Stability robustness improvement using constrained optimization techniques
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Mukhopadhyay, V.↗
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Results for “robust optimization”
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Designing robust control laws using genetic algorithms
The purpose of this research is to create a method of finding practical, robust control laws. The robustness of a controller is judged by Stochastic Robustness metrics and the level of robustness is optimized by searching for design parameters that minimize a robustness cost function.
Marrison, Chris↗
Robust eigenstructure assignment by a projection method - Applications using multiple optimization criteria
A methodology for robust eigenstructure assignment for multivariable feedback systems is presented. The algorithm is based upon a pole placement technique using projections onto subspaces of admissible eigenvectors. New ideas are introduced to generate target (desired) sets of unitary eigenvectors and determine optimal feasible eigenvectors in a least-square sense. Useful connections are established between the pole-placement by independent modal space control and the method introduced in this paper. A multicriterion optimization algorithm is also presented, which takes efficient advantage of the present eigenstructure assignment method. These developments show significant improvement over an earlier version of this algorithm in both computational cost and accuracy. This optimization process appears to be numerically robust and suitable for high-dimensional multicriterion optimizations; it is especially attractive for computer-aided design of control systems.
Rew, D. W.↗
Robustness, generality and efficiency of optimization algorithms in practical applications
The theoretical foundations of two approaches, sequential quadratic programming (SQP) and optimality criteria (OC), are analyzed and compared, with emphasis on the critical importance of parameters such as accuracy, generality, robustness, efficiency, and ease of use in large scale structural optimization. A simplified fighter wing and active control of space structures are considered with other example problems. When applied to general system identification problems, the OC methods are shown to lose simplicity and demonstrate lack of generality, accuracy and robustness. It is concluded that the SQP method with a potential constraint strategy is a better choice as compared to the currently prevalent mathematical programming and OC approaches.
Thanedar, P. B.↗
Trajectory optimization for the National Aerospace Plane
The primary objective of this research is to develop an efficient and robust trajectory optimization tool for the optimal ascent problem of the National Aerospace Plane (NASP). This report is organized in the following order to summarize the complete work: Section two states the formulation and models of the trajectory optimization problem. An inverse dynamics approach to the problem is introduced in Section three. Optimal trajectories corresponding to various conditions and performance parameters are presented in Section four. A midcourse nonlinear feedback controller is developed in Section five. Section six demonstrates the performance of the inverse dynamics approach and midcourse controller during disturbances. Section seven discusses rocket assisted ascent which may be beneficial when orbital altitude is high. Finally, Section eight recommends areas of future research.
Lu, Ping↗
An optimization program based on the method of feasible directions: Theory and users guide
The theory and user instructions for an optimization code based on the method of feasible directions are presented. The code was written for wide distribution and ease of attachment to other simulation software. Although the theory of the method of feasible direction was developed in the 1960's, many considerations are involved in its actual implementation as a computer code. Included in the code are a number of features to improve robustness in optimization. The search direction is obtained by solving a quadratic program using an interior method based on Karmarkar's algorithm. The theory is discussed, focusing on the important and often overlooked role played by the various parameters guiding the iterations within the program. Also discussed is a robust approach for handling infeasible starting points. The code was validated by solving a variety of structural optimization test problems that have known solutions obtained by other optimization codes. It has been observed that this code is accurate and robust: it has solved a variety of problems from different starting points. However, the code is inefficient in that it takes considerable CPU time as compared with certain other available codes. Further work is required to improve its efficiency while retaining its robustness.
Ashok D. Belegundu↗
Guidance, Navigation, and Control System Design in a Mass Reduction Exercise
Early Orion GN&C system designs optimized for robustness, simplicity, and utilization of commercially available components. During the System Definition Review (SDR), all subsystems on Orion were asked to re-optimize with component mass and steady state power as primary design metrics. The objective was to create a mass reserve in the Orion point of departure vehicle design prior to beginning the PDR analysis cycle. The Orion GN&C subsystem team transitioned from a philosophy of absolute 2 fault tolerance for crew safety and 1 fault tolerance for mission success to an approach of 1 fault tolerance for crew safety and risk based redundancy to meet probability allocations of loss of mission and loss of crew. This paper will discuss the analyses, rationale, and end results of this activity regarding Orion navigation sensor hardware, control effectors, and trajectory design.
Crain, Timothy↗
Robust control of systems with real parameter uncertainty and unmodelled dynamics
During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.
Chang, Bor-Chin↗
Rocket Design for the Future
The focus of the AA MDO team is to reduce product development cost through the capture and automation of best design and analysis practices and through increasing the availability of low-cost, high-fidelity analysis. Implementation of robust designs reduces costs associated with the Test-Fall-Fix cycle. RD is currently focusing on several technologies to improve the design process, including optimization and robust design, expert and rule-based systems, and collaborative technologies.
Follett, William W.↗
Design optimization for cost and quality: The robust design approach
Designing reliable, low cost, and operable space systems has become the key to future space operations. Designing high quality space systems at low cost is an economic and technological challenge to the designer. A systematic and efficient way to meet this challenge is a new method of design optimization for performance, quality, and cost, called Robust Design. Robust Design is an approach for design optimization. It consists of: making system performance insensitive to material and subsystem variation, thus allowing the use of less costly materials and components; making designs less sensitive to the variations in the operating environment, thus improving reliability and reducing operating costs; and using a new structured development process so that engineering time is used most productively. The objective in Robust Design is to select the best combination of controllable design parameters so that the system is most robust to uncontrollable noise factors. The robust design methodology uses a mathematical tool called an orthogonal array, from design of experiments theory, to study a large number of decision variables with a significantly small number of experiments. Robust design also uses a statistical measure of performance, called a signal-to-noise ratio, from electrical control theory, to evaluate the level of performance and the effect of noise factors. The purpose is to investigate the Robust Design methodology for improving quality and cost, demonstrate its application by the use of an example, and suggest its use as an integral part of space system design process.
Unal, Resit↗
Robust Design Under Uncertainty of Hypersonic Inlets
The objective of this work is to optimize scramjet inlet designs under uncertainty at multiple fidelity levels. Optimizations are performed for both deterministic and stochastic conditions. For stochastic conditions, robust design is used to minimize the variance in system performance in addition to optimizing mean system performance. Uncertainty quantification is performed using non-intrusive polynomial chaos. Comparisons are made between low-fidelity analysis and high-fidelity analysis, as well as deterministic optimization and robust optimization. Results indicate that the general design trend of previous inlet optimization techniques is recovered for the external compression portion of an inlet. For the internal compression portion of an inlet, when viscous effects become more significant and boundary layer separation becomes more likely, the optimal trend departs from previous results. Multifidelity uncertainty quantification methods are found to substantially reduce the computation time of robust design while obtaining results that nearly match those of high-fidelity analysis. Robust optimization is found to decrease the standard deviation of throat Mach number by up to 40% compared to deterministic optimization. Changes in the design variables and total turning that lead to robust scramjet inlets are identified and linked back to fundamental physical principles through the theta-beta-Mach function.
Hypersonic↗
Thermoplastic Matrix Composite Design for Cryotanks Using Multiscale Modeling and Bayesian Optimization
Designing lightweight, robust cryogenic storage tanks is critical for future launch vehicles, in-space propellant storage, and hydrogen powered aircraft. This work presents a multiscale modeling and Bayesian optimization framework for the design of thermoplastic matrix composite cryotanks. Molecular dynamics simulations are first used to determine temperature-dependent constituent properties for candidate thermoplastic matrices, which are homogenized to the lamina scale using NASA’s Multiscale Analysis Tool (NASMAT). These lamina properties, in combination with laminate family generation rules, are evaluated in HyperX structural optimization software to identify stacking sequences that meet all cryogenic load requirements. A Bayesian optimization framework is applied, with HyperX in the loop (via the HyperX API) to efficiently search across material and laminate design variables, yielding an optimized cryotank configuration with significant reductions in design cycle time compared to exhaustive search approaches.
thermoplastics↗
Optimized Trajectory Correction Burn Placement for NRHO Orbit Maintenance
NASA's future Artemis missions plan to utilize a near rectilinear halo orbit (NRHO) in the lunar vicinity to facilitate access to the lunar surface and place other critical assets to support human exploration. This exploration architecture requires a vehicle to remain in the NRHO for long periods of time ranging from several days, to weeks, to months, and even years. Consequently, periodic orbit maintenance burns become essential to ensure the spacecraft follows the desired reference trajectory in an efficient yet effective manner despite crew activity, navigation uncertainty, maneuver execution errors, disturbance accelerations, orbit insertion dispersions, and other system limitations. This work introduces a targeting algorithm that can be utilized to analyze a variety of targeting constraints and parameters that maximizes overall performance. Techniques associated with robust trajectory optimization are used to identify the optimized number and placement for NRHO trajectory correction (NTC) burns that accounts for the mission schedule, both a primary and backup navigation system, targeting strategies and burn plan configurations, vehicle venting, thruster selection, and integrated GN\&C performance. A notional scenario extracted from the NASA Artemis III mission is used to motivate and demonstrate these concepts and performance results.
Linear Covariance Analysis↗
Optimized Trajectory Correction Burn Placement for the NASA Artemis II Mission
The NASA Artemis II mission represents the first time humans plan to return to the lunar vicinity in over 50 years with a crew traveling to the Moon in the Orion spacecraft on a free return trajectory. This first crewed mission of the Artemis program will evaluate human-rated elements of Orion in preparation to sending astronauts to the lunar surface. The selected free-return cislunar trajectory profile that is reminiscent of the Apollo 8 mission that nominally requires no additional translational burns following the trans-lunar injection (TLI) burn. Due to crew activity, maneuver execution errors, navigation uncertainty, orbit insertion errors, disturbance accelerations, and other system limitations; periodic trajectory corrections burns are necessary to ensure proper entry interface (EI) conditions are satisfied for a safe return to Earth. Robust trajectory optimization techniques are utilized to determine the optimized placements for the Artemis II trajectory correction burns that accounts for the crew schedule, both the primary and backup navigation systems, targeting strategies and burn plan configurations, spacecraft venting, thruster selection, and the integrated GN&C performance.
Linear Covariance Analysis↗
A Robust Initialization Scheme for a Lateral Trajectory Optimization Problem with Time of Arrival Windows
We present a robust initialization scheme that estimates parameter values for the numerical solution of a two-point boundary value problem. The two-point boundary value problem formulation stems from the optimization of a cost functional subject to the dynamics of a simplified lateral aircraft model and other constraints. Leveraging regular perturbation methods, initial parameter estimates are analytically determined and used to initialize a gradient descent optimization routine which is shown to rapidly converge over a range of initial aircraft positions and heading angles. Additionally, the velocity of the aircraft is optimized to ensure the trajectory of the aircraft terminates within a desired region in both time and space.
lateral trajectory optimization↗
Autonomous frequency domain identification: Theory and experiment
The analysis, design, and on-orbit tuning of robust controllers require more information about the plant than simply a nominal estimate of the plant transfer function. Information is also required concerning the uncertainty in the nominal estimate, or more generally, the identification of a model set within which the true plant is known to lie. The identification methodology that was developed and experimentally demonstrated makes use of a simple but useful characterization of the model uncertainty based on the output error. This is a characterization of the additive uncertainty in the plant model, which has found considerable use in many robust control analysis and synthesis techniques. The identification process is initiated by a stochastic input u which is applied to the plant p giving rise to the output. Spectral estimation (h = P sub uy/P sub uu) is used as an estimate of p and the model order is estimated using the produce moment matrix (PMM) method. A parametric model unit direction vector p is then determined by curve fitting the spectral estimate to a rational transfer function. The additive uncertainty delta sub m = p - unit direction vector p is then estimated by the cross spectral estimate delta = P sub ue/P sub uu where e = y - unit direction vectory y is the output error, and unit direction vector y = unit direction vector pu is the computed output of the parametric model subjected to the actual input u. The experimental results demonstrate the curve fitting algorithm produces the reduced-order plant model which minimizes the additive uncertainty. The nominal transfer function estimate unit direction vector p and the estimate delta of the additive uncertainty delta sub m are subsequently available to be used for optimization of robust controller performance and stability.
Yam, Yeung↗
Description of Selected Algorithms and Implementation Details of a Concept-Demonstration Aircraft VOrtex Spacing System (AVOSS)
A ground-based system has been developed to demonstrate the feasibility of automating the process of collecting relevant weather data, predicting wake vortex behavior from a data base of aircraft, prescribing safe wake vortex spacing criteria, estimating system benefit, and comparing predicted and observed wake vortex behavior. This report describes many of the system algorithms, features, limitations, and lessons learned, as well as suggested system improvements. The system has demonstrated concept feasibility and the potential for airport benefit. Significant opportunities exist however for improved system robustness and optimization. A condensed version of the development lab book is provided along with samples of key input and output file types. This report is intended to document the technical development process and system architecture, and to augment archived internal documents that provide detailed descriptions of software and file formats.
Hinton, David A.↗
Multi-Sensor Registration of Earth Remotely Sensed Imagery
Assuming that approximate registration is given within a few pixels by a systematic correction system, we develop automatic image registration methods for multi-sensor data with the goal of achieving sub-pixel accuracy. Automatic image registration is usually defined by three steps; feature extraction, feature matching, and data resampling or fusion. Our previous work focused on image correlation methods based on the use of different features. In this paper, we study different feature matching techniques and present five algorithms where the features are either original gray levels or wavelet-like features, and the feature matching is based on gradient descent optimization, statistical robust matching, and mutual information. These algorithms are tested and compared on several multi-sensor datasets covering one of the EOS Core Sites, the Konza Prairie in Kansas, from four different sensors: IKONOS (4m), Landsat-7/ETM+ (30m), MODIS (500m), and SeaWIFS (1000m).
LeMoigne, Jacqueline↗