Search NASA⌕ Search

SEARCH · Search NASA

Results for “Tracking error”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Integrated path planning and control through proximal policy optimization for a marine current turbine

This paper presents an integrated path planning and tracking control framework for a marine current turbine (MCT), where the MCT is treated as an energy-harvesting autonomous underwater vehicle (AUV). Considering the ocean (space of action) is continuous, the proposed framework employs two modules to address path planning and path tracking enabled by the proximal policy optimization (PPO) algorithm, which is a policy gradient deep reinforcement learning (RL) method. Further, to enable fully autonomous operation in a stochastic oceanic environment, the proposed path planning seeks a primary objective of maximizing the harvested energy; then, the path tracking module is designed to minimize the tracking error and avoid collisions with static and dynamic obstacles. Using field-collected acoustic Doppler current profiler (ADCP) data, the performance of the proposed framework is evaluated. Comparative studies with baseline algorithms in three different scenarios of path planning, path tracking without an obstacle, and path tracking with collision avoidance verify the effectiveness of our proposed approach.

16 TIDAL AND WAVE POWER↗

Optimization of collision-free paths in a differential-drive robot by a smoothing piecewise-linear approach

This paper presents a methodology for optimizing pre-calculated collision-free paths of differential-drive wheeled robots. The main advantage of this methodology is that optimization is done by considering the kinematics and mechanical constraints of the mobile robot. In accordance to this proposal, the optimized path is achieved by applying recursively a local smoothing on an initial path which is originally modeled as a one-dimensional piecewise linear function. By this recursive smoothing, it can be ensured that the original piecewise linear function can be transformed into a smooth one that fulfill the constraints established by the kinematic equations of the wheeled mobile in terms of a minimum radius of curvature. As a result of this, a trajectory which guarantees lower power consumption and lower mechanical wear, is obtained. To show the better performance of the proposed approach, numerical simulation results are contrasted to those obtained from other reported methods with regards to path length, minimum radius of curvature, cross track error, continuity and resulting acceleration.

97 MATHEMATICS AND COMPUTING↗

New Insights Into Error Decomposition for Precipitation Products

Abstract It is very important to quantify errors of precipitation estimation products. However, the existing methods do not describe all error components and are therefore not comprehensive enough. In this study, we propose a four‐component error decomposition method (4CED) that decomposes the total errors of precipitation products into four independent parts: hit positive bias, hit negative bias, false bias, and missed bias. And we use it to evaluate the performance of the three latest satellite precipitation products in the eastern monsoon region of China. Our study reveals 4CED has apparent improvements compared with the previous method. Results also provide new insights for tracking error sources and quantifying the error magnitudes of precipitation products. Moreover, the proposed 4CED can be extended to different spatial and temporal scales. Our new method will not only contribute to product upgrades, but also provide guidance for potential applications.

58 GEOSCIENCES↗

An Uncertainty and Disturbance Estimator Based Voltage Control for Dual-Active-Bridge Converters

Nonlinearities and external disturbances, like deadtime effect, the on-state voltage drop of the power device, and load variations, can lead to tracking errors in the output voltage of dual-active-bridge (DAB) converters. To address these issues, first of all, a generic dynamic model for DAB converters is proposed, which integrates the DAB circuit model with the phase-shift control scheme. Then, an uncertainty and disturbance estimator (UDE) based voltage control scheme for DAB converters is proposed to improve the output tracking accuracy and dynamic performance. Using the proposed power model, the design procedure of the UDE controller is significantly simplified. Hardware-in-the-loop simulations as well as experimental studies on a scale-down prototype are performed to demonstrate the enhanced tracking and disturbance rejection performance of the proposed controller.

Wu, Yuheng↗

A Human-Machine Shared Control Framework Considering Time-Varying Driver Characteristics

The uncertainties of driver's behavior seriously affect road safety and bring significant challenges to the human-machine cooperative control. Here, this paper proposes a human-machine shared control framework considering driver's time-varying characteristics to improve the co-driving cooperation performance. Firstly, the driving intention is introduced to describe the driver's involvement level through using Gauss-Bernoulli restricted Boltzmann machine method. And the index of driving ability is proposed to evaluate driver skills based on path-tracking errors. Then, a novel human-machine authority allocation strategy is designed by combining the two driving behavior characteristics and used to construct the driver-vehicle interaction system. Subsequently, a T-S fuzzy robust state-feedback shared control system is developed considering time-varying driver behaviors and vehicle states. Finally, the proposed shared steering system is validated by the driver-in-the-loop test bench. The results show that the proposed control method can reduce human-machine conflicts and has obvious superiority in improving performance of driving comfort, path tracking, and vehicle stability for the co-driving vehicles.

33 ADVANCED PROPULSION SYSTEMS↗

Solid State Transformer Controls for Mitigation of E3a High-Altitude Electromagnetic Pulse Insults

This paper explores the use of a solid state transformer (SST) to mitigate the 𝐸 3𝐴 component of a high-altitude electromagnetic pulse (HEMP) insult using external energy storage optimal control techniques. In lieu of conventional passive blocking devices or feedback-controlled energy storage devices, a novel implementation of Hamiltonian error tracking is utilized to develop a feedback control law for the variable converter ratio in an SST. The findings of the simulations performed in this paper suggest that additional energy storage is not necessary to protect an individual load from a HEMP insult. The simulations performed examine the response of a single-phase SST connected to a single voltage source on a long transmission line on the one side and a single linear resistor on the other. The control law is specifically developed for the late-time, low-frequency portion of a HEMP insult, namely the 𝐸 3𝐴 components. The Hamiltonian error-based converter ratio control law is compared with nonlinear optimal feedforward controls to show that the HSSPFC is an external energy storage optimal controller.

HEMP mitigation↗

Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems

This paper focuses on a time-varying constrained nonconvex optimization problem, and considers the synthesis and analysis of online regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized primal-dual gradient method is implemented in a running fashion, in the sense that the underlying optimization problem changes during the execution of the algorithms. In order to study its performance, we first derive its continuous-time limit as a system of differential inclusions. We then study sufficient conditions for tracking a KKT trajectory, and also derive asymptotic bounds for the tracking error (as a function of the time-variability of a KKT trajectory). Further, we provide a set of sufficient conditions for the KKT trajectories not to bifurcate or merge, and also investigate the optimal choice of the parameters of the algorithm. Illustrative numerical results for a time-varying nonconvex problem are provided.

differential inclusion↗

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A phase model approach for thermostatically controlled load demand response

A significant portion of electricity consumed worldwide is used to power thermostatically controlled loads (TCLs) such as air conditioners, refrigerators, and water heaters. Because the short-term timing of operation of such systems is inconsequential as long as their long-run average power consumption is maintained, they are increasingly used in demand response (DR) programs to balance supply and demand on the power grid. Here, we present an ab initio phase model for general TCLs, and use the concept to develop a continuous oscillator model of a TCL and compute its phase response to changes in temperature and applied power. This yields a simple control system model that can be used to evaluate control policies for modulating the power consumption of aggregated loads with parameter heterogeneity and stochastic drift. We demonstrate this concept by comparing simulations of ensembles of heterogeneous loads using the continuous state model and an established hybrid state model. The developed phase model approach is a novel means of evaluating DR provision using TCLs, and is instrumental in estimating the capacity of ancillary services or DR on different time scales. We further propose a novel phase response based open-loop control policy that effectively modulates the aggregate power of a heterogeneous TCL population while maintaining load diversity and minimizing power overshoots. This is demonstrated by low-error tracking of a regulation signal by filtering it into frequency bands and using TCL sub-ensembles with duty cycles in corresponding ranges. As a result, control policies that can maintain a uniform distribution of power consumption by aggregated heterogeneous loads will enable distribution system management (DSM) approaches that maintain stability as well as power quality, and further allow more integration of renewable energy sources.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Dynamic Performance Enhancement for Nonlinear Stochastic Systems Using RBF Driven Nonlinear Compensation with Extended Kalman Filter

In this paper, a novel hybrid control method is proposed to enhance the control performance of the PI based control system for a class of nonlinear and non-Gaussian stochastic dynamic processes with unmeasurable states. Firstly, to enhance the tracking performance of the PI controller where the PI parameters are fixed in many actual control systems, the compensative signal is formed using the extended Kalman filter(EKF) based state estimator and driven by the radial basis function (RBF) neural network based compensator. In addition, the weights of RBF is trained to minimize the entropy criterion of tracking error as the process is subjected to non-Gaussian disturbances. Meanwhile, since the precise statistical property of noises is hard to obtain for many industrial processes, the kernel density estimation (KDE) technique is employed in this paper to estimate the entropy. The convergence of RBF network is discussed and the stability of the resulted closed-loop hybrid control system is analyzed in mean square sense. Finally, a numerical example and a practical system testing are given to illustrate the effectiveness of the proposed control method.

stochastic systems, PI Controller, Entropy, Extend↗

Reinforcement learning for online adaptation of model predictive controllers: Application to a selective catalytic reduction unit

Here we present a novel application of reinforcement learning (RL) for online dynamic tuning of model predictive controllers (MPC). Applying a state-action-reward-state-action (SARSA) algorithm for temporal difference learning with a control-specific reward function improves the error tracking performance of a standard MPC formulation. The proposed RL approach is also readily adaptable to other MPCs, or entirely different control approaches. Practical details for the implementation of the RL-MPC algorithm are also presented. The proposed algorithm is applied to a case study of controlling nitrogen oxide (NO x ) emissions in an industrial selective catalytic reduction (SCR) unit, a control problem characterized by significant nonlinearity and time delay. Along with an RL-MPC formulation for NOx control, another MPC is proposed to mitigate ammonia slip and decrease ammonia consumption in the SCR. Results showing the efficacy of the RL-MPC for NO x control through learning and implementation on the nonlinear SCR dynamic model are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A signal compensation based cascaded PI control for an industrial heat exchange system

Since the characteristics of the industrial heat exchange system (HES) are drastically affected by variations of the steam pressure, ambient temperature and water quality, it is difficult for the classical cascade PI control system to meet the desirable control objectives. Therefore, in this paper, a deterministic linear model with unmodeled dynamics is used to describe the dynamic characteristics of the HES. It should be noted that the unmodeled dynamics at the previously sampled instant can be calculated using actual measurements and that the tracking error, which includes effects of the rate of changes of unmodeled dynamics on the controlled model, can be accurately determined. An additional compensating signal is obtained with the feedforward control together with a one-step optimal control law. Consequently, the cascade PI control strategy with the signal compensation is established. Furthermore, the simulation and industrial application show that the proposed method can effectively improve the performance of the cascade PI control system, especially when the unmodeled dynamics is subjected to unknown variations.

42 ENGINEERING↗

Nuclear microreactor transient and load-following control with deep reinforcement learning

The economic feasibility of nuclear microreactors will depend on minimizing operating costs through advancements in autonomous control, especially when these microreactors are operating alongside other types of energy systems (e.g., renewable energy). This study explores the application of deep reinforcement learning (RL) for real-time drum control in microreactors, exploring performance in regard to load-following scenarios. By leveraging a point kinetics model with thermal and xenon feedback, we first establish a baseline using a single-output RL agent, then compare it against a traditional proportional–integral–derivative (PID) controller. This study demonstrates that RL controllers, including both single- and multi-agent RL (MARL) frameworks, can achieve similar or even superior load-following performance as traditional PID control across a range of load-following scenarios. In short transients, the RL agent was able to reduce the tracking error rate in comparison to PID by one half to one third. Over extended 300-minute load-following scenarios in which xenon feedback becomes a dominant factor, PID maintained better accuracy, but RL still remained within a 1% error margin despite being trained only on short-duration scenarios. This highlights RL’s strong ability to generalize and extrapolate to longer, more complex transients, affording substantial reductions in training costs and reduced overfitting. Furthermore, when control was extended to multiple drums, MARL enabled independent drum control as well as maintained reactor symmetry constraints without sacrificing performance---an objective that standard single-agent RL could not learn. We also found that, as increasing levels of Gaussian noise were added to the power measurements, the RL controllers were able to maintain lower error rates than PID, and to do so with at least 10% and upwards of 150% less control effort. These findings illustrate RL's potential for autonomous nuclear reactor control, laying the groundwork for future integration into high-fidelity simulations and experimental validation efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

A Real-Time Optimization with Warm-Start of Multiperiod AC Optimal Power Flows

We present a real-time optimization strategy based on warm-start for solving a moving horizon of multi period AC optimal power flow (ACOPF) problems. In each horizon, ACOPFs are temporally interlinked via generator ramp constraints, and we assume that each horizon needs to be solved every few seconds or minutes. We introduce two approximate tracking schemes that closely follow a solution path consisting of strongly regular points. We present theoretical results bounding the tracking error by the square of the parameter changes between time periods. Experimental results for networks of sizes up to 9K buses show a fast computation time while maintaining a good solution quality, thus making our approach well suited for real-time circumstances.

moving horizon↗

Distributed output-feedback model predictive control for multi-agent consensus

We introduce a distributed output-feedback model predictive control approach for achieving consensus among multiple agents. Each agent computes a distributed control action based on an output-feedback measurement of a local neighborhood tracking error and communicates information only to its neighbors, according to a communication network modeled as a directed graph. Each agent computes its distributed control action by solving a local min–max optimization problem that simultaneously computes a local state estimate and control input under worst-case assumptions on unmeasured input disturbances and measurement noise. Under easily verified controllability and observability assumptions, this distributed output-feedback model predictive control approach provides an upper bound on the group consensus error, thereby ensuring practical consensus in the presence of unmeasured disturbances and noise. A numerical example with four agents connected in a directed graph is demonstrated to illustrate the results.

42 ENGINEERING↗

Studies of x-ray localization and thickness dependence in atomic-scale elemental mapping by STEM energy-dispersive x-ray spectroscopy using single-frame scanning method

The delocalization of x-ray signals limits the spatial resolution in atomic-scale elemental mapping by scanning transmission electron microscopy (STEM) using energy-dispersive x-ray spectroscopy (EDS). In this study, using a SrTiO 3 [001] single crystal, we show that the x-ray localization to atomic columns is strongly dependent on crystal thickness, and a thin crystal is critical for improving the spatial resolution in atomic-scale EDS mapping. A single-frame scanning technique is used in this study instead of the multiple-frame technique to avoid peak broadening due to tracking error. The strong thickness dependence is realized by measuring the full width at half maxima (FWHM) as well as the peak-to-valley (P/V) ratio of the EDS profiles for Ti K and Sr K+L, obtained at several crystal thicknesses. A FWHM of about 0.16 nm and a P/V ratio of greater than 7.0 are obtained for Ti K for a crystal thickness of less than 20 nm. In conclusion, with increasing crystal thickness, the FWHM and P/V ratio increases and decreases, respectively, indicating the advantage of using a thin crystal for high-resolution EDS mapping.

36 MATERIALS SCIENCE↗

Adaptive neural network backstepping control for a class of uncertain fractional-order chaotic systems with unknown backlash-like hysteresis

In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Leader–follower fixed-time consensus of multi-agent systems with high-order integrator dynamics

The leader-follower fixed-time consensus of high-order multi-agent systems with external disturbances is investigated in this paper. A novel sliding manifold is designed to ensure that the tracking errors converge to zero in a fixed-time during the sliding motion. Then, a distributed control law is designed based on Lyapunov technique to drive the system states to the sliding manifold in finite-time independent of initial conditions. Finally, the efficiency of the proposed method is illustrated by numerical simulations.

42 ENGINEERING↗