Full Nonlinear Model Research Articles

Market Clearing and Settlement Using Participant Based Distributed Slack Optimal Power Flow Model for a Double Sided Electricity Auction Market – Part II

Even though non-linear Optimal Power Flow model proposed in part I of this paper provide accurate results there are difficulties in solving a full non-linear Optimal Power Flow model since it is a very time consuming. Due to speed and robustness, Linear Programming model is preferred by the system operators for nodal price calculations. It is a challenge to incorporate transmission losses into the losses linear DC power model. In this paper to model line flow operating limit inequality constraint a lossless Participant Based Distributed Slack DC Power Flow model is derived from Newton-Raphson state correction scheme used in part I of this work. An equivalent lumped linear model for the Participant Based Distributed Slack Lumped Nonlinear Optimal Power Flow model called Participant Based Distributed Slack Lumped Linear Optimal Power Flow model is developed in part II of this paper. The results for market clearing and settlement of double sided electricity market by the proposed lumped linear model are compared with the nonlinear model proposed in part I of this work using case studies on PJM system, IEEE 30 bus system and IEEE 118 bus system. The results obtained indicate the speed and robustness of the proposed linear model.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax–Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge–Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Modelling and Control of Gene Regulatory Networks for Perturbation Mitigation.

Synthetic Biologists are increasingly interested in the idea of using synthetic feedback control circuits for the mitigation of perturbations to gene regulatory networks that may arise due to disease and/or environmental disturbances. Models employing Michaelis-Menten kinetics with Hill-type nonlinearities are typically used to represent the dynamics of gene regulatory networks. Here, we identify some fundamental problems with such models from the point of view of control system design, and argue that an alternative formalism, based on so-called S-System models, is more suitable. Using tools from system identification, we show how to build S-System models that capture the key dynamics of an example gene regulatory network, and design a genetic feedback controller with the objective of rejecting an external perturbation. Using a sine sweeping method, we show how the S-System model can be approximated by a linear transfer function and, based on this transfer function, we design our controller. Simulation results using the full nonlinear S-System model of the network show that the synthetic control circuit is able to mitigate the effect of external perturbations. Our study is the first to highlight the usefulness of the S-System modelling formalism for the design of synthetic control circuits for gene regulatory networks.

Introduction to Koopman Mode Decomposition for Data-Based Technology of Power System Nonlinear Dynamics

Abstract Data-based technology of power system dynamics has attracted a lot of interest in the modern power system with the so-called Wide-Area Measurement System (WAMS). Concerted efforts are currently being made to develop the technology based on linearized dynamic models. In contrast, the full nonlinear models have received less attention in this research community. We present the research challenges to go beyond the conventional linear framework by focusing on Koopman Mode Decomposition (KMD), which is a nonlinear generalization of linear oscillatory modes guided by operator theory of nonlinear dynamical systems. Our discussion begins with a review of the main tools—Koopman operator and Prony approximation of KMD. We pose several distinct problems on data analysis, computation, monitoring, situational awareness, and control for the future power system architecture. Our idea is then illustrated on how the Prony approximation of KMD is distributed in WAMS.

Impact of load dynamics and load sharing among distributed generations on stability and dynamic performance of islanded AC microgrids

Microgrids comprising of inverter-interfaced distributed generation (IIDG) units can be subjected to a high penetration level of dynamic induction motor (IM) loads and rectifier interfaced active loads, which may act as constant power loads. Constant power loads present a negative incremental resistance leading to the degradation of stability. Whereas, the highly non-linear IM load, which couples voltage, supply frequency, active power and reactive power dynamics, challenges the stability of islanded AC microgrids (ACMGs). Further, the stability of these microgrids is also affected by the load sharing among IIDG units. To address the aforementioned difficulties, this paper investigates the impact of load dynamics and load sharing among IIDG units on the stability and dynamic performance of islanded ACMGs. To explore this, a full dynamical non-linear state-space model of a studied islanded AC microgrid with both static and dynamic IM loads has been developed in synchronous (DQ) reference frame. The developed non-linear state-space model is linearized around its steady-state operating point to analyze the small-signal stability. Selective modal analysis and time-domain simulation results have been presented to observe the impact of load dynamics as well as load sharing among IIDG units on the stability and dynamic performance of islanded ACMGs.

Parameter reduction in nonlinear state-space identification of hysteresis

Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of science and engineering problems. The identification of hysteretic systems from input-output data is a challenging task. Recent work on black-box polynomial nonlinear state-space modeling for hysteresis identification has provided promising results, but struggles with a large number of parameters due to the use of multivariate polynomials. This drawback is tackled in the current paper by applying a decoupling approach that results in a more parsimonious representation involving univariate polynomials. This work is carried out numerically on input-output data generated by a Bouc-Wen hysteretic model and follows up on earlier work of the authors. The current article discusses the polynomial decoupling approach and explores the selection of the number of univariate polynomials with the polynomial degree, as well as the connections with neural network modeling. We have found that the presented decoupling approach is able to reduce the number of parameters of the full nonlinear model up to about 50\%, while maintaining a comparable output error level.

An experimental and theoretical analysis of a foil-air bearing rotor system

Although there is considerable research on the experimental testing of foil-air bearing (FAB) rotor systems, only a small fraction has been correlated with simulations from a full nonlinear model that links the rotor, air film and foil domains, due to modelling complexity and computational burden. An approach for the simultaneous solution of the three domains as a coupled dynamical system, introduced by the first author and adopted by independent researchers, has recently demonstrated its capability to address this problem. This paper uses this approach, with further developments, in an experimental and theoretical study of a FAB-rotor test rig. The test rig is described in detail, including issues with its commissioning. The theoretical analysis uses a recently introduced modal-based bump foil model that accounts for interaction between the bumps and their inertia. The imposition of pressure constraints on the air film is found to delay the predicted onset of instability speed. The results lend experimental validation to a recent theoretically-based claim that the Gümbel condition may not be appropriate for a practical single-pad FAB. The satisfactory prediction of the salient features of the measured nonlinear behavior shows that the air film is indeed highly influential on the response, in contrast to an earlier finding.

Vehicle lateral control in the presence of uncertainty for lane change maneuver using adaptive sliding mode control with fuzzy boundary layer

Recent researches on advanced driver-assistance systems indicate great advances in terms of safety and comfort in automated driving. Advanced driver-assistance systems use control systems to perform most of the maneuvers as performed by the driver in the past. One of the useful advanced driver-assistance systems is automatic lane change system in order to avoid accidents. This study designs the controller of an automatic lane change system for an autonomous vehicle. The control law in this study is adaptive sliding mode control. To avoid chattering in adaptive sliding mode control, fuzzy boundary layer is used. Also, adaptive law is used for sliding-based switching gain. This adaptive controlling law is used to avoid the calculation of upper bound of system uncertainties. In this study, based on the boundary conditions, the vehicle lane change path planning and different maneuver periods are evaluated. To simulate the designed controller, CarSim–Simulink joint simulation model is used. This linkage leads to a full non-linear vehicle model. The results of simulation show excellent tracking for dry road conditions and acceptable tracking in icy and wet roads in some maneuvers of above 4-s long.

Rigid–flexible coupled dynamics analysis for solar sails

The coupled orbit, attitude, and structural dynamics are established for the sailcraft with sliding mass, which is modeled as the Euler beam and merely experiences the pitch motion. The von Karman’s nonlinear strain–displacement relation and Kelvin–Voigt model are adopted to consider the geometric nonlinearity and damping of the structure, respectively. The torques generated by the gravity gradient of the two-body sailcraft, the center-of-mass (cm) and center-of-pressure (cp) offset, the motion of the sliding mass, and the coupled attitude-vibration motion are deduced in detail, respectively. The dynamics responses influenced by the flexibility of the sail structure are examined by analyzing the simulation results for the dynamics models with (m1) and without (m2) the geometric nonlinearity and the rigid-body model (m3), respectively. The pitch responses and corresponding torques are calculated and compared for various cases adopting a range of velocities and initial positions of the sliding mass to see how the pitch motion is affected by the parameters. The transient and steady-state dynamics responses are also identified in the simulation cases. It is suggested that the full nonlinear model should be adopted for the sailcraft in long duration missions and the restricted position of the sliding mass could be selected elaborately to utilize the resultant torque by the gravitational and cm/cp torques.

Yaw moment Lyapunov based control for In-Wheel-Motor-Drive Electric Vehicle

The new generation of electric vehicles, also called in-wheel-motor-drive electric vehicles (IWM-EVs), will replace the traditional power-train by on-hub motors. Consequently, it will offer new options and flexibilities in motion control due to its structural merits, i.e the longitudinal force of each wheel could be controlled independently. This paper proposes an advanced direct yaw moment control strategy to improve IWM-EV steerability and stability. The proposed integrated control involves two coordinated standalone Lyapunov model-based controllers. Coordination is ensured according to the vehicle dynamic states evolution in the phase plane defined by the body sideslip angle and its rate. The control objective in the linear driving zone is to enhance the vehicle steering response by tracking a certain reference yaw rate. However, when the vehicle reaches the handling limits, the primary objective becomes to stabilize the vehicle while reducing a vehicle stability index. The yaw moment generated to provide control goals is then converted into four torque inputs of the four in-wheel motors. An algorithm is proposed for an effective torques distribution to maintain vehicle longitudinal velocity. Simulation results carried out on a full nonlinear IWM-EV model confirm the ability of the developed control scheme to improve vehicle handling and directional stability.

Robust H∞ Control for Autonomous Scooters

This paper studies the trajectory tracking problem for the nonlinear model of a scooter and presents a robust H∞ controller based on measurements of the tracking errors, the roll angle, the yaw angle and the steering angle. The study first introduces the full nonlinear model developed in Autosim which has 12 degrees of freedom. This is far more complex than a simple bicycle model and provides a good description of the scooter. Then a robust H∞ controller based on the linearization of the nonlinear model is designed. Finally, the effectiveness of the controller is verified by means of two case studies.

Adaptive Path-Following Control for an Unmanned Surface Vessel Using an Identified Dynamic Model

This paper proposes a path-following control method for an unmanned surface vessel (USV) based on an identified dynamic model. To handle the USV dynamic model effectively, a three degree-of-freedom model is employed instead of a full nonlinear dynamic model and linearized at specific equilibrium condition. The linearized model is identified with real data from several experiments by utilizing a particle swarm optimization method. Then, based on the identified model, an adaptive control algorithm is proposed to follow several waypoints and velocity command. The proposed control method utilizes virtual control input, dynamic surface control method, and adaptive terms to handle matched and unmatched uncertainties simultaneously. The overall closed-loop stability is analyzed by introducing deadzone errors composed of tracking error and saturation function. Finally, some experiment with a remodeled commercial fishing boat are conducted and analyzed to validate the performance of the proposed methods.

Analytical extension of the effective axle characteristics concept for the development of a structured chassis design process

ABSTRACTThe lateral vehicle dynamics is defined by the effects of side forces at the front and rear axle. These forces are caused by the slip and camber angle at the individual tyres, which are results of the kinematics and compliances of the chassis. This paper extends the approach of the effective axle characteristics by Paceyka to the analytical expression of the axle cornering stiffness and the axle relaxation behaviour with the aim of the development of a chassis design process as it applies in the early design stage. The obtained expression is integrated into a single track model and validated against a full nonlinear two-track model. By this means of these analytical expressions for the axle cornering stiffness and the axle relaxation behaviour it is possible to directly calculate and analyse the effective slip angles for linear quasi-static and dynamic driving manoeuvres.

Nonlinear trilateral teleoperation stability analysis subjected to time-varying delays

A trilateral teleoperation system facilitates the collaboration of two users to share control of a single robot in a remote environment. While various applications of shared-control trilateral haptic teleoperation systems have recently emerged, they have mostly been studied in the context of single-DOF, LTI robotic systems. On the other hand, robotic manipulators with multiple degrees of freedom (DOF) and therefore nonlinear dynamics have recently found many applications such as in robotic-assisted surgery and therapy, space exploration and navigation systems. In this paper, considering the full nonlinear dynamical models of multi-DOF robots, stability analysis of a dual-user haptic teleoperation system is considered over a communication network subjected to asymmetrical time varying delays and through a dominance factor suitable for trainer–trainee applications. Stability in free motion and contact motion and asymptotic position tracking of the trilateral haptic teleoperation system in free motion are proven via Lyapunov stability analysis and Barbalat's lemma where operators and the environment are assumed to be passive. Simulation and experimental results concerning robot position tracking and user-perceived forces for three 2-DOF robots and experimental analysis of user-perceived stiffnesses for three 3-DOF robots validate the theoretical findings pertaining to the system stability and demonstrate the efficiency of the proposed controller.

Model Predictive Control of an Underactuated Spacecraft with Two Reaction Wheels

This paper presents an application of model predictive control to the attitude dynamics of an underactuated spacecraft with two reaction wheels and zero angular momentum. Such a system cannot be stabilized by any smooth or continuous time-invariant feedback law. However, model predictive control has a remarkable ability to generate control laws that are discontinuous in the state and, as such, can be applied to this problem. The model predictive control formulation is analyzed in depth and shown to produce an asymptotically stabilizing controller, which is discontinuous and enforces constraints. Simulations on the full nonlinear model demonstrate that model predictive control can successfully control the attitude of an underactuated spacecraft when the attitude maneuvers are sufficiently small.

Linear Versus Nonlinear Response of a Cantilevered Beam Under Harmonic Base Excitation: Theory and Experiment

A computational and experimental study of a uniform cantilever beam with a tip mass under base excitation was performed. The beam was excited at various levels of base displacement to provoke tip displacements greater than 15% of the beam length. Damping and yield stress of the beam were both considered. It was found that a large tip displacement causes nonlinear inertial (NLI) and structural (NLS) effects to arise. Each of the structural and inertial nonlinearities has an opposite effect on the resulting resonance frequency, which are nearly mutually canceling. The result was that resonant frequency calculated using the full nonlinear (FNL) model was essentially equal to the value calculated by linear (LIN) theory, and the tip displacement amplitude varied only modestly from the LIN value. It was also observed that the damping in this system is likely nonlinear, and depends on tip displacement amplitude. A theoretical model for fluid damping is suggested. Initial investigation shows encouraging agreement between the theoretical fluid damping and the measured values.

Reduced-order model of cascade-type PEM fuel cell stack with integrated humidifiers and water separators

In this paper, model order reduction (MOR) of cascade-type polymer electrolyte membrane (PEM) fuel cell stack with integrated humidifiers and water separators is investigated. The purpose of this work is to attain orders of magnitude improvement in numerical simulation speed. Both the anode and the cathode of stack operate in a dead-end mode. The reduced-order model (ROM) is developed for continuous and discrete form of the cascade-type PEM fuel cell models. The obtained ROM is verified with the full nonlinear model, which full-order model itself is validated using experimental data from cascade-type 4-cells PEM fuel cell stack. Responses of different orders of ROMs are compared to those of full-order model to determine the minimum order of the model that approximates the behavior of the original model properly. The results predicted by the developed reduced-order model nearly follow the full nonlinear model and experimental results. According to the low computational cost of ROM, the derived model can be further used for real-time control and diagnostic applications.

Analysis of cornea curvature using radial basis functions – Part II: Fitting to data-set

In part I we discussed the solution of corneal curvature using a 2D meshless method based on radial basis functions (RBFs). In Part II we use these methods to fit a full nonlinear thin membrane model to a measured data-set in order to generate a topological mathematical description of the cornea. In addition, we show how these results can lead to estimations for corneal radius of curvature and certain physical properties of the cornea; namely, tension and elasticity coefficient. Again all calculations and graphics generation were performed using the R language programming environment.The model describes corneal topology extremely well, and the estimated properties fall well within the expected range of values. The method is straight forward to implement and offers scope for further analysis using more detailed 3D models that include corneal thickness.

Charge Central Interpretation of the Full Nonlinear PB Equation: Implications for Accurate and Scalable Modeling of Solvation Interactions.

Continuum solvation modeling based upon the Poisson-Boltzmann equation (PBE) is widely used in structural and functional analysis of biomolecules. In this work, we propose a charge-central interpretation of the full nonlinear PBE electrostatic interactions. The validity of the charge-central view or simply charge view, as formulated as a vacuum Poisson equation with effective charges, was first demonstrated by reproducing both electrostatic potentials and energies from the original solvated full nonlinear PBE. There are at least two benefits when the charge-central framework is applied. First the convergence analyses show that the use of polarization charges allows a much faster converging numerical procedure for electrostatic energy and forces calculation for the full nonlinear PBE. Second, the formulation of the solvated electrostatic interactions as effective charges in vacuum allows scalable algorithms to be deployed for large biomolecular systems. Here, we exploited the charge-view interpretation and developed a particle-particle particle-mesh (P3M) strategy for the full nonlinear PBE systems. We also studied the accuracy and convergence of solvation forces with the charge-view and the P3M methods. It is interesting to note that the convergence of both the charge-view and the P3M methods is more rapid than the original full nonlinear PBE method. Given the developments and validations documented here, we are working to adapt the P3M treatment of the full nonlinear PBE model to molecular dynamics simulations.

Nonlinear disturbance observer based robust backstepping control for a flexible air-breathing hypersonic vehicle

This paper presents a robust backstepping approach for a flexible air-breathing hypersonic vehicle in the longitudinal plane. The control design and stability analysis of the backstepping approach are based on a control-oriented model, which treats the flexible dynamics as dynamic perturbations. The backstepping method in this study utilizes a command filter to avoid the problem of “explosion of complexity” that occurs in the traditional backstepping method. To suppress the flexible dynamics and parameter uncertainties, a nonlinear disturbance observer is proposed to estimate these uncertainties during the tracking process. By introducing a group of virtual states, a Lyapunov-based stability analysis of the closed-loop system indicates that the tracking errors vanish asymptotically. A guideline for tuning the controller is given from a physical perspective to avoid exciting the flexible modes. This approach presents a good tracking performance with respect to both the flexible modes and parameter uncertainties. Simulation results of the full nonlinear model show the effectiveness of the proposed approach.