Simplified Nonlinear Dynamic Model Research Articles

Modelling and Extremum Seeking Control of Gas Lifted Oil Wells

This paper addresses the design of a perturbation-based extremum seeking control (ESC) method to maintain the oil production around the optimum point of the well-performance curve in gas lifted wells. The method uses periodic perturbation which is injected into the plant with intention to extract the information about the gradient of the well-performance curve. A simple nonlinear dynamic model is proposed and the essential dynamics of the Eikrem's model are captured, i.e., the transient behavior and the optimal steady state well- performance curve. Based on this simple model, a pre-compensation is developed which allows the application of the ESC scheme without reducing excessively the perturbation frequency. The control performance is evaluated via numerical simulations using an appropriate environment for modelling, simulation and optimization (EMSO) of process dynamic systems.

Dört rotorlu bir insansiz hava aracinin geri-adimlama yöntemi ile yol takibi kontrolü

ÖzetDört rotorlu(quadrotor), son yıllarda bir çok araştırmacı tarafından çalışılan çok popüler bir insansız hava aracıdır(İHA). Dört rotorlu, dikey iniş kalkış(VTOL) özelliği ve yüksek manevra kabiliyeti sayesinde klasik insansız hava araçlarına göre bir çok avantaja sahiptir. VTOL özelliği sayesinde, özellikle engebeli ve kısıtlı ortamlarda, uzun iniş ve kalkış pistine ihtiyaç duymadan kullanılabilmektedir. Ayrıca, dört rotorlu, VTOL özelliği taşıyan diğer İHA'lara göre, mekanik olarak daha basit bir yapıya sahiptir. Fakat, belirtilen avantajların yanı sıra, dört rotorlu, yüksek derecede doğrusal olmayan ve kararsız bir dinamiğe sahiptir. Bu nedenle, dört rotorlu'nun otonom kontrolü çeşitli zorluklar içermektedir ve bir çok araştırmacının ilgisini çekmektedir.Bu çalışmada, dört rotorlu bir insansız hava aracının, doğrusal olmayan bir kontrol metodu olan geri-adımlama yöntemi kullanılarak, yol(yörünge) takibi kontrolü sağlanmıştır. Kontrol sistemi oluşturulurken, dört rotorlu'nun yönelimi iç döngü olarak, pozisyonu ise dış döngü olarak kontrol edilerek, hava aracının istenilen yolu yüksek doğrulukla takip etmesi amaçlanmıştır. İlk olarak, dört rotorlu'nun doğrusal olmayan dinamik modeli Newton hareket denklemleri kullanılarak elde edilmiştir. Doğrusal olmayan bu model simülasyonlarda dinamik model olarak kullanılmıştır. Daha sonrasında, doğrusal olmayan dinamik model, kontrolcü tasarımında kullanılmak üzere, belirli varsayımlar aracılığıyla basitleştirilmiştir. Basitleştirilmiş dinamik model kullanılarak, geri adımlamalı kontrolcü, üç aşamada elde edilmiştir. Elde edilen kontrolcü, MATLAB/Simulink ortamında modellenmiş ve test edilmiştir. Ayrıca, kontrolcünün güçlü derecedeki bozuculara karşı dayanıklılığı da simülasyon ortamında denenmiştir. Elde edilen simülasyon sonuçları, geri-adımlamalı kontrolcü sayesinde, istenilen yolun yüksek doğrulukta takip edildiğini göstermiştir. Ayrıca, bozucular eklenerek yapılan simülasyonlarda, kontrolcünün güçlü derecedeki çeşitli bozucuları etkili şekilde bastırdığı görülmüştür.

The Quadrotor Dynamic Modeling and Indoor Target Tracking Control Method

A reliable nonlinear dynamic model of the quadrotor is presented. The nonlinear dynamic model includes actuator dynamic and aerodynamic effect. Since the rotors run near a constant hovering speed, the dynamic model is simplified at hovering operating point. Based on the simplified nonlinear dynamic model, the PID controllers with feedback linearization and feedforward control are proposed using the backstepping method. These controllers are used to control both the attitude and position of the quadrotor. A fully custom quadrotor is developed to verify the correctness of the dynamic model and control algorithms. The attitude of the quadrotor is measured by inertia measurement unit (IMU). The position of the quadrotor in a GPS-denied environment, especially indoor environment, is estimated from the downward camera and ultrasonic sensor measurements. The validity and effectiveness of the proposed dynamic model and control algorithms are demonstrated by experimental results. It is shown that the vehicle achieves robust vision-based hovering and moving target tracking control.

Analysis on Model Nonlinearity for Control System of Heat Supply Unit

With the rapid development of renewable energy power, the task of peak load regulation and frequency control for the power grid is very severe. Using the heat storage of the heat supply unit to take part in peak load regulation and frequency control is imperative. On the basis of the simplified nonlinear dynamic model of the typical heat supply unit, the model was linearized under different operation point conditions. The control performances of three typical coordinated control system modes were compared under the typical operation point conditions. The experiment results show that if the parameters of the controller are set well on any operation point, the control system of heat supply unit can adapt the normal variation of the load around the operation point, which can provide support for utilization of the heat storage of the heat supply unit.

Combined Levitation Design and Control of a Novel M-DOF Actuator Based on Air Bearing and Electromagnetic Principle

Supporting and levitation control are important for actuators or motors with complicated structures. Based on the presented configuration design, the simplified torque calculation model and non-linear system dynamic model have been proposed, and air bearing combined with magnetic levitation mechanism is developed for alleviating the friction and resistance to improve the dynamic performance of this M-DOF actuator. The fluid field model is built in computational fluid dynamics software. Different structure parameters and conditions are computed and compared with the vortex torque characteristics and pressure distribution. A linear mathematical model of the magnetic levitation force is deduced and corresponding control scheme with power drive unit is discussed. Experiment results show that the actuator can effectively implement 3-DOF motion combined with the combined levitation modes, and that the proposed approach can be applied to m-DOF actuators of the same kind effectively.DOI: http://dx.doi.org/10.5755/j01.eee.19.3.1387

Modeling and levitation control of a novel M-DOF actuator based on neural network

Modeling andtorque characteristicsanalysisareimportantfor actuatorsor motorswithcomplicatedstructures. Based on the presented configuration design, the magnetic field and torque calculation for a multiple degrees-of-freedom (M-DOF) spherical actuator are performed using 3D FEM. To reduce the computation workload, a simplified torque calculation model and non-linear system dynamic model have been proposed, and magnetic levitation mechanism is developed for alleviating the friction and resistance to improve the dynamic performance of this M-DOF actuator. A linear mathematical model of the levitation force is deduced and corresponding control scheme with power drive unit is discussed. Then the diagonal recurrent neural network (DRNN) based control scheme is presented to improve the performance of levitation by adjusting parameters online as identifiers. Simulation and experiment results show that the actuator can effectively implement 3-DOF motion combined with levitation mode, and that the proposed approach can be applied to M-DOF actuators of the same kind effectively.

A simplified nonlinear dynamic model for the analysis of pipe structures with bolted flange joints

Bolted flange joints are widely used in engineering structures; however, the dynamic behavior of this connection is complex in nature. In this paper, a simplified nonlinear dynamic model with bi-linear springs is proposed and validated for pipe structures with bolted flange joints. First, static mechanical properties of the bolted flange joint are investigated. The analytical solution reveals that the axial stiffness of the bolted flange joint is different in tension and compression. Then, nonlinear springs with different stiffness in tension and compression are employed to represent the bolted flange joint. A special type of dynamic behavior, coupling vibration in the transverse and longitudinal directions, is observed in analytical derivation. Finally, relevant physical experiments and numerical simulations are performed. The physical experiments confirm the existence of the coupling vibration behavior. The relationship of longitudinal and transverse vibration frequencies is discussed. The numerical solutions reveal that the simplified nonlinear dynamic model better fits the physical response than conventional reduced linear beam model.

Enhancing particle image tracking performance with a sequential Monte Carlo method: The bootstrap filter

One of the common problems of current pattern match and particle image tracking algorithms is the deployment of constant velocity assumption for particle motion between two frames, which would result in serious errors when high velocity gradient flows are measured. To address this issue, a new particle image tracking method—bootstrap filter tracking is proposed. In this new method, a simple nonlinear dynamic model which takes particle acceleration into account is employed and a sequential Monte Carlo method—bootstrap filter is used in conjunction with pattern match algorithm to strengthen the particle image tracking performance. By using the nonlinear system model and bootstrap filter, particle location at next time step can be predicted accurately and the new method is able to measure high velocity gradient flows with better performance than the traditional particle image tracking algorithms. This new method is validated by using numerically generated particle images. Its accuracy in terms of particle image density, out-of-plane displacement and displacement gradient is compared with the Kalman filter tracking (Takehara et al., 2000 [34]) and the Super-PIV (Keane et al., 1995 [30]) methods. The three algorithms are also compared by using a set of real turbulent jet images. The test results demonstrate that the bootstrap filter tracking method is superior than the Kalman filter tracking and the Super-PIV methods for measuring low density, high velocity gradient flows.

The study on nonlinear dynamic behaviors of the structures with bolted-flange joint

With multiple nonlinear behaviors involved, bolted-flange joints are complex in nature, especially when exposed to dynamic loads. In this paper, a simplified nonlinear dynamic model is proposed for a cylinder assembled by the bolted-flange joint. The geometric, material and contact nonlinearity is modeled by nonlinear spring elements with different tensile and compressive stiffness. The moduli of the springs are obtained from physical tests or numerical simulations. It is discovered that there exists a special type of conditional coupling behaviors between transverse and longitudinal vibration. To overcome the system energy dissipation, the implicit method in ANSYS and extremely small time step are employed. The data of displacement response, coupled with the response frequencies obtained thru FFT, validates the existence of the coupling vibration response.

Evaluation of periodic operation of a trickle-bed reactor based on empirical modeling

In this paper, we propose a new procedure for fast evaluation of the potential of periodic operations in trickle-bed reactors, based on empirical modeling. Step response experiments, with different input amplitudes, were performed on a laboratory trickle-bed reactor, in order to derive a simple nonlinear dynamic model. α-methylstyrene (AMS) hydrogenation was used as a test reaction and the feed AMS concentration was used as the modulated input. An empirical nonlinear model was postulated and used for simulation of periodic operations. The simulation of a periodic operation with sinusoidal modulation of the inlet AMS concentration with 40 % amplitude resulted up to 35% higher time-averaged conversion than the corresponding steady-state one.

Deriving dynamical models from paleoclimatic records: Application to glacial millennial-scale climate variability

A method for systematically deriving simple nonlinear dynamical models from ice-core data is proposed. It offers a tool to integrate models and theories with paleoclimatic data. The method is based on the unscented Kalman filter, a nonlinear extension of the conventional Kalman filter. Here, we adopt the abstract conceptual model of stochastically driven motion in a potential that allows for two distinctly different states. The parameters of the model-the shape of the potential and the noise level-are estimated from a North Greenland ice-core record. For the glacial period from 70 to 20 ky before present, a potential is derived that is asymmetric and almost degenerate. There is a deep well corresponding to a cold stadial state and a very shallow well corresponding to a warm interstadial state.

On Instability in Gas Lift Wells and Schemes for Stabilization by Automatic Control

Summary In this paper, we present a simple nonlinear dynamic model that is shown to capture the essential dynamics of the casing-heading instability in gas lift wells despite the complex nature of two-phase flow. Using the model, stability maps are generated showing regions of stable and unstable settings for the production valve governing the flow of produced oil and gas from the tubing. Optimal steady-state production is shown to lie well within the unstable region, corresponding to an oil-production rate that cannot be sustained without automatic control. Three simple control structures are suggested that successfully stabilize the casing-heading instability in simulations, and more importantly in laboratory experiments.

Vision-based tracking with projective mapping for parameter identification of remotely operated vehicles

Parameter identification of a remotely operated vehicle (ROV) is often based on the dynamic responses collected by its onboard sensors. However, for commercial ROVs, the required data for identification may not be available due to the absence of suitable sensors or limitations in accessing onboard sensor data. Therefore, this study proposes a vision-based tracking system to measure the dynamic response of an ROV. The tracking system is independent of the ROV, and is able to localize an ROV to a high degree of precision by means of projective mapping. The validity of the proposed tracking system is demonstrated through identification of a commercial ROV. A simplified nonlinear ROV dynamic model with six degrees of freedom (DOF) is used for identification. Uncoupled motions, including surge, sway, and yaw, are obtained from the ROV dynamic model, and the corresponding experiments are carried out for each DOF. Hydrodynamic parameters are then estimated with numerical optimizations by comparing the measured ROV responses with the output of the mathematical model. The experimental results show that the vision-based tracking system can accurately measure the transient and steady-state responses of an ROV. Additionally, the simulations of the ROV dynamic model, with the optimal parameter estimates, give results in agreement with the measured data.

A stochastic analysis for a phytoplankton–zooplankton model

A simple phytoplankton-zooplankton nonlinear dynamical model was proposed to study the coexistence of all the species and a Hopf bifurcation was observed. In order to study the effect of environmental robustness on this system, we have stochastically perturbed the system with respect to white noise around its positive interior equilibrium. We have observed that the system remains stochastically stable around the positive equilibrium for same parametric values in the deterministic situation.

A Simple Nonlinear Dynamic Model for Unemployment: Explaining the Spanish Case

Spanish unemployment is characterized by three distinct regimes of low, medium, and high unemployment and by a fast transition between them. This paper presents a simple nonlinear dynamic model that is able to explain this behavior with multiple equilibria and jumps describing the transition between equilibria. The model has only a small number of parameters capturing the fundamentals of labor markets and macroeconomic and institutional factors. The model is capable of generating unemployment dynamics that encompass the “unique” natural rate hypothesis, the structuralist hypothesis, and the hysteresis hypothesis.

Closure tests for mean field magnetohydrodynamics using a self-consistent reduced model

The mean electromotive force and alpha effect are computed for a forced turbulent flow using a simple nonlinear dynamical model. The results are used to check the applicability of two basic analytic ansatze of mean-field magnetohydrodynamics - the second order correlation approximation (SOCA) and the tau approximation. In the numerical simulations the effective Reynolds number Re is 2-20, while the magnetic Prandtl number varies from 0.1 to $10^{7}$. We present evidence that the $\tau$ approximation may be appropriate in dynamical regimes where there is a small-scale dynamo. Catastrophic quenching of the $\alpha$ effect is found for high $P_{m}$. Our results indicate that for high $P_{m}$ SOCA gives a very large value of the $\alpha$ coefficient compared with the ``exact'' solution. The discrepancy depends on the properties of the random force that drives the flow, with a larger difference occuring for $\delta$-correlated force compared with that for a steady random force.

A simple dynamic model of the primary circuit in VVER plants for controller design purposes

A simple low dimensional nonlinear dynamic model of the primary circuit in a VVER-type nuclear power plant is developed from first engineering principles that is able to capture the most important dynamics of the system in normal operating modes. The model includes the description of the main control loops in the system, too. The model has been verified and validated by using measured data from three VVER-440 units of Paks Nuclear Power Plant in Hungary, and a good fit has been obtained. This qualifies the model to be the basis for the integrated re-design of the primary control loops.

Hydrodynamic lubrication in nanoscale bearings under high shear velocity

The setting up process in a nanoscale bearing has been modeled by molecular dynamics simulation. Contrary to the prediction from the classical Reynolds' theory, simulation results show that the load capacity of the nanoscale bearing does not increase monotonically with the operation speed. This is attributed to the change of the local shear rate, which will decrease with the shear velocity of the bearing as the shear velocity exceeds a critical value, i.e., the local shear rate has an upper limit. A simple nonlinear dynamic model indicates that the momentum exchange between the liquid and the solid wall is reduced with the shear velocity when the shear velocity is above a critical value. The weak momentum exchange results in a decrease of the local shear rate, which in turn causes a sharp increase of the slip length.

Nonlinear statistical modeling and model discovery for cardiorespiratory data.

We present a Bayesian dynamical inference method for characterizing cardiorespiratory (CR) dynamics in humans by inverse modeling from blood pressure time-series data. The technique is applicable to a broad range of stochastic dynamical models and can be implemented without severe computational demands. A simple nonlinear dynamical model is found that describes a measured blood pressure time series in the primary frequency band of the CR dynamics. The accuracy of the method is investigated using model-generated data with parameters close to the parameters inferred in the experiment. The connection of the inferred model to a well-known beat-to-beat model of the baroreflex is discussed.

Role of the hydrological cycle in regulating the planetary climate system of a simple nonlinear dynamical model

Abstract. We present the construction of a dynamic area fraction model (DAFM), representing a new class of models for an earth-like planet. The model presented here has no spatial dimensions, but contains coupled parameterizations for all the major components of the hydrological cycle involving liquid, solid and vapor phases. We investigate the nature of feedback processes with this model in regulating Earth's climate as a highly nonlinear coupled system. The model includes solar radiation, evapotranspiration from dynamically competing trees and grasses, an ocean, an ice cap, precipitation, dynamic clouds, and a static carbon greenhouse effect. This model therefore shares some of the characteristics of an Earth System Model of Intermediate complexity. We perform two experiments with this model to determine the potential effects of positive and negative feedbacks due to a dynamic hydrological cycle, and due to the relative distribution of trees and grasses, in regulating global mean temperature. In the first experiment, we vary the intensity of insolation on the model's surface both with and without an active (fully coupled) water cycle. In the second, we test the strength of feedbacks with biota in a fully coupled model by varying the optimal growing temperature for our two plant species (trees and grasses). We find that the negative feedbacks associated with the water cycle are far more powerful than those associated with the biota, but that the biota still play a significant role in shaping the model climate. third experiment, we vary the heat and moisture transport coefficient in an attempt to represent changing atmospheric circulations.