Second-order Dynamic Model Research Articles

Assessing possible mutual orbit period change by shape deformation of Didymos after a kinetic impact in the NASA-led Double Asteroid Redirection Test

The Asteroid Impact & Deflection Assessment (AIDA) targets binary near-Earth asteroid (65803) Didymos. As part of this mission, the NASA-led Double Asteroid Redirection Test (DART) will make a kinetic impactor collide with the smaller secondary of Didymos to test kinetic impact asteroid deflection technology, while the ESA-led Hera mission will evaluate the efficiency of the deflection by conducting detailed on-site observations. Research has shown that the larger primary of Didymos is spinning close to its critical spin, and the DART-impact-driven ejecta would give kinetic energy to the primary. It has been hypothesized that such an energy input might cause structural deformation of the primary, affecting the mutual orbit period, a critical parameter for assessing the kinetic impact deflection by the DART impactor. A key issue in the previous work was that the secondary was assumed to be spherical, which may not be realistic. Here, we use a second-order inertia-integral mutual dynamics model to analyze the effects of the shapes of the primary and the secondary on the mutual orbit period change of the system. We first compare the second-order model with three mutual dynamics models, including a high-order inertia-integral model that takes into account the detailed shapes of Didymos. The comparison tests show that the second-order model may have an error of ∼10% for computing the mutual orbit period change, compared to the high-order model. We next use the second-order model to analyze how the original shape and shape deformation change the mutual orbit period. The results show that when the secondary is elongated, the mutual orbit period becomes short. Also, shape deformation of the secondary further changes the mutual orbit period. A better understanding of this mechanism allows for detailed assessment of DART’s kinetic impact deflection capability for Didymos.

A simplified model of gas turbine unit adaptive control

The article explores the possibilities of building automatic control systems for gas turbine power plants. The use of the principles of adaptive control with a reference model and a signal effect is being studied. As an adaptation method, a method based on the Lyapunov function is used, in order to reduce the time for searching for an extremum. There is a need to ensure the specified indicators of electricity the quality in a constantly changing electrical load and changes in operating modes of the power plant in gas turbine units. The article presents a model of a gas turbine installation for the study of adaptive control. It is shown that the improvement of one coordinate is possible to obtain due to some deterioration of the other coordinate. For further study of this problem, a simplified second-order dynamic model has been constructed. With the help of such a model, complex studies of various stages of adaptive control were carried out. Results were obtained by varying the parameters of adaptive control and simulation parameters. The research results are designed to find the optimal ratios of adaptive automatic control systems parameters for power industry gas turbine plants.

Neural network-based target tracking control of underactuated autonomous underwater vehicles with a prescribed performance

In this paper, the target tracking control problem is addressed for underactuated autonomous underwater vehicles (AUV) with a prescribed performance. For this purpose, the range and bearing angles of the AUV relative to an underwater target are transformed to a second-order open-loop error dynamic model by using the prescribed performance bound technique. Then, a new tracking controller is proposed such that the tracking errors converge to an arbitrary small ultimate bound and their transient performance are guaranteed with a pre-specified maximum overshoot and the convergence rate. To overcome unmodeled dynamics and external disturbances that are imposed on the vehicle by the wind, waves, and ocean currents, a multi-layer neural network and an adaptive robust controller are adopted. A Lyapunov stability synthesis shows that all signals of the control system are bounded, and tracking errors converge to a small region containing the origin with a prescribed performance. Finally, simulations are performed in MATLAB software and a comparative study verifies the theoretical results.

DEVELOPMENT OF A TRANSFER FUNCTION FOR WEIGHT PREDICTION OF LIVE BROILER CHICKEN USING MACHINE VISION

The objective of this study was to process digital images to investigate the possibility of broilers body weight estimation based on the dynamic model. For this experiment, 2440 images were recorded by a top-view camera from 30 birds. An ellipse fitting algorithm was applied to localize chickens within the pen, by using generalized Hough transform. Chickens’ head and tail were removed efficiently using the Chan-Vese method. After that, using image processing, six body measures were calculated. Next, they were used to design a Transform Function (TF) model with weight measurements as output. Second-order dynamic models were used to predict the weight of life broiler chicken, without delay, stable and with the highest R2 were predominantly selected according to the Young Identification Criterion (YIC) criterion chosen models. It was observed that predicted values rigorously follow the real values. Moreover, the relative body weight errors of chickens in the early days of grow-out was much more than last days. The accuracy of TF for body weight prediction from a comparison between measured (absolute) and predicted total life body weights were estimated for all studied broiler chicken (R2=0.98).

Dynamics of eye movements under time varying stimuli.

In this paper we study the pure-slow and pure-fast dynamics of the disparity convergence of the eye movements second-order linear dynamic mathematical model under time varying stimuli. Performing simulation of the isolated pure-slow and pure-fast dynamics, it has been observed that the pure-fast component corresponding to the eye angular velocity displays abrupt and very fast changes in a very broad range of values. The result obtained is specific for the considered second-order mathematical model that does not include any saturation elements nor time-delay elements. The importance of presented results is in their mathematical simplicity and exactness. More complex mathematical models can be built starting with the presented pure-slow and pure-fast first-order models by appropriately adding saturation and time-delay elements independently to the identified isolated pure-slow and pure-fast first-order models.

Sequential Articulated Motion Reconstruction from a Monocular Image Sequence

In this article, we present a sequential approach for articulated motion estimation from a 2D skeleton sequence. This is a challenging task due to the complexity of human movements and the inherent depth ambiguities. The proposed approach models the human movement on a kinematic manifold with the tangent bundle, which is a natural geometrical representation of articulated motion. Combined with a second-order stochastic dynamic model based on the Markov hypothesis, we generalize the Extended Rauch Tung Striebel smoother to a Riemannian manifold to simulate the process of human movement. The human motor system might violate the Markov hypothesis when the human body is subject to external forces, and therefore a refinement stage is introduced to correct the estimation error. Specifically, the current estimation is refined in a feasible solution region consisting of a set of local estimations. This region is called a simplex, in which each element can be represented by a convex hull of all ingredients. We have proved that the refinement problem can be converted into a convex optimization problem with the simplicial constraint. Since the proposed formulation conforms to the principles of kinematic and spatio-temporal continuity of articulated motion, the reconstruction ambiguity can be alleviated essentially. The performance of the proposed algorithm is conducted on multiple synthetic sequences from the CMU and the HDM05 MoCap databases. The results show that, without requiring any training data, the proposed approach achieves greater accuracy over state-of-the-art baselines. Furthermore, the proposed approach outperforms two baselines on real sequences from the Human3.6m MoCap database.

Closed-Form Approximation for the Steady-State Performance of Second-Order Kalman Filters

The Kalman filter is adopted in a myriad of applications for providing the minimum mean square error estimation of time-varying parameters in a simple and systematic manner. However, determining the Kalman filter performance is not so straightforward, particularly when process noise is present. In that case, one must often resort to numerical evaluations of the recursive Bayesian Cramer–Rao bound, or alternatively to implement the filter and assess the performance through Montecarlo simulations. This letter is intended to circumvent this limitation. It proposes a closed-form approximation for the steady-state performance of a Kalman filter based on a second-order dynamic model, while at the same time providing a novel closed-form upper bound for the convergence time. These two results are obtained by reformulating the Kalman filter in batch mode and analyzing the inner structure of the Bayesian information matrix. Simulation results are provided to illustrate the goodness of the proposed approach.

Three-dimensional tracking control of autonomous underwater vehicles with limited torque and without velocity sensors

SUMMARYMost of the previous works on the motion control of autonomous underwater vehicles (AUVs) assume that (i) the vehicle actuators are able to tolerate every level of the control signals, and (ii) the vehicle is equipped with the velocity sensors in all degrees of freedom. These assumptions are not desirable in practice. Toward this end, this paper addresses the trajectory tracking control of the underactuated AUVs with the limited torque, without the velocity measurements and under environmental disturbances in a three-dimensional space. At first, a variable transformation is introduced which helps us to derive a second-order dynamic model for underactuated AUVs. Then, a saturated tracking controller is proposed by employing the saturation functions to bound the closed-loop error variables. This technique reduces the risk of the actuators saturation by decreasing the amplitude of the generated control signals. In addition, a nonlinear saturated observer is introduced to remove the velocity sensors from the control system. The proposed controller copes with the uncertain vehicle parameters, and constant or time-varying environmental disturbances induced by the waves and ocean currents. Lyapunov's direct method is used to show the semi-global uniform ultimate boundedness of the tracking and state estimation errors. Finally, some simulation results illustrate the effectiveness of the proposed controller.

Modeling Time Variations of Boiler Efficiency

Boiler's efficiency is one of the important performance indicators of boiler. To keep track of operation cost, efficiency needs to be calculated with adequate accuracy by employing effective mathematical tools. In this work, a new modification in conventional mathematical formulation of efficiency is presented based on time-varying efficiency using time-varying operational variables of boiler. This modification was accomplished using indirect method of efficiency by applying experimental data of variables for certain time span. Moreover a second-order dynamic model of flue gas temperature (FGT) has been derived to construct the mathematical formulation of efficiency only in terms of available inputs. The resulting input–output-based model proved to be in quite agreement with efficiency calculated from experimental data. After modeling, influence of variations in air to fuel ratio (AFR) and fuel flow rate (FFR) upon efficiency has been discussed and it has been shown that time-varying efficiency covers deeper aspect of dynamic relation between efficiency and other input of boiler especially AFR and FFR. Moreover, it has been established that efficiency interacts with the dynamics of boiler, and in this respect, a dynamic relation between combustion process and boiler dynamics has been constructed via efficiency.

Position and angle control for a two-wheel robot

In this paper, a two-wheel robot (TWR) system is implemented based on a position and angle decoupled intelligent backstepping control system. The decoupled method provides a simple method to achieve asymptotic stability control for a fourth-order nonlinear TWR system using a second-order dynamics model. Moreover, adaptive output recurrent cerebellar model articulation control (AORCMAC) is designed in this study to imitate an ideal backstepping controller (IBC). Furthermore, to compensate for the difference between the two controllers mentioned, a compensator is used. Based on the Lyapunov stability method, the stability of the closed-loop system can be guaranteed. To train the AORCMAC effectively, the variable learning rates that guarantee the convergence of the system are proposed. Finally, simulation and experimental results demonstrate the effectiveness of the proposed control method for TWR control.

A Generalized Quasi-MMSE Controller for Run-to-Run Dynamic Models

ABSTRACTThis study proposes a generalized quasi-minimum mean square error (qMMSE) controller for implementing a run-to-run process control where the process input–output relationship follows a general-order dynamical model with added noise. The expression of the process output, the long-term stability conditions and the optimal discount factor of this controller are derived analytically. Furthermore, we use the proposed second-order dynamical model to illustrate the effects of mis-identification of the process I-O model on the process total mean square error (TMSE). Via a comprehensive simulation study, the model demonstrates that the TMSE may inflate by more than 150% if a second-order dynamical model with moderately large carryover effects is wrongly identified as that of a first-order model. This means that the effects of mis-identification of the process I-O model on the process total mean square error (TMSE) is not negligible for implementing a dynamic run-to-run (RTR) process control. Supplementary materials for this article are available online.

Numerical simulation of the flow around a subsea pipeline with different protection methods

Hydrodynamic stress induced by marine currents subject subsea pipelines to failure vulnerability. Therefore, several methods have been established to protect such pipelines from hydrodynamic forces. The objective of this work is to investigate the performance of two different protection methods using computational fluid dynamics. A second-order accurate upwind finite volume computational fluid dynamics model was used to simulate isotropic turbulent flow around a subsea pipeline located on flat seabed. A comparison between four turbulence models revealed that both Menter’s shear stress transport k[Formula: see text] and the standard k[Formula: see text] models yield the best agreement with experimental measurements. Pipeline trenching and double-barrier protection methods were simulated with different geometrical characteristics. A comparison between those two methods was conducted and discussed. It is found that at small aspect ratios, the double-barrier method prevails over trenching in terms of its ability to isolate the pipe from the main current. While at large aspect ratio, trenching provides near-zero pressure coefficient along the pipe wall, which demonstrate its prevalence in protecting the pipeline.

Macroscopic modeling of pedestrian flow based on a second-order predictive dynamic model

This work presents a second-order predictive dynamic model for pedestrian flow to investigate movement patterns and non-equilibrium phenomena in pedestrian traffic. This model is described as a system of nonlinear hyperbolic conservation laws with relaxation under the hypothesis that a group of pedestrians are regarded as a continuous anisotropic medium. The desired or preferred walking direction of pedestrians is assumed to minimize the total actual walking cost based on predictive traffic conditions, which satisfies the predictive dynamic user-equilibrium assignment. To solve this model, a cell-centered finite volume method for hyperbolic conservation laws coupled with a self-adaptive method of successive averages for an arisen discrete fixed point problem is adopted. The proposed model and algorithm are validated by comparing the results carried out by the model with experimental observations under non-congested conditions. Numerical examples are designed to investigate macroscopic features and path-choice behaviors of pedestrian flow. Numerical results indicate that the proposed model is able to reproduce some complex nonlinear phenomena in pedestrian traffic, such as the formation of congestions and stop-and-go waves.

Neural network formation control of underactuated autonomous underwater vehicles with saturating actuators

This paper addresses a neural network-based formation control of underactuated AUVs with limited torque input under environmental disturbances in three-dimensional space. For this purpose, a second-order dynamic model is developed based on a coordinate transformation for underactuated AUVs. Then, a saturated formation controller is proposed by employing saturation functions in order to bound closed-loop error variables. This technique effectively reduces the risk of actuators saturation by decreasing the amplitude of generated control signals. Multi-layer neural networks are combined with an adaptive robust control strategy to deal with the actuator saturation and model uncertainties including unknown vehicle parameters, approximation errors, and constant or time-varying environmental disturbances induced by waves and ocean currents. A Lyapunov synthesis is used to guarantee semi-global uniform ultimate boundedness of tracking errors for all AUVs. Finally, simulation results demonstrate the performance of the proposed formation controller.

Steady State Analysis of the TCP Network with RED Algorithm

The transmission control protocol with a random early detection (TCP/RED) is an important algorithm for a TCP congestion control. It has been expressed as a simple second-order discrete-time hybrid dynamical model, and shows unique and typical nonlinear phenomena, e.g., bifurcation phenomena or chaotic attractors. However, detailed behavior is unclear due to discontinuity that describes the switching of transmission phases in TCP/RED, but we have proposed its analysis method in previous study. This letter clarifies bifurcation structures with it.

A Terminal Guidance Law Based on Motion Camouflage Strategy of Air-to-Ground Missiles

A guidance law for attacking ground target based on motion camouflage strategy is proposed in this paper. According to the relative position between missile and target, the dual second-order dynamics model is derived. The missile guidance condition is given by analyzing the characteristic of motion camouflage strategy. Then, the terminal guidance law is derived by using the relative motion of missile and target and the guidance condition. In the process of derivation, the three-dimensional guidance law could be designed in a two-dimensional plane and the difficulty of guidance law design is reduced. A two-dimensional guidance law for three-dimensional space is derived by bringing the estimation for target maneuver. Finally, simulation for the proposed guidance law is taken and compared with pure proportional navigation. The simulation results demonstrate that the proposed guidance law can be applied to air-to-ground missiles.

Low-Complexity Least-Squares Dynamic Synchrophasor Estimation Based on the Discrete Fourier Transform

In this paper, the expressions for the phasor parameter estimates returned by the Taylor-based weighted least-squares (TWLS) approach, achieved using either complex-valued or real-valued variables, are derived. In particular, the TWLS phasor estimator and its derivatives are expressed as weighted sums of the discrete-time Fourier transform (DTFT) of the analyzed waveform and its derivatives. The derived expressions show that the TWLS algorithm is sensitive to lower order harmonics and interharmonics located close to the waveform frequency when few waveform cycles are analyzed. Also, the algorithm sensitivity to wideband noise is explained. The relationship between the TWLS phasor estimator and the waveform DTFT is then specifically analyzed when either a static or a second-order dynamic phasor model is assumed. Moreover, a simple and accurate procedure for evaluating the TWLS estimator of the dynamic phasor parameters is proposed. The derived expressions for the real-valued version are then approximated in order to reduce the required computational burden so as to achieve the simplified TWLS (STWLS) procedure. That procedure can be advantageously employed in real-time low-cost applications when the reference frequency used in the TWLS approach is estimated in runtime to improve estimation accuracy. Finally, computer simulations show that the phasor parameter estimates returned by the STWLS procedure when the waveform frequency is estimated by the interpolated discrete Fourier transform method comply with the M-class of performance if an appropriate number of waveform cycles is considered.

Neural adaptive robust control of underactuated marine surface vehicles with input saturation

This paper proposes a saturated tracking controller for underactuated autonomous marine surface vehicles with limited torque. First, a second-order open-loop error dynamic model is developed in the actuated degrees of freedom to simplify the design procedure. Then, a saturated tracking controller is designed by utilizing generalized saturation functions to reduce the risk of actuator saturation. This, in turn, improves the transient performance of the control system. A multi-layer neural network and adaptive robust control techniques are also employed to preserve the controller robustness against unmodeled dynamics and environmental disturbances induced by waves and ocean currents. A Lyapunov stability analysis shows that all signals of the closed-loop system are bounded and tracking errors are semi-globally uniformly ultimately bounded. Finally, simulation results are provided for a hovercraft vehicle to illustrate the effectiveness of the proposed controller as a qualified candidate for real implementations in offshore applications.

Leader–follower formation control of underactuated autonomous marine surface vehicles with limited torque

This paper proposes a leader–follower formation tracking controller for underactuated autonomous marine surface vehicles with limited torque under environmental disturbances. A second-order formation dynamic model is developed in the actuated degrees of freedom of the followers to simplify the design procedure. Then, a formation tracking controller is designed by utilizing generalized saturation functions to reduce the risk of actuator saturation. Radial basis function neural network and adaptive robust control techniques are also adopted to preserve the controller robustness against unmodeled dynamics and environmental disturbances induced by waves and ocean currents. A Lyapunov-based stability analysis shows that all signals of the closed-loop system are bounded and tracking errors are semi-globally uniformly ultimately bounded. Finally, simulation results are provided for a group of surface vessels to illustrate the effectiveness of the proposed controller as a qualified candidate for real implementations in offshore applications.

A Sense of Balance: Experimental Investigation and Modeling of a Malonyl-CoA Sensor in Escherichia coli.

Production of value-added chemicals in microorganisms is regarded as a viable alternative to chemical synthesis. In the past decade, several engineered pathways producing such chemicals, including plant secondary metabolites in microorganisms have been reported; upscaling their production yields, however, was often challenging. Here, we analyze a modular device designed for sensing malonyl-CoA, a common precursor for both fatty acid and flavonoid biosynthesis. The sensor can be used either for high-throughput pathway screening in synthetic biology applications or for introducing a feedback circuit to regulate production of the desired chemical. Here, we used the sensor to compare the performance of several predicted malonyl-CoA-producing pathways, and validated the utility of malonyl-CoA reductase and malonate-CoA transferase for malonyl-CoA biosynthesis. We generated a second-order dynamic linear model describing the relation of the fluorescence generated by the sensor to the biomass of the host cell representing a filter/amplifier with a gain that correlates with the level of induction. We found the time constants describing filter dynamics to be independent of the level of induction but distinctively clustered for each of the production pathways, indicating the robustness of the sensor. Moreover, by monitoring the effect of the copy-number of the production plasmid on the dose–response curve of the sensor, we managed to coarse-tune the level of pathway expression to maximize malonyl-CoA synthesis. In addition, we provide an example of the sensor’s use in analyzing the effect of inducer or substrate concentrations on production levels. The rational development of models describing sensors, supplemented with the power of high-throughput optimization provide a promising potential for engineering feedback loops regulating enzyme levels to maximize productivity yields of synthetic metabolic pathways.