Extension of modern control system theory Final report
Analysis and synthesis techniques for linear systems and methods of minimizing sensitivity of optimal control systems to large parameter variations
Dangelo, H.↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Optimal time invariant output feedback controllers, volume 1 Final report, 4 Nov. 1969 - 4 Apr. 1970
Determining optimal time-invariant output feedback controllers for linear dynamic systems
Mc Brinn, D. E.↗
Relative control effectiveness technique with application to airplane control coordination
A method to select optimal combinations of the control variables of a linear system is reported. The combinations are chosen so that the control channels have their principal influences on selected fundamental modes of the system. A series of algebraic maximization problems is used to maximize the effects of the control channels on selected modes while simultaneously minimizing the effects on the remaining modes. The method is applied to the lateral and directional control of a linearized airplane model having ailerons, a rudder, and differential tail surfaces. Integration of these control eliminates oscillations present in the roll rate for a step lateral-control input and improves the sideslip response with reduced rolling motions for a step directional-control input. Inclusion of thrust-vectoring engine nozzles improves the roll rate capability of the airplane.
Lallman, F. J.↗
Singular optimal control and the identically non-regular problem in the calculus of variations
A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.
Menon, P. K. A.↗
Integrated structure/control design - Present methodology and future opportunities
Attention is given to current methodology applied to the integration of the optimal design process for structures and controls. Multilevel linear decomposition techniques proved to be most effective in organizing the computational efforts necessary for ISCD (integrated structures and control design) tasks. With the development of large orbiting space structures and actively controlled, high performance aircraft, there will be more situations in which this concept can be applied.
Weisshaar, T. A.↗
Approximations For Controls Of Hereditary Systems
Convergence properties of controls, trajectories, and feedback kernels analyzed. Report discusses use of factorization techniques to approximate optimal feedback gains in finite-time, linear-regulator/quadratic-cost-function problem of system governed by retarded-functional-difference equations RFDE's with control delays. Presents approach to factorization based on discretization of state penalty leading to simple structure for feedback control law.
Milman, Mark H.↗
Frequency domain state-space system identification
An algorithm for identifying state-space models from frequency response data of linear systems is presented. A matrix-fraction description of the transfer function is employed to curve-fit the frequency response data, using the least-squares method. The parameters of the matrix-fraction representation are then used to construct the Markov parameters of the system. Finally, state-space models are obtained through the Eigensystem Realization Algorithm using Markov parameters. The main advantage of this approach is that the curve-fitting and the Markov parameter construction are linear problems which avoid the difficulties of nonlinear optimization of other approaches. Another advantage is that it avoids windowing distortions associated with other frequency domain methods.
Chen, Chung-Wen↗
Small Body GN&C Research Report: A Guidance and Control Technique for Small-Body Proximity Operations with Guaranteed Guidance Resolvability and Required Thruster Silent Time
The guidance and control (G&C) algorithms for enabling small-body proximity operations are developed by using a model predictive control approach along with a convexification of the governing dynamics, control constraints, and trajectory/state constraints. The open-loop guidance is solved ahead of time or in a resolvable, real-time manner through the use of PWG (Pseudo Way-point Generation), a technique developed in this research. The PWG scheme ensures required thruster silent times during trajectory maneuvers. The feedback control is implemented to track the PWG trajectories in a manner that guarantees the resolvability for the open-loop problem, enabling the ability to update the G&C in a model-predictive manner. The schemes incorporate gravity models and thruster ring times into discrete dynamics that are solved as a optimal control problem to minimize fuel consumption or thruster energy expenditure. The optimal control problem is cast as an LMI (Linear Matrix Inequality) and then solved through Semi-Definite Programming techniques in a computationally efficient manner that provides convergence and constraint guarantees.
guidance and control (G&C)↗
Exit Presentation -- Maintaining Balance
This slide presentation reviews the projects which the author engaged in during an internship at Johnson Space Center. Project 1 was involved with Stochastic Resonance (SR). Stochastic resonance is a phenomenon in which the response of a non-linear system to a weak input signal is optimized by the presence of a particular non-zero level of noise. The goal of this project was to develop a countermeasure for sensorimotor disturbances that are experienced after long duration space flight. The second project was a pilot study that was to examine how adaptation to a novel functional task was affected by postural disturbance.
Heap, Erin↗
A Linear Programming Approach to the Development of Contrail Reduction Strategies Satisfying Operationally Feasible Constraints
A class of strategies has been proposed to reduce contrail formation in the United States airspace. A 3D grid based on weather data and the cruising altitude level of aircraft is adjusted to avoid the persistent contrail potential area with the consideration to fuel-efficiency. In this paper, the authors introduce a contrail avoidance strategy on 3D grid by considering additional operationally feasible constraints from an air traffic controller's aspect. First, shifting too many aircraft to the same cruising level will make the miles-in-trail at this level smaller than the safety separation threshold. Furthermore, the high density of aircraft at one cruising level may exceed the workload for the traffic controller. Therefore, in our new model we restrict the number of total aircraft at each level. Second, the aircraft count variation for successive intervals cannot be too drastic since the workload to manage climbing/descending aircraft is much larger than managing cruising aircraft. The contrail reduction is formulated as an integer-programming problem and the problem is shown to have the property of total unimodularity. Solving the corresponding relaxed linear programming with the simplex method provides an optimal and integral solution to the problem. Simulation results are provided to illustrate the methodology.
Wei, Peng↗
A Numerical Testbed for Remote Sensing of Aerosols, and its Demonstration for Evaluating Retrieval Synergy from a Geostationary Satellite Constellation of GEO-CAPE and GOES-R
We present a numerical testbed for remote sensing of aerosols, together with a demonstration for evaluating retrieval synergy from a geostationary satellite constellation. The testbed combines inverse (optimal-estimation) software with a forward model containing linearized code for computing particle scattering (for both spherical and non-spherical particles), a kernel-based (land and ocean) surface bi-directional reflectance facility, and a linearized radiative transfer model for polarized radiance. Calculation of gas absorption spectra uses the HITRAN (HIgh-resolution TRANsmission molecular absorption) database of spectroscopic line parameters and other trace species cross-sections. The outputs of the testbed include not only the Stokes 4-vector elements and their sensitivities (Jacobians) with respect to the aerosol single scattering and physical parameters (such as size and shape parameters, refractive index, and plume height), but also DFS (Degree of Freedom for Signal) values for retrieval of these parameters. This testbed can be used as a tool to provide an objective assessment of aerosol information content that can be retrieved for any constellation of (planned or real) satellite sensors and for any combination of algorithm design factors (in terms of wavelengths, viewing angles, radiance and/or polarization to be measured or used). We summarize the components of the testbed, including the derivation and validation of analytical formulae for Jacobian calculations. Benchmark calculations from the forward model are documented. In the context of NASA's Decadal Survey Mission GEOCAPE (GEOstationary Coastal and Air Pollution Events), we demonstrate the use of the testbed to conduct a feasibility study of using polarization measurements in and around the O2 A band for the retrieval of aerosol height information from space, as well as an to assess potential improvement in the retrieval of aerosol fine and coarse mode aerosol optical depth (AOD) through the synergic use of two future geostationary satellites, GOES-R (Geostationary Operational Environmental Satellite R-series) and TEMPO (Tropospheric Emissions: Monitoring of Pollution). Strong synergy between GEOS-R and TEMPO are found especially in their characterization of surface bi-directional reflectance, and thereby, can potentially improve the AOD retrieval to the accuracy required by GEO-CAPE.
Aerosols↗
Multi-Robot Assembly Scheduling for the Lunar Crater Radio Telescope on the Far-Side of the Moon
The Lunar Crater Radio Telescope (LCRT) is a pro- posed ultra-long-wavelength radio telescope to be constructed on the far side of the moon. The proposed telescope will be constructed by deploying a 1km wire mesh in a 3-5km crater using a team of wall-climbing DuAxel robots. In this work, we consider the problem of generating minimum-time assembly sequences for LCRT, using realistic models of travel speed and lighting. Specifically, we pose the assembly sequencing problem as a mixed-integer linear program (MILP), which we solve to global optimality using commercial solvers. We present methods for modeling time-varying travel and assembly times, based on variable lighting conditions (including crater shadowing), and show how such time-varying parameters can be incorporated into the MILP. Finally, we present numerical studies of our method, showing how makespan varies with the number of assembly robots.
Schwager, Mac↗
Evaluating Nationwide Supply Chain for Circularity of PET and Olefin Plastics
PET (Polyethylene Terephthalate, #1) and olefin plastics including HDPE (High Density Polyethylene, #2), LDPE/LLDPE (Low Density/Linear Low-Density Polyethylene, #4) and PP (Polypropylene, #5) together comprise nearly 80% of the U.S. plastic market. Due to their high market share and extensive application in packaging these polymers have better potential for circularity than other polymer types. To understand the potential of future scenarios with higher recycling rates, supply chain scenarios for PET and olefin plastic packaging need to be analyzed with increased availability and collection of plastics. Currently there exists a knowledge gap to understand the circular supply chain on a national level. Performing a nationwide analysis introduces certain challenges such as variability in the plastic mix of the recycling stream in different municipalities, lack of collection of some types of plastics, regional differences in cost and estimating a national supply curve based on state level access rate and participation rate. Currently, a limited number of Plastic Reclaimers recycle the nation’s collected plastic involving transportation over long distances surpassing state boundaries. Modeling a nationwide scenario instead of regional/state based scenario will facilitate transportation beyond state boundaries for the development of a circular economy. A Mixed-integer Linear Programming model was developed, to identify the optimal location and capacity of the Material Recovery Facilities (MRFs) nationwide subject to maximizing the profit margin of the industrial entities within the model. We considered three different scenarios including the base case scenario (S1) collecting 2.27 million metric tons/year as well as two additional scenarios with available plastic supply of 1.8 times (S2) and 2.2 times (S3) of the base case scenario. The model identified 166, 275 and 319 counties as potential MRF locations for scenarios S1, S2 and S3 respectively. Compared to the existing number of counties having MRFs in the US, the model results indicated a reduction of 38% of MRFs for S1. For S2 and S3, the number of counties with MRFs increased 3% and 20% respectively compared to counties currently with MRFs. The average profit remains constant between $180-$181/ton regardless of the increased plastic collection.
54 - ENVIRONMENTAL SCIENCES/GLOBAL CLIMATE CHANGE ↗
Online Primal-Dual Methods With Measurement Feedback for Time-Varying Convex Optimization
This paper addresses the design and analysis of feedback-based online algorithms to control systems or networked systems based on performance objectives and engineering constraints that may evolve over time. The emerging timevarying convex optimization formalism is leveraged to model optimal operational trajectories of the systems, as well as explicit local and network-level operational constraints. Departing from existing batch and feed-forward optimization approaches, the design of the algorithms capitalizes on an online implementation of primal-dual projected-gradient methods; the gradient steps are, however, suitably modified to accommodate feedback from the system in the form of measurements - hence, the term 'online optimization with feedback.' By virtue of this approach, the resultant algorithms can cope with model mismatches in the algebraic representation of the system states and outputs, they avoid pervasive measurements of exogenous inputs, and they naturally lend themselves to a distributed implementation. Under suitable assumptions, analytical convergence claims are established in terms of dynamic regret. Furthermore, when the synthesis of the feedback-based online algorithms is based on a regularized Lagrangian function, Q-linear convergence to solutions of the time-varying optimization problem is shown.
97 MATHEMATICS AND COMPUTING↗
Optimization and guidance of penetration landing trajectories in a windshear
The optimization and guidance of penetration landing trajectories in a windshear are considered. It is assumed that the aircraft is controlled by the angle of attack and the power setting. For the optimal trajectory, the performance index being minimized measures the deviation of the flight trajectory from the nominal trajectory. In turn, the nominal trajectory includes two parts: the approach part (nominal glide slope constant) and the flare part (nominal glide slope varying linearly with the horizontal distance). Numerical results show that the optimal trajectory deviates somewhat from the nominal trajectory in the shear region. A guidance scheme is developed to approximate the optimal trajectory. The angle of attack is determined by the windshear intensity, the absolute path inclination, and the glide slope angle, while the power setting is determined by the windshear intensity and the velocity. Numerical results indicate that the guidance trajectory is close to the optimal trajectory.
Miele, A.↗
A Linear Programming Approach to Backtracking for Single-Axis Trackers on Rolling Terrain
In this article, we present a computationally efficient method for determining optimal backtracking rotations for single-axis solar trackers on nonuniform terrain. The method allows for ganged tracking, mechanical rotation constraints, uneven row spacing, and arbitrary maximum allowable shaded fractions (to enable “fractional backtracking”). As with previous 2-D approaches, the method is suitable for terrain that varies in the transverse direction with respect to the rotation axis of the trackers. The novelty of the method lies in formulating the problem of shade avoidance as a linear problem, which is achieved by using the row interception width as the optimization variable instead of rotation angles. Formulating backtracking as a linear problem enables the use of extremely efficient linear programming algorithms, making the method highly scalable, requiring less than 1 min to compute optimal rotation schedules for hundreds of trackers. It also produces more effective backtracking rotations, reducing the frequency of shading by 4× and improving system energy output by 1%–2%.
Optimization↗
Parameter estimation of the vibrational model for the SCOLE experimental facility
The objective of this study is to experimentally determine an empirical model of the vibrational dynamics of the Spacecraft COntrol Laboratory Experiment (SCOLE) facility. The first two flexible modes of this test article are identified using a linear least-square identification procedure and the data utilized for this procedure are obtained by exciting the structure from a quiescent state with torque wheels. The time history data of rate gyro sensors and accelerometers due to excitation and after excitation in terms of free-decay are used in the parameter estimation of the vibrational model. The free-decay portion of the data is analyzed using the Discrete Fourier transform to determine the optimal model order to use in modelling the response. Linear least-square analysis is then used to select the parameters that best fit the output of an Autoregressive (AR) model to the data. The control effectiveness of the torque wheels is then determined using the excitation portion of the test data, again using linear least squares.
Crotts, B. D.↗
Optimal Equilibrium Selection of Price-Maker Agents in Performance-Based Regulation Market
This paper analyzes the oligopolistic equilibrium of multiple price-maker agents in performance-based regulation (PBR) markets. In these markets, there are price-maker agents representing some frequency regulation (FR) providers and a number of independent price-taker FR providers. An equilibrium problem with equilibrium constraints (EPEC) model is employed in this paper to study the equilibria of a PBR market in the presence of price-maker agents and pricetaker FR providers. Due to the incorporation of the FR providers' dynamics, the proposed model is reformulated as a mixed-integer linear programming (MILP) problem over innovative mathematical techniques. An optimal equilibrium point is also selected for the market, where none of the agents is unique deviator and the dynamic performance of power system is improved simultaneously. The effectiveness of proposed optimal equilibrium point is evaluated in the numerical results section by comparing the outputs with conventional optimal dispatches of the FR providers.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗