Numerical procedures for roll stability studies
Numerical procedure for performing roll stability analyses of Saturn space vehicles
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Numerical procedure for performing roll stability analyses of Saturn space vehicles
Abstract The numerical estimation of the position of the water table in unconfined aquifers is important for many practical applications. Its determination through observations or analytical methods is restricted to a few cases. Therefore, it is often estimated through numerical simulations, which may be affected by numerical artifacts and/or poor stability. We use MODFLOW to estimate the position of the water table for a seemingly simple example problem and demonstrate difficulties that can be faced when performing this kind of numerical simulation. We explain the causes for the numerical challenges that originate from the properties of the mathematical equations that must be solved. Based on the results of more than 600 steady‐state simulations, we show how the stability of the numerical solution can be affected by the values of physical parameters that define the problem (e.g., recharge rate, anisotropy ratio, and other parameters that control the numerical algorithm such as settings of the linear and nonlinear solution methods). Finally, we comment on some best practices to apply numerical simulations to estimate the water table position.
A line-of-sight performance criterion is derived for a proposed Controls Structures Interaction model, and its many uses in the control design process for fine pointing control are illustrated. A linearized line-of-sight (LOS) criterion is used for direct controller design and as a performance measure to judge different control methodologies. Numerical simulation results are shown where the three approaches: linear quadratic Gaussian theory, robust eigensystem assignment, and local velocity feedback are used for vibration control. Results indicate that the linear quadratic Gaussian controller, which incorporates a linearized LOS weighting matrix directly, yields good performance without wasting energy to control motions that have no influence on the LOS.
The computed torque control problem is examined for a robot arm with flexible, geared, joint drive systems which are typical in many industrial robots. The standard computed torque algorithm is not directly applicable to this class of manipulators because of the dynamics introduced by the joint drive system. The proposed approach to computed torque control combines a computed torque algorithm with torque controller at each joint. Three such control schemes are proposed. The first scheme uses the joint torque control system currently implemented on the robot arm and a novel form of the computed torque algorithm. The other two use the standard computed torque algorithm and a novel model following torque control system based on model following techniques. Standard tasks and performance indices are used to evaluate the performance of the controllers. Both numerical simulations and experiments are used in evaluation. The study shows that all three proposed systems lead to improved tracking performance over a conventional PD controller.
As space exploration expands, atmospheric descent requirements will tighten to improve landing accuracy to areas of interest. One way to meet higher landing accuracy requirements is by increasing vehicle maneuverability. This study explores the concept of manipulating a transpiration cooling scheme for entry capsules that could provide both active aerodynamic control as well as thermal protection for external surfaces. Numerical methods of fluid dynamics and heat transfer are presented to study the effectiveness of the concept in both thermal protection and entry vehicle attitude control. This effort works through development of an entry vehicle model at aeromaneuvering conditions with designated boundary activated for effects of transpiration cooling. Preliminary results show calculated values of heat flux and aerodynamic forces as a function of varying transpiration cooling flow rates. This contributes evidence of asymmetric cooling utilization as an additional mechanism for vehicle attitude control.
Numerical analysis and programming techniques for orbit determination
We address the problem of navigating a set of moving agents, e.g. automated guided vehicles, through a transportation network so as to bring each agent to its destination at a specified time. Each pair of agents is required to be separated by a minimal distance, generally agent-dependent, at all times. The speed range, initial position, required destination, and required time of arrival at destination for each agent are assumed provided. The movement of each agent is governed by a controlled differential equation (state equation). The problem consists in choosing for each agent a path and a control strategy so as to meet the constraints and reach the destination at the required time. This problem arises in various fields of transportation, including Air Traffic Management and train coordination, and in robotics. The main contribution of the paper is a model that allows to recast this problem as a decoupled collection of problems in classical optimal control and is easily generalized to the case when inertia cannot be neglected. Some qualitative insight into solution behavior is obtained using the Pontryagin Maximum Principle. Sample numerical solutions are computed using a numerical optimal control solver.
We address the problem of navigating a set (fleet) of aircraft in an aerial route network so as to bring each aircraft to its destination at a specified time and with minimal distance separation assured between all aircraft at all times. The speed range, initial position, required destination, and required time of arrival at destination for each aircraft are assumed provided. Each aircraft's movement is governed by a controlled differential equation (state equation). The problem consists in choosing for each aircraft a path in the route network and a control strategy so as to meet the constraints and reach the destination at the required time. The main contribution of the paper is a model that allows to recast this problem as a decoupled collection of problems in classical optimal control and is easily generalized to the case when inertia cannot be neglected. Some qualitative insight into solution behavior is obtained using the Pontryagin Maximum Principle. Sample numerical solutions are computed using a numerical optimal control solver. The proposed model is first step toward increasing the fidelity of continuous time control models of air traffic in a terminal airspace. The Pontryagin Maximum Principle implies the polygonal shape of those portions of the state trajectories away from those states in which one or more aircraft pair are at minimal separation. The model also confirms the intuition that, the narrower the allowed speed ranges of the aircraft, the smaller the space of optimal solutions, and that an instance of the optimal control problem may not have a solution at all (i.e., no control strategy that meets the separation requirement and other constraints).
This paper outlines the development of methods for the combined control-structure optimization of physical systems encountered in the technology of large space structures. The objectives of the approach taken in this paper is not to produce the 'best' optimized design, but rather to efficiently produce a family of design options so as to assist in early trade studies, typically before hard design constraints are imposed. The philosophy is that these are candidate designs to be passed on for further considerations, and their function is more to guide the development of the system design rather than to represent the ultimate product. A homotopy approach involving multi-objective functions is developed for this purpose. Analytical and numerical examples are also presented.
Predicting bulk behavior from microscale features constitutes a key objective in multiscale modeling research, often involving numerical models composed of finite elements that capture the diversity of constituent phases, shapes, and orientations within the material. The Grain2mesh toolbox allows the user to input unprocessed mesoscopic images for automatic segmentation, pre-processing, quality control, and numerical mesh generation. The numerical mesh generation incorporates Cubit routines to generate robust multi-phase mesh structure for use in computational mechanics solvers. The python classes developed contain detailed documentation and examples to support standard usage and case-specific alternative options.
To support the National Aeronautics and Space Administration’s (NASA) Space Launch System (SLS) rocket and the Orion capsule, designed to take humans back to the moon in 2024, Kennedy Space Center (KSC) has developed the Spaceport Command and Control System (SCCS) to monitor and control the launch. Within SCCS, the Launch Control System (LCS) is designed to allow console engineers to control and monitor the status of the launch and flight hardware, as well as issue commands to ground control systems and launch vehicles. The messaging software of LCS is responsible for handling the various data types that can be sent between the hardware and software components of the LCS. Since this system is interacting with numerous devices, controllers, and viewports in real time, the distribution of data across the system must be fast, but also reliable and accurate. To verify the accuracy and reliability of the system, developers on the project have created a set of tests to be performed that covers all operations allowed by the system. Given the extensive Application Programming Interface(API) provided by the messaging software, these unit tests are rather time-consuming and costly (in terms of man-hours) to perform. Therefore, an automated testing framework is used to perform supplemental tests automatically when updates are made to the code base.
In this paper, we develop a grid-interactive multi-zone building controller based on a deep reinforcement learning (RL) approach. The controller is designed to facilitate building operation during normal conditions and demand response events, while ensuring occupants comfort and energy efficiency. We leverage a continuous action space RL formulation, and devise a two-stage global-local RL training framework. In the first stage, a global fast policy search is performed using a gradient-free RL algorithm. In the second stage, a local fine-tuning is conducted using a policy gradient method. In contrast to the state-of-the-art model predictive control (MPC) approach, the proposed RL controller does not require complex computation during real-time operation and can adapt to nonlinear building models. We illustrate the controller performance numerically using a five-zone commercial building.
In this paper, we develop a grid-interactive multi-zone building controller based on a deep reinforcement learning (RL) approach. The controller is designed to facilitate building operation during normal conditions and demand response events, while ensuring occupants comfort and energy efficiency. We leverage a continuous action space RL formulation, and devise a two-stage global-local RL training framework. In the first stage, a global fast policy search is performed using a gradient-free RL algorithm. In the second stage, a local fine-tuning is conducted using a policy gradient method. In contrast to the state-of-the-art model predictive control (MPC) approach, the proposed RL controller does not require complex computation during real-time operation and can adapt to non-linear building models. We illustrate the controller performance numerically using a five-zone commercial building.
In this paper we present numerical solutions to several optimal control problems for an unsteady viscous flow. The main thrust of this work is devoted to simulation and control of an unsteady flow generated by a circular cylinder undergoing rotary motion. By treating the rotation rate as a control variable, we can formulate two optimal control problems and use a central difference/pseudospectral transform method to numerically compute the optimal control rates. Several types of rotations are considered as potential controls, and we show that a proper synchronization of forcing frequency with the natural vortex shedding frequency can greatly influence the flow. The results here indicate that using moving boundary controls for such systems may provide a feasible mechanism for flow control.
A linear time-varying aggregate traffic flow model can be used to develop Traffic Flow Management (tfm) strategies based on optimization algorithms. However, there are no methods available in the literature to translate these aggregate solutions into actions involving individual aircraft. This paper describes and implements a computationally efficient disaggregation algorithm, which converts an aggregate (flow-based) solution to a flight-specific control action. Numerical results generated by the optimization method and the disaggregation algorithm are presented and illustrated by applying them to generate TFM schedules for a typical day in the U.S. National Airspace System. The results show that the disaggregation algorithm generates control actions for individual flights while keeping the air traffic behavior very close to the optimal solution.
Thermal energy storage (TES) for a cooling plant is a crucial resource for load flexibility. Traditionally, simple, heuristic control approaches, such as the storage priority control which charges TES during the nighttime and discharges during the daytime, have been widely used in practice, and shown reasonable performance in the past benefiting both the grid and the end-users such as buildings and district energy systems. However, the increasing penetration of renewables changes the situation, exposing the grid to a growing duck curve, which encourages the consumption of more energy in the daytime, and volatile renewable generation which requires dynamic planning. The growing pressure of diminishing greenhouse gas emissions also increases the complexity of cooling TES plant operations as different control strategies may apply to optimize operations for energy cost or carbon emissions. This paper presents a model predictive control (MPC), site demonstration and evaluation results of optimal operation of a chiller plant, TES and behind-meter photovoltaics for a campus-level district cooling system. The MPC was formulated as a mixed-integer linear program for better numerical and control properties. Compared with baseline rule-based controls, the MPC results show reductions of the excess PV power by around 25%, of the greenhouse gas emission by 10%, and of peak electricity demand by 10%.
The NASA Numerical Propulsion System Simulation (NPSS) project is exploring the use of computer simulation to facilitate the design of new jet engines. Several key issues raised in this research are being examined in an NPSS-related research project: zooming, monitoring and control, and support for heterogeneity. The design of a simulation executive that addresses each of these issues is described. In this work, the strategy of zooming, which allows codes that model at different levels of fidelity to be integrated within a single simulation, is applied to the fan component of a turbofan propulsion system. A prototype monitoring and control system has been designed for this simulation to support experimentation with expert system techniques for active control of the simulation. An interconnection system provides a transparent means of connecting the heterogeneous systems that comprise the prototype.
The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.