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The application of optimal control technqiues to advanced manned missions, volume 1

Two problems are presented in the area of optimal control and its application to the design of attitude control systems for advanced complex aerospace vehicles. The problems discussed are specification of performance criteria in terms of structural load minimization and/or maximum orbital payload injection requirements of the controlled vehicle; and formulation and solution of the optimization problem such that practical control systems are obtained.

Connor, C. L.

Application of numerical optimization to the design of advanced supercritical airfoils

An application of numerical optimization to the design of advanced airfoils for transonic aircraft showed that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while minimizing the drag coefficient at the design Mach number. This multiple design-point numerical optimization has been implemented with the use of airfoil shape functions which permit a wide range of attainable profiles during the optimization process. Analytical data for the starting airfoil shape, a single design-point optimized shape, and a double design-point optimized shape are presented. Experimental data obtained in the NASA Ames two-by two-foot wind tunnel are also presented and discussed.

Johnson, R. R.

Real-time approximate optimal guidance laws for the advanced launch system

An approach to optimal ascent guidance for a launch vehicle is developed using an expansion technique. The problem is to maximize the payload put into orbit subject to the equations of motion of a rocket over a rotating spherical earth. It is assumed that the thrust and gravitational forces dominate over the aerodynamic forces. It is shown that these forces can be separated by a small parameter epsilon, where epsilon is the ratio of the atmospheric scale height to the radius of the earth. The Hamilton-Jacobi-Bellman or dynamic programming equation is expanded in a series where the zeroth-order term (epsilon = 0) can be obtained in closed form. The zeroth-order problem is that of putting maximum payload into orbit subject to the equations of motion of a rocket in a vacuum over a flat earth. The neglected inertial and aerodynamic terms are included in higher order terms of the expansion, which are determined from the solution of first-order linear partial differential equations requiring only quadrature integrations. These quadrature integrations can be performed rapidly, so that real-time approximate optimization can be used to construct the launch guidance law.

Speyer, Jason L.

Advanced launch system trajectory optimization using suboptimal control

The maximum-final mass trajectory of a proposed configuration of the Advanced Launch System is presented. A model for the two-stage rocket is given; the optimal control problem is formulated as a parameter optimization problem; and the optimal trajectory is computed using a nonlinear programming code called VF02AD. Numerical results are presented for the controls (angle of attack and velocity roll angle) and the states. After the initial rotation, the angle of attack goes to a positive value to keep the trajectory as high as possible, returns to near zero to pass through the transonic regime and satisfy the dynamic pressure constraint, returns to a positive value to keep the trajectory high and to take advantage of minimum drag at positive angle of attack due to aerodynamic shading of the booster, and then rolls off to negative values to satisfy the constraints. Because the engines cannot be throttled, the maximum dynamic pressure occurs at a single point; there is no maximum dynamic pressure subarc. To test approximations for obtaining analytical solutions for guidance, two additional optimal trajectories are computed: one using untrimmed aerodynamics and one using no atmospheric effects except for the dynamic pressure constraint. It is concluded that untrimmed aerodynamics has a negligible effect on the optimal trajectory and that approximate optimal controls should be able to be obtained by treating atmospheric effects as perturbations.

Shaver, Douglas A.

The Third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization

The third Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization was held on 24-26 Sept. 1990. Sessions were on the following topics: dynamics and controls; multilevel optimization; sensitivity analysis; aerodynamic design software systems; optimization theory; analysis and design; shape optimization; vehicle components; structural optimization; aeroelasticity; artificial intelligence; multidisciplinary optimization; and composites.

V.B. Venkayya

Optimal design application on the advanced aeroelastic rotor blade

The vibration and performance optimization procedure using regression analysis was successfully applied to an advanced aeroelastic blade design study. The major advantage of this regression technique is that multiple optimizations can be performed to evaluate the effects of various objective functions and constraint functions. The data bases obtained from the rotorcraft flight simulation program C81 and Myklestad mode shape program are analytically determined as a function of each design variable. This approach has been verified for various blade radial ballast weight locations and blade planforms. This method can also be utilized to ascertain the effect of a particular cost function which is composed of several objective functions with different weighting factors for various mission requirements without any additional effort.

Wei, F. S.

Improved Broadband Liner Optimization Applied to the Advanced Noise Control Fan

The broadband component of fan noise has grown in relevance with the utilization of increased bypass ratio and advanced fan designs. Thus, while the attenuation of fan tones remains paramount, the ability to simultaneously reduce broadband fan noise levels has become more desirable. This paper describes improvements to a previously established broadband acoustic liner optimization process using the Advanced Noise Control Fan rig as a demonstrator. Specifically, in-duct attenuation predictions with a statistical source model are used to obtain optimum impedance spectra over the conditions of interest. The predicted optimum impedance information is then used with acoustic liner modeling tools to design liners aimed at producing impedance spectra that most closely match the predicted optimum values. Design selection is based on an acceptance criterion that provides the ability to apply increased weighting to specific frequencies and/or operating conditions. Constant-depth, double-degree of freedom and variable-depth, multi-degree of freedom designs are carried through design, fabrication, and testing to validate the efficacy of the design process. Results illustrate the value of the design process in concurrently evaluating the relative costs/benefits of these liner designs. This study also provides an application for demonstrating the integrated use of duct acoustic propagation/radiation and liner modeling tools in the design and evaluation of novel broadband liner concepts for complex engine configurations.

Nark, Douglas M.

Finite element method for optimal guidance of an advanced launch vehicle

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

Hodges, Dewey H.

A weak Hamiltonian finite element method for optimal guidance of an advanced launch vehicle

A temporal finite-element method based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables, which are expanded in terms of nodal values and simple shape functions. Time derivatives of the states and costates do not appear in the governing variational equation; the only quantities whose time derivatives appear therein are virtual states and virtual costates. Numerical results are presented for an elementary trajectory optimization problem; they show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The feasibility of this approach for real-time guidance applications is evaluated. A simplified model for an advanced launch vehicle application that is suitable for finite-element solution is presented.

Hodges, Dewey H.

A Web Centric Architecture for Deploying Multi-Disciplinary Engineering Design Processes

There are continuous needs for engineering organizations to improve their design process. Current state of the art techniques use computational simulations to predict design performance, and optimize it through advanced design methods. These tools have been used mostly by individual engineers. This paper presents an architecture for achieving results at an organization level beyond individual level. The next set of gains in process improvement will come from improving the effective use of computers and software within a whole organization, not just for an individual. The architecture takes advantage of state of the art capabilities to produce a Web based system to carry engineering design into the future. To illustrate deployment of the architecture, a case study for implementing advanced multidisciplinary design optimization processes such as Bi-Level Integrated System Synthesis is discussed. Another example for rolling-out a design process for Design for Six Sigma is also described. Each example explains how an organization can effectively infuse engineering practice with new design methods and retain the knowledge over time.

Woyak, Scott

Approximate optimal guidance for the advanced launch system

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

Feeley, T. S.

An approach to optimal guidance of an advanced launch vehicle concept

An approximate solution for the maximum payload trajectory of a two-stage launch vehicle using a regular perturbation technique is presented. A zero-order solution for a two-stage vehicle based on a flat-earth approximation and negligible atmospheric effects is obtained in closed form. High-order correction terms are obtained from the solution of nonhomogeneous, first-order linear differential equations by quadrature. This promises the capability for an onboard optimal guidance law implementation.

Leung, Martin S.

Optimal 3D Viewing with Adaptive Stereo Displays for Advanced Telemanipulation

A method of optimal 3D viewing based on adaptive displays of stereo images is presented for advanced telemanipulation. The method provides the viewer with the capability of accurately observing a virtual 3D object or local scene of his/her choice with minimum distortion.

3D viewing advanced telemanipulation telemanipulat

Orbit Transfer Vehicle Engine Study. Phase A, extension 1: Advanced expander cycle engine optimization

The performance optimization of expander cycle engines at vacuum thrust levels of 10K, 15K, and 20K lb is discussed. The optimization is conducted for a maximum engine length with an extendible nozzle in the retracted position of 60 inches and an engine mixture ratio of 6.0:1. The thrust chamber geometry and cycle analyses are documented. In addition, the sensitivity of a recommended baseline expander cycle to component performance variations is determined and chilldown/start propellant consumptions are estimated.

Mellish, J. A.

Advanced air revitalization for optimized crew and plant environments

The Hybrid Air Revitalization System (HARS) closed ecosystem concept presented encompasses electrochemical CO2 and O2 separators, in conjunction with a mechanical condenser/separator for maintaining CO2, O2, and humidity levels in crew and plant habitats at optimal conditions. HARS requires no expendables, and allows flexible process control on the bases of electrochemical cell current, temperature, and airflow rate variations. HARS capacity can be easily increased through the incorporation of additional chemical cells. Detailed system flowcharts are provided.

Lee, M. G.

Recent advances in integrated multidisciplinary optimization of rotorcraft

A joint activity involving NASA and Army researchers at NASA LaRC to develop optimization procedures to improve the rotor blade design process by integrating appropriate disciplines and accounting for all of the important interactions among the disciplines is described. The disciplines involved include rotor aerodynamics, rotor dynamics, rotor structures, airframe dynamics, and acoustics. The work is focused on combining these five key disciplines in an optimization procedure capable of designing a rotor system to satisfy multidisciplinary design requirements. Fundamental to the plan is a three-phased approach. In phase 1, the disciplines of blade dynamics, blade aerodynamics, and blade structure are closely coupled while acoustics and airframe dynamics are decoupled and are accounted for as effective constraints on the design for the first three disciplines. In phase 2, acoustics is integrated with the first three disciplines. Finally, in phase 3, airframe dynamics is integrated with the other four disciplines. Representative results from work performed to date are described. These include optimal placement of tuning masses for reduction of blade vibratory shear forces, integrated aerodynamic/dynamic optimization, and integrated aerodynamic/dynamic/structural optimization. Examples of validating procedures are described.

Adelman, Howard M.