Stability of single-loop nonlinear feedback systems.
Sufficient conditions of stability of single-loop nonlinear feedback systems
SYSTEM STABILITY↗
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Results for “nonlinear controls”
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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Control of spinning flexible spacecraft by modal synthesis
A procedure is presented for the active control of a spinning flexible spacecraft. Such a system exhibits gyroscopic effects. The design of the controller is based on modal decomposition of the gyroscopic system. This modal decoupling procedure leads to a control mechanism implemented in modular form, which represents a distinct computational advantage over the control of the coupled system. Design procedures are demonstrated for two types of control algorithms, linear and nonlinear. The first represents classical linear feedback approach, and the second represents an application of on-off control, both types made feasible by the modal decomposition scheme.
Meirovitch, L.↗
Control of spinning flexible spacecraft by modal synthesis
A procedure is presented for the active control of a spinning flexible spacecraft. Such a system exhibits gyroscopic effects. The design of the controller is based on modal decomposition of the gyroscopic system. This modal decoupling procedure leads to a control mechanism implemented in modular form, which represents a distinct computational advantage over the control of the coupled system. Design procedures are demonstrated for two types of control algorithms, linear and nonlinear. The first represents classical linear feedback approach and the second represents an application of on-off control, both types made feasible by the modal decomposition scheme.
Meirovitch, L.↗
Cancellation control law for lateral-directional dynamics of a supermaneuverable aircraft
Cancellation control laws are designed which reduce the high levels of lateral acceleration encountered during aggressive rolling maneuvers executed at high angle of attack. Two independent problem are examined. One is to reduce lateral acceleration at the mass center, while the other focuses on lateral acceleration at the pilot's station, located 7.0 m forward of the mass center. Both of these problems are challenging and somewhat different in their limitations. In each case the design is based on a linearization of the lateral-directional dynamics about a high angle of attack condition. The controllers incorporate dynamic inversion inner loops to provide control of stability-axis roll- and yaw-rates and then employ cancellation filters in both feed-forward and feed-back signal paths. The relative simplicity of the control laws should allow nonlinear generalizations to be devised. Although it is shown that lateral acceleration can be reduced substantially by such control laws, this is at the cost of slowed roll response, poor dutch-roll damping or a combination of the two.
Snell, Antony↗
Convex Optimization Guidance for Precision Landing on Titan
Precision landing is an anticipated technology for future interplanetary missions. Autonomous spacecraft Entry, Descent and Landing (EDL) on the surface of a planetary body with a degree of precision in the order of meters is highly challenging. In this paper, a successive convexification guidance algorithm is utilized to simulate autonomous precision landing sequences on Saturn’s moon Titan. Due to its unique geophysical features, studying the science of matter within Titan’s atmosphere and beneath its surface is one of NASA’s most important planetary science objectives. As part of the Space Exploration Technology Directorate, a parafoil is proposed for landing on Titan due to its cost effectiveness, ease of deployment, low mass compared to the prospective payload and capabilities of precise autonomous delivery. This paper focuses on path optimization and guidance law development for high-fidelity dynamics parafoil tuning in the dense and adverse wind atmosphere of Titan, defined as a nonlinear and nonconvex optimal control problem. The powerful successive convexification method is used to solve the problem accordingly. The algorithm is designed such that the converged solution adheres to the nonlinear dynamics and kinematics in accordance with the original formulation, while respecting the state and control constraints. The six-degree-of-freedom (6DoF) simulations results show that this robust method is suitable for autonomous interplanetary applications.
Mooij, Edwin↗
Automatic Control Of Length Of Welding Arc
Nonlinear relationships among current, voltage, and length stored in electronic memory. Conceptual microprocessor-based control subsystem maintains constant length of welding arc in gas/tungsten arc-welding system, even when welding current varied. Uses feedback of current and voltage from welding arc. Directs motor to set position of torch according to previously measured relationships among current, voltage, and length of arc. Signal paths marked "calibration" or "welding" used during those processes only. Other signal paths used during both processes. Control subsystem added to existing manual or automatic welding system equipped with automatic voltage control.
Iceland, William F.↗
A controllability-stabilizability result for the NASA-IEEE Spacecraft Control Laboratory Experiment (SCOLE) configuration
A nonlinear distributed parameter model for the NASA-Institute of Electrical and Electronics Engineers' Spacecraft Control Laboratory Experiment (SCOLE) configuration is considered. A linear feedback control law is proposed that points the line of sight of the antenna to any given target direction and at the same time stabilizes the oscillations of the entire flexible configuration.
Araya, Roberto↗
Nonlinear effects of a modal domain optical fiber sensor in a vibration suppression control loop for a flexible structure
Recently, a modal domain optical fiber sensor has been demonstrated as a sensor in a control system for vibration suppression of a flexible cantilevered beam. This sensor responds to strain through a mechanical attachment to the structure. Because this sensor is of the interferometric type, the output of the sensor has a sinusoidal nonlinearity. For small levels of strain, the sensor can be operated in its linear region. For large levels of strain, the detection electronics can be configured to count fringes. In both of these configurations, the sensor nonlinearity imposes some restrictions on the performance of the control system. In this paper we investigate the effects of these sensor nonlinearities on the control system, and identify the region of linear operation in terms of the optical fiber sensor parameters.
Lindner, D. K.↗
Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators
The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.
Burns, John A.↗
Optimal Control of SOEC-Based Hydrogen Production Systems for Demand Response Using Deep Reinforcement Learning in Smart Grids
Solid oxide electrolysis cell (SOEC) hydrogen production technology can range in size from small, appliance-size equipment to large-scale, central production facilities that can be tied directly to renewable or non-greenhouse-gas-emitting forms of electricity production, making it an ideal resource for demand response (DR). The SOEC hydrogen production system is a complex integrated system that encompasses fluid dynamics, electrical dynamics, and electrochemical and thermal dynamics, all of which involve non-linearity and non-convexity. Proper control of the SOEC hydrogen production system is crucial to enable its participation in the DR program. Here, to overcome the difficulty of designing an explicit control law for such nonlinear systems with nonconvex optimization features in DR applications, deep reinforcement learning (DRL) is explored to achieve the optimal control of the SOEC system for DR participation. Specifically, a twin delayed deterministic policy gradient (TD3) control framework is applied to achieve optimal response performance during DR events by considering power tracking error and hydrogen production efficiency with a suitable reward function. Two case studies with grid connections for tracking different DR commands were investigated. The first case study involved operating conditions reaching the boundaries, while the second involved operating conditions within the boundaries. The results showed that the proposed DRL-based control for SOEC can track the DR signal in a timely manner while maintaining high energy efficiency.
08 HYDROGEN↗
Cooperative control of two arms in the transport of an inertial load in zero gravity
In designing a robot control system for dual arm configurations, the control engineer is faced with two challenges: to derive the equations of motion for a given situation, and to meet certain desired control requirements (for instance, minimum energy). The former may involve closed kinematic chains, such as the case when the two arms are grasping a common object. The latter usually involves nonlinear optimization. These issues are considered in the context of transporting an inertial load using two planar three-link arms. A generalized 'reduction transformation' is applied to the dynamics to remove the singularity in the system equations. A suboptimal minimum energy method is presented to reduce a difficult 12-state, six-control nonlinear optimization to two independent, nonconflicting suboptimizations. A simulation example is provided to illustrate the degree of energy reduction possible using the optimal arm torque distribution that was developed.
Carignan, Craig R.↗
Nonlinear combustion instability in liquid propellant rocket motors
Fluid dynamic model and diffusion-controlled flame analysis data on nonlinear combustion instability in liquid propellant rocket engines
Burstein, S. Z.↗
The discrete complementary variational principle and optimal control systems
A discrete complementary variational principle is developed and applied to linear and nonlinear discrete-time optimal control systems. Using the variational approach, a primal-dual relationship is established. This relationship provides a precise measure of system suboptimality independent of any a priori knowledge of the optimal solution.
Chan, W. L.↗
Point to Point Control of the Hydrogen Mixer
We continue to build on the theoretical modelling of a liquid hydrogen (LH2) and gas hydrogen (GH2) mixer subsystem. The mixer described in this work is responsible for combining high pressure LH2 and GH2 to produce a hydrogen flow that meets certain thermodynamic properties. The desired properties are maintained by precise control of the LH2 and GH2 flows. The mixer is modelled as a general multi-flow lumped volume for single constituent fluids using density and internal energy as states. The set of nonlinear differential equations is modelled in the SIMULINK environment including a table look-up feature of the fluid thermodynamic properties. A small signal (linear) model is developed based on the nonlinear model and simulated as well. Pulse disturbances are introduced to the valve positions and the quality of the linear model is ascertained by comparing its behavior against the nonlinear model simulations. Valve control strategies that simulate an operator-in-the-loop scenario are then explored demonstrating the need for automatic feedback control. Finally, optimal single-output and multi-output Proportional/Integral controllers are designed based on the linear model and applied to the nonlinear model with excellent results to track simultaneous, constant setpoint changes in desired exit flow, exit temperature, and mixer pressure, as well as to reject unmeasureable but bounded additive step perturbations in the valve positions.
Barbieri, Enrique↗
Small Signal Point-to-Point Tracking of a Propellant Mixer
This paper addresses some theoretical modelling and control issues for a mixing chamber used in rocket engine testing at NASA Stennis Space Center. The mixer is responsible for combining high pressure LH2 and GH2 to produce a hydrogen flow that meets certain thermodynamic properties before it is fed into a test article. The desired properties are maintained by precise control of the LH2 and GH2 flows. The mixer is modelled as a general multi-flow lumped volume for single constituent fluids using density and internal energy as states. The set of nonlinear differential equations is modelled in the SIMULINK environment including a table look-up feature of the fluid thermodynamic properties. a small-signal (linear) model is developed based on the nonlinear model and simulated as well. Pulse disturbances are introduced to the valve positions and the quality of the linear model is ascertained by comparing its behavior against the nonlinear model simulations. Valve control strategies that simulate an operator-in-the-loop scenario are then explored demonstrating the need for automatic feedback control. Finally, classical optimal single-output and multi-output Proportional/Integral controllers are designed based on the linear model and applied to the nonlinear model with excellent results to track simultaneous, constant setpoint changes in desired exit flow, exit temperature, and mixer pressure, as well as to reject unmeasurable but bounded additive step perturbations in the valve positions.
Barbieri, Enrique↗
Linear approximations of nonlinear systems
The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model.
Hunt, L. R.↗
Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems
In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.
97 MATHEMATICS AND COMPUTING↗
Application of constrained optimization to active control of aeroelastic response
Active control of aeroelastic response is a complex in which the designer usually tries to satisfy many criteria which are often conflicting. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear-Quadratic-Gaussian (LQG) method are of the same high order as the aeroelastic plant. To overcome this disadvantage of the LQG mode, an approach developed for designing low order optimal control laws which uses a nonlinear programming algorithm to search for the values of the control law variables that minimize a composite performance index, was extended to the constrained optimization problem. The method involves searching for the values of the control law variables that minimize a basic performance index while satisfying several inequality constraints that describe the design criteria. The method is applied to gust load alleviation of a drone aircraft.
Newsom, J. R.↗