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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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A method is presented for process control which has the properties of being incremental, cyclic and top-down. It is described on the basis of the development of an expert controller for a simple, but nonlinear control route. A quality comparison between expert controller and process operator shows the ability of the method for knowledge acquisition.
The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.
This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.
A high-altitude electromagnetic pulse (HEMP) or similar geomagnetic disturbance (GMD) has the potential to impact the operation of large-scale electric power grids. By introducing low-frequency common-mode (CM) currents, these events can degrade the performance of critical system components, such as large power transformers by introducing CM currents which can lead to magnetic saturation of the transformer core. In this work, a solid-state transformer (SST) is developed to replace susceptible equipment and improve grid resiliency by safely absorbing these CM disturbances. This device will be referred to as a common-mode solid-state transformer (CM-SST). An SST architecture based on a four-legged AC/DC converter is developed. This architecture enables active control of CM signals without disturbing the AC voltages or the real and reactive power delivery capabilities. A system-level model of this architecture is created, and time-domain simulations are performed to evaluate the SST’s performance in response to simulated CM disturbances. A control strategy for mitigating CM current is also investigated. Hamiltonian surface shaping and power flow control (HSSPFC) is used to design a nonlinear controller for the SST’s output inverter. The objectives of the controller are to suppress CM-induced AC current offsets and regulate AC currents to desired setpoints. Nonlinear system analysis is applied to design and validate the controller. Two cases are tested: (a) the proposed four-leg inverter and (b) a standard three-leg inverter. The results show that the proposed controller rapidly mitigates CM disturbances while maintaining high-quality AC current waveforms in the four-leg configuration. Finally, the hardware performance of an SST prototype is evaluated. In particular, the ability of the SST to safely redirect and absorb CM currents is demonstrated, showing how it can protect neighboring conventional transformers in the system. The study confirms that appropriate control laws allow the SST to protect both itself and adjacent transformers during a HEMP or GMD event.
A nonlinear control law for large angle rotational maneuvers of spacecraft using reaction wheels in the presence of uncertainty is presented. The derivation of this suboptimal control law does not require any information on the values of the system parameters and the disturbance torques acting on the spacecraft. The controller includes a dynamic system in the feedback path. The control law is a nonlinear function of the attitude error, the rate of the attitude error and the compensator state. Simulation results are presented to show that large angle rotational maneuvers can be performed in spite of the uncertainty in the system.
The Rapid Advancement Preview Tracking (RAPT) control method uses both a nonlinear system model and a linearized system model to provide a form of feedback/preview control for nonlinear systems. It uses measurements of the states to calculate the current preview control signal from a local linearization of the state equations, and then iteratively calculates a perturbation correction for that control using the nonlinear equations. The corrected control signal is then applied to the system, driving the end-effector to the next position along a specified trajectory. Computer simulations of tracking control for two-link planar manipulators indicate that this algorithm may be fast enough for real-time control.
Time-optimal control problem studied for system representing second-order nonlinear differential equation
Neighboring optimal feedback control of multi-input nonlinear dynamic systems
In this article we derive a form of the recursive Newton-Euler algorithm that satisfies the skew-symmetry property M-2C = -(M-2C)^T required in a variety of nonlinear control laws occurring throughout the fields of robotics and multibody dynamics.
Computational technique for constructing Liapunov functions for estimating domain of asymptotic stability of nonlinear control systems
In this paper, we define and quantify resiliency of a power network and propose data-driven algorithms for computing the same for the power grid. To do this, we use the Koopman operator framework to lift the controlled dynamical system to an abstract (possibly higher) dimensional space, where the evolution is linear. The linear system representation allows us to relate small time local controllability and observability of a general nonlinear control system to the controllability and observability of the lifted linear system. Finally, we define the resiliency of the underlying power grid in terms of the controllability and observability gramians of the lifted linear system. We illustrate the proposed approach to compute the resiliency metrics on time-series data obtained from a microgrid.
Liapunov approach to nonlinear dynamic systems controllability, deriving conditions for linear dynamic systems
Analysis of control system containing two nonlinearities to determine existence, stability, and values of amplitude and limit cycles frequency
Abstract Marine Hydrokinetic (MHK) cycloturbines generate sustainable power by exploiting tidal currents. By powering the turbines and using pitching foils for control, a vehicle comprised of MHK cycloturbines also has the ability to station keep and maneuver. The vehicle consists of four counter-rotating cycloturbines, with hydrofoils oriented perpendicular to the flow in a paddlewheel configuration. Lift and drag generated from these foils sum together to produce thrust. An experimentally tuned simulation model that solves the six-degrees-of-freedom rigid body equations of motion for the MHK vehicle subject to hydrodynamic, hydrostatic, and propulsive forces is used to aid the design of vehicle controllers. Global feedback controllers are initially designed by applying classical control methods to an approximate linear model of the system dynamics. A higher performing nonlinear controller is designed using the nonlinear dynamic inversion (NDI) method. NDI accounts for the nonlinearities of the MHK system and therefore is suitable for a wide range of operating conditions. The response of the classical and NDI controllers to speed, depth, roll, pitch, and yaw commands are evaluated and compared in simulation. The classical controller outperforms the NDI controller for small amplitude maneuvers, although the degradation with NDI is minor. However, in the nonlinear operating regime the NDI controller outperforms the classical controller and the classical controller exhibits instability.
Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.
This paper presents a bounded linear stability analysis for a hybrid adaptive control that blends both direct and indirect adaptive control. Stability and convergence of nonlinear adaptive control are analyzed using an approximate linear equivalent system. A stability margin analysis shows that a large adaptive gain can lead to a reduced phase margin. This method can enable metrics-driven adaptive control whereby the adaptive gain is adjusted to meet stability margin requirements.
Asymptotic and periodic behavior prediction for nonlinear control system with mathematical model of rigid body vehicle
A recently developed nonlinear control method, sliding mode control, is examined as a means of advancing the achievable performance of space-based precision pointing and tracking systems that use nonlinear magnetic actuators. Analytic results indicate that sliding mode control improves performance compared to linear control approaches. In order to realize these performance improvements, precise knowledge of the plant is required. Additionally, the interaction of an estimating scheme and the sliding mode controller has not been fully examined in the literature. Estimation schemes were designed for use with this sliding mode controller that do not seriously degrade system performance. The authors designed and built a laboratory testbed to determine the feasibility of utilizing sliding mode control in these types of applications. Using this testbed, experimental verification of the authors' analyses is ongoing.