mystic: tools for AI, UQ, ML, model validation, and robust design under uncertainty
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McKerns, Michael↗
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Advanced Design Methodology for Robust Aircraft Sizing and Synthesis
Contract efforts are focused on refining the Robust Design Methodology for Conceptual Aircraft Design. Robust Design Simulation (RDS) was developed earlier as a potential solution to the need to do rapid trade-offs while accounting for risk, conflict, and uncertainty. The core of the simulation revolved around Response Surface Equations as approximations of bounded design spaces. An ongoing investigation is concerned with the advantages of using Neural Networks in conceptual design. Thought was also given to the development of systematic way to choose or create a baseline configuration based on specific mission requirements. Expert system was developed, which selects aerodynamics, performance and weights model from several configurations based on the user's mission requirements for subsonic civil transport. The research has also resulted in a step-by-step illustration on how to use the AMV method for distribution generation and the search for robust design solutions to multivariate constrained problems.
Mavris, Dimitri N.↗
Robust controller design for structures with displacement sensors
The passivity theorem may be used to design robust controllers for structures with positive transfer functions. The authors obtain a similar result for systems with displacement sensors. In order to illustrate the ideas discussed, a specific second-order dynamic system is considered.
Morris, K. A.↗
Robust Crossfeed Design for Hovering Rotorcraft
Control law design for rotorcraft fly-by-wire systems normally attempts to decouple angular responses using fixed-gain crossfeeds. This approach can lead to poor decoupling over the frequency range of pilot inputs and increase the load on the feedback loops. In order to improve the decoupling performance, dynamic crossfeeds may be adopted. Moreover, because of the large changes that occur in rotorcraft dynamics due to small changes about the nominal design condition, especially for near-hovering flight, the crossfeed design must be 'robust'. A new low-order matching method is presented here to design robust crossfeed compensators for multi-input, multi-output (MIMO) systems. The technique identifies degrees-of-freedom that can be decoupled using crossfeeds, given an anticipated set of parameter variations for the range of flight conditions of concern. Cross-coupling is then reduced for degrees-of-freedom that can use crossfeed compensation by minimizing off-axis response magnitude average and variance. Results are presented for the analysis of pitch, roll, yaw and heave coupling of the UH-60 Black Hawk helicopter in near-hovering flight. Robust crossfeeds are designed that show significant improvement in decoupling performance and robustness over nominal, single design point, compensators. The design method and results are presented in an easily used graphical format that lends significant physical insight to the design procedure. This plant pre-compensation technique is an appropriate preliminary step to the design of robust feedback control laws for rotorcraft.
Catapang, David R.↗
Design of robust line-of-sight pointing control system for the SCOLE configuration
Robust compensator design for attitude control of the Spacecraft Control Laboratory Experiment (SCOLE) configuration is considered. A loop-shaping procedure similar to that used in the LQG/LTR method is used to iteratively design the compensator. A satisfactory compensator is obtained by including the rigid modes and three elastic modes in the design model.
Joshi, S. M.↗
Using Design Capability Indices to Satisfy Ranged Sets of Design Requirements
For robust design it is desirable to allow the design requirements to vary within a certain range rather than setting point targets. This is particularly important during the early stages of design when little is known about the system and its requirements. Toward this end, design capability indices are developed in this paper to assess the capability of a family of designs, represented by a range of top-level design specifications, to satisfy a ranged set of design requirements. Design capability indices are based on process capability indices from statistical process control and provide a single objective, alternate approach to the use of Taguchi's signal-to- noise ratio which is often used for robust design. Successful implementation of design capability indices ensures that a family of designs conforms to a given ranged set of design requirements. To demonstrate an application and the usefulness of design capability indices, the design of a solar powered irrigation system is presented. Our focus in this paper is on the development and implementation of design capability indices as an alternate approach to the use of the signal-to-noise ratio and not on the results of the example problem, per se.
Chen, Wei↗
Robust control design for aerospace applications
Time-domain control design for stability robustness of linear systems with structured uncertainty is addressed. Upper bounds on the linear perturbation of an asymptotically stable linear system are obtained, making it possible to maintain stability by using the structural information of the uncertainty. A quantitative measure called the stability robustness index is introduced and used to design controllers for robust stability. The proposed state feedback control design algorithm can be used, for a given set of perturbations, to select the range of control effort for which the system is stability-robust. Conversely it can be used, for a given control effort, to determine the size of the tolerable perturbation. The algorithm is illustrated with examples from aircraft control and large-space-structure control problems.
Yedavalli, Rama K.↗
Robust crossfeed design for hovering rotorcraft
Control law design for rotorcraft fly-by-wire systems normally attempts to decouple angular responses using fixed-gain crossfeeds. This approach can lead to poor decoupling over the frequency range of pilot inputs and increase the load on the feedback loops. In order to improve the decoupling performance, dynamic crossfeeds may be adopted. Moreover, because of the large changes that occur in rotorcraft dynamics due to small changes about the nominal design condition, especially for near-hovering flight, the crossfeed design must be 'robust.' A new low-order matching method is presented here to design robost crossfeed compensators for multi-input, multi-output (MIMO) systems. The technique identifies degrees-of-freedom that can be decoupled using crossfeeds, given an anticipated set of parameter variations for the range of flight conditions of concern. Cross-coupling is then reduced for degrees-of-freedom that can use crossfeed compensation by minimizing off-axis response magnitude average and variance. Results are presented for the analysis of pitch, roll, yaw, and heave coupling of the UH-60 Black Hawk helicopter in near-hovering flight. Robust crossfeeds are designed that show significant improvement in decoupling performance and robustness over nominal, single design point, compensators. The design method and results are presented in an easily-used graphical format that lends significant physical insight to the design procedure. This plant pre-compensation technique is an appropriate preliminary step to the design of robust feedback control laws for rotorcraft.
Catapang, David R.↗
Designing for Damage: Robust Flight Control Design using Sliding Mode Techniques
A brief review of sliding model control is undertaken, with particular emphasis upon the effects of neglected parasitic dynamics. Sliding model control design is interpreted in the frequency domain. The inclusion of asymptotic observers and control 'hedging' is shown to reduce the effects of neglected parasitic dynamics. An investigation into the application of observer-based sliding mode control to the robust longitudinal control of a highly unstable is described. The sliding mode controller is shown to exhibit stability and performance robustness superior to that of a classical loop-shaped design when significant changes in vehicle and actuator dynamics are employed to model airframe damage.
Vetter, T. K.↗
Robust control design with real parameter uncertainty using absolute stability theory
The purpose of this thesis is to investigate an extension of mu theory for robust control design by considering systems with linear and nonlinear real parameter uncertainties. In the process, explicit connections are made between mixed mu and absolute stability theory. In particular, it is shown that the upper bounds for mixed mu are a generalization of results from absolute stability theory. Both state space and frequency domain criteria are developed for several nonlinearities and stability multipliers using the wealth of literature on absolute stability theory and the concepts of supply rates and storage functions. The state space conditions are expressed in terms of Riccati equations and parameter-dependent Lyapunov functions. For controller synthesis, these stability conditions are used to form an overbound of the H2 performance objective. A geometric interpretation of the equivalent frequency domain criteria in terms of off-axis circles clarifies the important role of the multiplier and shows that both the magnitude and phase of the uncertainty are considered. A numerical algorithm is developed to design robust controllers that minimize the bound on an H2 cost functional and satisfy an analysis test based on the Popov stability multiplier. The controller and multiplier coefficients are optimized simultaneously, which avoids the iteration and curve-fitting procedures required by the D-K procedure of mu synthesis. Several benchmark problems and experiments on the Middeck Active Control Experiment at M.I.T. demonstrate that these controllers achieve good robust performance and guaranteed stability bounds.
How, Jonathan P.↗
Penetrating transmission zeros in the design of robust servomechanism systems
In the design of a robust servomechanism system, it is well known that the system cannot track a reference signal whose frequency coincides with the transmission zeros of the system. This paper proposes a new design method for overcoming this difficulty. The controller to be used employs a sampler and holding device with exponential decay. It is shown that the transmission zeros of the discretized system can be shifted by changing the rate of the exponential decay of the holding device. Thus, it is possible to design a robust controller for the discretized system to track any reference signal of given frequency, even if the given frequency coincides with the transmission zeros of the original continuous-time system.
Wang, S. H.↗
Control design for robust stability in linear regulators: Application to aerospace flight control
Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.
Yedavalli, R. K.↗
Robust Control Design for Uncertain Nonlinear Dynamic Systems
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
Kenny, Sean P.↗
Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares
A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.
Dorobantu, Andrei↗
Robust multivariable controller design for flexible spacecraft
Large, flexible spacecraft are typically characterized by a large number of significant elastic modes with very small inherent damping, low, closely spaced natural frequencies, and the lack of accurate knowledge of the structural parameters. Summarized here is some recent research on the design of robust controllers for such spacecraft, which will maintain stability, and possible performance, despite these problems. Two types of controllers are considered, the first being the linear-quadratic-Gaussian-(LQG)-type. The second type utilizes output feedback using collocated sensors and actuators. The problem of designing robust LQG-type controllers using the frequency domain loop transfer recovery (LTR) method is considered, and the method is applied to a large antenna model. Analytical results regarding the regions of stability for LQG-type controllers in the presence of actuator nonlinearities are also presented. The results obtained for the large antenna indicate that the LQG/LTR method is a promising approach for control system design for flexible spacecraft. For the second type of controllers (collocated controllers), it is proved that the stability is maintained in the presence of certain commonly encountered nonlinearities and first-order actuator dynamics. These results indicate that collocated controllers are good candidates for robust control in situations where model errors are large.
Joshi, Suresh M.↗
Advances in robust flight design
Current launch vehicle trajectory design philosophies, generally based on maximizing payload capability, result in an expensive and time-consuming iteration in trajectory design for each mission. However, for a launch system that is not performance-driven, a flight design that is robust to variations in missions and provides single-engine-out capability can be highly cost-effective. This philosophy has led to the development of two flight design concepts to reduce recurring costs: standard trajectories and command multiplier steering. Preliminary analyses of these two concepts had proven the feasibility and showed encouraging results in applications to an Advanced Launch System vehicle. Recent progress has demonstrated the effective and efficient integration of the two concepts with minimal payload penalty.
Wong, Kelvin K.↗
Robust Optimization Design Algorithm for High-Frequency TWTs
Traveling-wave tubes (TWTs), such as the Ka-band (26-GHz) model recently developed for the Lunar Reconnaissance Orbiter, are essential as communication amplifiers in spacecraft for virtually all near- and deep-space missions. This innovation is a computational design algorithm that, for the first time, optimizes the efficiency and output power of a TWT while taking into account the effects of dimensional tolerance variations. Because they are primary power consumers and power generation is very expensive in space, much effort has been exerted over the last 30 years to increase the power efficiency of TWTs. However, at frequencies higher than about 60 GHz, efficiencies of TWTs are still quite low. A major reason is that at higher frequencies, dimensional tolerance variations from conventional micromachining techniques become relatively large with respect to the circuit dimensions. When this is the case, conventional design- optimization procedures, which ignore dimensional variations, provide inaccurate designs for which the actual amplifier performance substantially under-performs that of the design. Thus, this new, robust TWT optimization design algorithm was created to take account of and ameliorate the deleterious effects of dimensional variations and to increase efficiency, power, and yield of high-frequency TWTs. This design algorithm can help extend the use of TWTs into the terahertz frequency regime of 300-3000 GHz. Currently, these frequencies are under-utilized because of the lack of efficient amplifiers, thus this regime is known as the "terahertz gap." The development of an efficient terahertz TWT amplifier could enable breakthrough applications in space science molecular spectroscopy, remote sensing, nondestructive testing, high-resolution "through-the-wall" imaging, biomedical imaging, and detection of explosives and toxic biochemical agents.
Wilson, Jeffrey D.↗
Analytical redundancy and the design of robust failure detection systems
The Failure Detection and Identification (FDI) process is viewed as consisting of two stages: residual generation and decision making. It is argued that a robust FDI system can be achieved by designing a robust residual generation process. Analytical redundancy, the basis for residual generation, is characterized in terms of a parity space. Using the concept of parity relations, residuals can be generated in a number of ways and the design of a robust residual generation process can be formulated as a minimax optimization problem. An example is included to illustrate this design methodology. Previously announcedd in STAR as N83-20653
Chow, E. Y.↗