, M. K.↗

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗

Development of a turbomachinery design optimization procedure using a multiple-parameter nonlinear perturbation method

An investigation was carried out to complete the preliminary development of a combined perturbation/optimization procedure and associated computational code for designing optimized blade-to-blade profiles of turbomachinery blades. The overall purpose of the procedures developed is to provide demonstration of a rapid nonlinear perturbation method for minimizing the computational requirements associated with parametric design studies of turbomachinery flows. The method combines the multiple parameter nonlinear perturbation method, successfully developed in previous phases of this study, with the NASA TSONIC blade-to-blade turbomachinery flow solver, and the COPES-CONMIN optimization procedure into a user's code for designing optimized blade-to-blade surface profiles of turbomachinery blades. Results of several design applications and a documented version of the code together with a user's manual are provided.

Stahara, S. S.↗

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Lan, C. Edward↗

Optimal design of a class of nonlinear networks.

The problem of synthesizing nth order nonlinear nonautonomous networks with a prescribed small signal behavior is considered. It is shown that, in the absence of coupling elements, the solution of this problem reduces to synthesizing a set of first order nonlinear characteristics. These characteristics can then be determined using a recently developed generalized steepest descent criterion.

Peikari, B.↗

MACOS Version 3.31

Version 3.31 of Modeling and Analysis for Controlled Optical Systems (MACOS) has been released. MACOS is an easy-to-use computer program for modeling and analyzing the behaviors of a variety of optical systems, including systems that have large, segmented apertures and are aligned with the technology of wavefront sensing and control. Two previous versions were described in "Improved Software for Modeling Controlled Optical Systems" (NPO-19841) NASA Tech Briefs, Vol. 21, No. 12 (December 1997), page 42 and "Optics Program Modified for Multithreaded Parallel Computing" (NPO-40572) NASA Tech Briefs, Vol. 30, No. 1 (January 2006) page 13a. The present version incorporates the following enhancements over prior versions: a) A powerful system-optimization facility includes algorithms for linear, nonlinear, unconstrained, and constrained optimization of optical systems under a variety of settings. b) There is now enhanced capability to perturb optical components individually and on subsystem levels, and to optimize system performance by adjusting selected individual components as well as subsystems. c) Capabilities for modeling a variety of new optical aperture types have been added. d) Effects of multilayer thin-film coats on optical surfaces can now be taken into account when tracing polarized rays. e) Major software-engineering work was performed to make MACOS more reliable, flexible, and manageable for purposes of maintenance and further development.

Redding, David↗

Model-Based Control of a Nonlinear Aircraft Engine Simulation using an Optimal Tuner Kalman Filter Approach

This paper covers the development of a model-based engine control (MBEC) methodology featuring a self tuning on-board model applied to an aircraft turbofan engine simulation. Here, the Commercial Modular Aero-Propulsion System Simulation 40,000 (CMAPSS40k) serves as the MBEC application engine. CMAPSS40k is capable of modeling realistic engine performance, allowing for a verification of the MBEC over a wide range of operating points. The on-board model is a piece-wise linear model derived from CMAPSS40k and updated using an optimal tuner Kalman Filter (OTKF) estimation routine, which enables the on-board model to self-tune to account for engine performance variations. The focus here is on developing a methodology for MBEC with direct control of estimated parameters of interest such as thrust and stall margins. Investigations using the MBEC to provide a stall margin limit for the controller protection logic are presented that could provide benefits over a simple acceleration schedule that is currently used in traditional engine control architectures.

Control Theory↗

Application of Sequential Quadratic Programming to Minimize Smart Active Flap Rotor Hub Loads

In an analytical study, SMART active flap rotor hub loads have been minimized using nonlinear programming constrained optimization methodology. The recently developed NLPQLP system (Schittkowski, 2010) that employs Sequential Quadratic Programming (SQP) as its core algorithm was embedded into a driver code (NLP10x10) specifically designed to minimize active flap rotor hub loads (Leyland, 2014). Three types of practical constraints on the flap deflections have been considered. To validate the current application, two other optimization methods have been used: i) the standard, linear unconstrained method, and ii) the nonlinear Generalized Reduced Gradient (GRG) method with constraints. The new software code NLP10x10 has been systematically checked out. It has been verified that NLP10x10 is functioning as desired. The following are briefly covered in this paper: relevant optimization theory; implementation of the capability of minimizing a metric of all, or a subset, of the hub loads as well as the capability of using all, or a subset, of the flap harmonics; and finally, solutions for the SMART rotor. The eventual goal is to implement NLP10x10 in a real-time wind tunnel environment.

HUB LOADS↗

Integrated nonlinear structural analysis and design

An integrated approach to the design optimization of structures which require nonlinear analysis is proposed. The optimization process begins with a linearized structural response and the amount of nonlinearity is increased as the optimum design becomes closer. The proposed approach has the potential of reducing substantially the computational cost of the optimization. Two truss examples are used for demonstration.

Haftka, Raphael T.↗

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Parrish, Nathan L.↗

Power converter design optimization

Utilizing the demonstrated capability of nonlinear programming algorithms, a practical design optimization approach for power converters is established to conceive a design to meet all power-circuit performance requirements and concurrently optimize a defined quantity such as weight or losses. In addition, to facilitate a cost-effective design, the computer-aided approach provides a means to readily assess (1) the weight-efficiency tradeoff, (2) impacts of converter requirements and component characteristics on a given design, and (3) optimum power system configurations.

Yu, Y.↗

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

Feng, Dan↗

Estimation and filter stability of stochastic delay systems

Linear and nonlinear filtering for stochastic delay systems are studied. A representation theorem for conditional moment functionals is obtained, which, in turn, is used to derive stochastic differential equations describing the optimal linear or nonlinear filter. A complete characterization of the optimal filter is given for linear systems with Gaussian noise. Stability of the optimal filter is studied in the case where there are no delays in the observations. Using the duality between linear filtering and control, asymptotic stability of the optimal filter is proved. Finally, the cascade of the optimal filter and the deterministic optimal quadratic control system is shown to be asymptotically stable as well.

Kwong, R. H.↗

Applying optimization software libraries to engineering problems

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.↗