Nonlinear Simulation Results Research Articles

Smart homing guidance strategy with control saturation against a cooperative target-defender team

A smart homing guidance strategy with control saturation against a target-defender team is derived. It is noteworthy that a cooperative strategy of the target-defender team is applied, which has been proved more challenging for the homing guidance. The defender missile is launched by the target and guided by a cooperative augmented proportional navigation (APN). At the same time, the target performs a one-switch maneuver to cooperate and minimize the defender's acceleration requirement. The problem is analyzed for arbitrary-order linear dynamics of the agents in the linearized form but validated by the mathematical simulations by using nonlinear kinematics. The perfect information of three agents' states is assumed. Then, a method to deal with the target-defender team is proposed. It contains a combined performance index penalizing the miss distance relative to the target and energy consumption in the whole duration. Besides, the specific miss distance related to the defender is regarded as an inequality constraint. An analytical solution for the smart guidance strategy against the APN guided defender is derived. Meanwhile, the control saturations are introduced to get more realistic and reasonable insights to this practical target-missile-defender problem. A simple but effective iterative searching technique is proposed to determine the saturation time points. The solution provides an optimal homing strategy to evade the defender with a specific miss distance and intercept the target with the minimum miss distance in the minimum energy manner. Nonlinear two-dimensional simulation results are used to validate the theoretical analysis. By comparison with the optimal differential game guidance (ODGG) and the combined minimum effort guidance (CMEG), the superiority of this smart guidance strategy is concluded.

Barrier Lyapunov function-based integrated guidance and control with input saturation and state constraints

In this paper, input saturation and constraints of attack angle, sideslip angle and velocity deflection angle are taken into consideration in integrated guidance and control (IGC) design for skid-to-turn missile. The novel adaptive IGC scheme is proposed by combing dynamic surface control with barrier Lyapunov function (BLF). The BLF and modified saturation function are incorporated to prevent the constrained states from overstepping the constraints. To handle input saturation, auxiliary system is constructed. According to the stability analysis, all signals in closed-loop system are uniformly ultimately bounded while the constrained states remain in the constraint sets. The performance of the proposed adaptive IGC scheme is demonstrated by nonlinear numerical simulation results.

Risk of Cyber-Physical Attack via Load With Emulated Inertia Control

The intrinsic electromechanical coupling of power and frequency across a power system creates the possibility of indirect cyber-physical attacks, where the attack's impact occurs at locations far removed from the intrusion point. The work here explores this vulnerability, demonstrating mechanisms by which an attacker could cause system-wide unstable oscillations and trips of generators, by an attack altering only local control characteristics of customer loads. This extends previous work on malicious control in generator governor control loops in three ways. First, the fidelity and size of the study system is improved, with each generator represented via detailed models in a non-linear dynamic simulation. Second, we study an increasingly plausible attack, in which loads (prior to attack) are enlisted to enhance system stability through the exercise of emulated inertia control. Finally, the work demonstrates methodologies which an attacker might employ to choose the generator(s) targeted to experience large oscillations (and tripping through protective relay action) and the locations, where compromised control systems would have greatest impact. Nonlinear simulation results indicate that malicious control destabilizes the power system, with targeted generators experiencing large magnitude oscillations, and probable tripping of rate of change of frequency protective relays. These results are demonstrated as robust over variations in parameters, topology, and loading.

Passive subharmonic elimination

This paper investigates an approach to passively eliminate subharmonic responses in nonlinear oscillators forced at resonance. A general framework is developed for identifying asymptotic levels where parameter values can be passively tuned to achieve dynamic cancellation of subharmonics. The results apply to oscillators with an arbitrary nonlinear structure. Due to its breadth of application from atomic force microscopy to aeromechanics, the methodology is demonstrated using a reduced-order model for an inextensible cantilevered beam carrying a concentrated mass. The concentrated mass provides a simple opportunity to vary parameters to achieve subharmonic elimination characteristics. Nonlinear simulation results indicate that parameter choices derived from the perturbation scheme are robust for a significant range of forcing amplitudes. Limits of the harmonic elimination and the sensitivity of the result to control parameters are discussed as well.

Ordered high aspect ratio nanopillar formation based on electrical and thermal reflowing of prepatterned thin films

Creating well-ordered, submicron-sized pillars have been stated as main limitation for electrically induced patterning of nanofilms (thickness <100 nm) [1]. In our previous works, it was shown that the aspect ratio of formed nanopillars was increased to about 0.35 when thermocapillary induced instabilities (Thermally Induced Patterning, TIP) is combined with electrodynamics instabilities (Electrically Induced Patterning, EIP). However, further reduction of pillar size resulted in a coarse and randomly distributed pillars [2,3]. Here, the reflowing of initially prepatterned nanofilms are examined in the EIP and combined EIP-TIP process to create a well-ordered and high aspect ratio nanopillar arrays without sacrificing the fidelity of the final structure. The long-wave approximation is used to simplify the governing equations and boundary conditions leading to a fourth order nonlinear partial differential equation called thin film equation that describes the spatio-temporal evolution of the interface. The mechanism of pattern reflowing is discussed for both linear (initial) and nonlinear (long-term) deformations in EIP and EIP-TIP process. The optimum initial pattern width, height and the center-to-center distance is found based on the characteristic wavelength for growth of instabilities predicted by linear stability analysis and nonlinear simulation results.

Nonlinear studies of tumor morphological stability using a two-fluid flow model.

We consider the nonlinear dynamics of an avascular tumor at the tissue scale using a two-fluid flow Stokes model, where the viscosity of the tumor and host microenvironment may be different. The viscosities reflect the combined properties of cell and extracellular matrix mixtures. We perform a linear morphological stability analysis of the tumors, and we investigate the role of nonlinearity using boundary-integral simulations in two dimensions. The tumor is non-necrotic, although cell death may occur through apoptosis. We demonstrate that tumor evolution is regulated by a reduced set of nondimensional parameters that characterize apoptosis, cell-cell/cell-extracellular matrix adhesion, vascularization and the ratio of tumor and host viscosities. A novel reformulation of the equations enables the use of standard boundary integral techniques to solve the equations numerically. Nonlinear simulation results are consistent with linear predictions for nearly circular tumors. As perturbations develop and grow, the linear and nonlinear results deviate and linear theory tends to underpredict the growth of perturbations. Simulations reveal two basic types of tumor shapes, depending on the viscosities of the tumor and microenvironment. When the tumor is more viscous than its environment, the tumors tend to develop invasive fingers and a branched-like structure. As the relative ratio of the tumor and host viscosities decreases, the tumors tend to grow with a more compact shape and develop complex invaginations of healthy regions that may become encapsulated in the tumor interior. Although our model utilizes a simplified description of the tumor and host biomechanics, our results are consistent with experiments in a variety of tumor types that suggest that there is a positive correlation between tumor stiffness and tumor aggressiveness.

Power System Transient Stability Enhancement by Tuning of SSSC and PSS Parameters Using PSO Technique

In this paper, the tuning design of SSSC and PSS was examined in increasing the damping of system oscillations and improve the stability of the power system during disturbances. The design problem of the SSSC controller and PSS is designed as problem of optimization and the technique uses (PSO) technique to find for optimal control parameters. By minimizing the objective function based on the speed deviation and time domain, which deliberately deviates at the oscillation angle of the alternator rotor to improve performance of transient stability of the system. The proposed controllers are tested on the system of weak bonding ability exposed to severe disturbance. Nonlinear simulation results are presented to demonstrate the proposed controller's effectiveness and its ability to give efficient damping. It is also noted that the proposed controllers of SSSC and PSS greatly improves the power system stability.

Analytical formulations to assess the energy dissipated at the base of an offshore wind turbine jacket impacted by a ship

This paper presents some new analytical developments carried out to assess the energy dissipated plastically at the base of an offshore wind turbine jacket impacted by a ship. The jacket components involved in this mechanism are both the impacted leg and the rear leg, considered as clamped at the foundation level, as well as the horizontal bottom brace considered as rigidly fixed on the legs. The foundation system is assumed to be piles inserted into sleeves with cement grout. The base of the jacket is divided into four zones and a kinematically admissible displacement field is assumed for each of them. Based on plastic limit analysis, new analytical formulations are derived to assess the resistance and the dissipated energy for each considered area and therefore of the whole jacket base. To validate the method, full scale ship-jacket collisions are simulated both analytically and numerically and plastic energy dissipated at the base of the jacket is compared successfully with nonlinear finite element simulation results.

Multiplicative Fault Estimation‐Based Adaptive Sliding Mode Fault‐Tolerant Control Design for Nonlinear Systems

This article deals with the sliding mode fault‐tolerant control (FTC) problem for a nonlinear system described under Takagi‐Sugeno (T‐S) fuzzy representation. In particular, the nonlinear system is corrupted with multiplicative actuator faults, process faults, and uncertainties. We start by constructing the separated FTC design to ensure robust stability of the closed‐loop nonlinear system. First, we propose to conceive an adaptive observer in order to estimate nonlinear system states, as well as robust multiplicative fault estimation. The novelty of the proposed approach is that the observer gains are obtained by solving the multiobjective linear matrix inequality (LMI) optimization problem. Second, an adaptive sliding mode controller is suggested to offer a solution to stabilize the closed‐loop system despite the occurrence of real fault effects. Compared with the separated FTC, this paper provides an integrated sliding mode FTC in order to achieve an optimal robustness interaction between observer and controller models. Thus, in a single‐step LMI formulation, sufficient conditions are developed with multiobjective optimization performances to guarantee the stability of the closed‐loop system. At last, nonlinear simulation results are given to illustrate the effectiveness of the proposed FTC to treat multiplicative faults.

Damping Characteristic Analysis and Experiment of Air Suspension with Auxiliary Chamber

In this paper, the damping characteristics of air suspension with auxiliary chamber are studied. A single degree of freedom nonlinear mathematical model of air suspension with auxiliary chamber was established based on theories of aerodynamics, engineering thermodynamics and fluid dynamics. Secondly, the damping characteristics are simulated by Matlab/Simulink, and the relationship of relative damping coefficient and natural frequency with the opening degree of throttle hole under different excitation amplitude were discussed, a basic control strategy for damping control of air suspension with auxiliary chamber was proposed. Finally, the relation between valve opening and driving voltage of proportional flow control valve was studied experimentally, the hydraulic vibration test bench was set up and the damping characteristics experiment of air suspension with auxiliary chamber was carried out, the nonlinear mathematical model and simulation results were also verified at the same time. The results showed that experiment and the simulation have good consistency, verifying the correctness of the established mathematical model. The research would provide a theoretical reference for how to design and control of air suspension with auxiliary chamber.

Gain-scheduled $H_\infty$ loop-shaping autopilot design for spin-stabilized canard-guided projectiles

This article is dedicated to the design of a complete guidance & control system for the roll/pitch/yaw-channels of a 155 mm dual-spin projectile equipped with nosemounted trajectory correction canards. The projectile airframe parameter-dependent nonlinear model including aerodynamic and actuator/sensor uncertainty descriptions is given and the subsequently computed linearized models necessary for autopilot design are presented. The pitch/yaw-channel dynamics linearized system is useful for highlighting important properties specific to these dynamics, in particular in relation with the parameter vector dimension and the sensor position. The computation of a linear structured controller for the nose roll-axis and of a gain-scheduled structured compensator for the airframe pitch/yaw-axes, using an H∞ loop-shaping design approach, is detailed with the assessment of the obtained performance and robustness properties. Finally, various guided flight nonlinear 7DoF simulation results are exposed for the purpose of evaluating over the projectile flight envelope the effectiveness of the proposed guidance & control scheme.

Enhanced Electrically Induced Micropatterning of Confined Thin Liquid Films: Thermocapillary Role and Its Limitations

Electrohydrodynamic (EHD) and thermocapillary (TC) forces are used to destabilize the interface of ultra-thin liquid films and create submicron sized features. EHD instabilities result from normal component of Maxwell stress while the TC induces shear stress to the interface. In this study the accuracy of linear stability (LS) analysis for the prediction of final structures which undergo non-linear stages during pattern evolution are investigated by using new normalizing factors. Then the reason for the deviation between LS analysis and non-linear simulation results are discussed. It is found that despite the positive effect of TC in reducing the structure sizes compared to the EHD case, it causes lateral movement of pillars which results in faster coarsening in later stages of pattern formation. To control the movement of patterns and create well-ordered features, non-uniform electrostatic and TC induced instabilities of the film are examined by using ridge and square block shaped electrodes.

Nonlinear co-existence of beta-induced Alfvén eigenmodes and beta-induced Alfvén-acoustic eigenmodes

The nonlinear co-existence of β–induced Alfvén eigenmode (BAE) and β–induced Alfvén-acoustic eigenmode (BAAE) is found in simulations using the gyrokinetic toroidal code, which provides a new mechanism responsible for BAAE excitation in tokamaks. Here, the normalized pressure β is the ratio between plasma thermal pressure and magnetic pressure. The nonlinear simulation results show that the BAAE branch emerges after the BAE branch is saturated. The mode structure's evolution shows that existence of BAAE will change the original BAE mode structure. The perturbed distribution functions in the velocity phase space show that a new resonance region manifesting the wave-particle resonance in the BAAE branch appears during the nonlinear co-existence stage.

The development of magnetic field line wander by plasma turbulence

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

Analysing and modelling non‐linearity in superconducting metamaterial filter based on stepped impedance resonators

There are non-linear behaviours in superconductive circuits such as superconducting metamaterial filter. In this study, the authors propose a distributed non-linear equivalent circuit model for the superconducting metamaterial filter based on the stepped impedance resonator. This model can be used to predict the non-linear behaviours like the third-order intermodulation distortion and the harmonic generation. In the proposed non-linear model, to have an accurate prediction, the authors considered both quadratic and modulus non-linearity dependence on the current. Thereafter, this model analyses the non-linearly using harmonic balance (HB) method at different temperatures and different input powers. There are good agreements between non-linear simulation results and the measured ones. Moreover, based on the proposed model, the authors consider effects of the non-linear behaviours on main parameters in the metamaterial structures such as phase constant, attenuation factor, plasma frequency, relative permittivity and permeability. Finally, the results related to variation of these parameters at different temperatures and specific input power are presented in linear and non-linear regimes.

Ascent trajectory tracking for an air-breathing hypersonic vehicle with guardian maps

The emphasis of this article lies in the development of a gain scheduling algorithm for the constant dynamic pressure ascent trajectory. Due to the broad flight envelope and nonlinear characteristics of hypersonic vehicles, a design method of adaptive control based on guardian maps is proposed. Two types of ascent trajectory are considered: acceleration within Scram mode and acceleration across the Ram–Scram mode transition. A velocity-based linear parameter varying model of an air-breathing hypersonic vehicle is established. The gain vector of controller is determined via optimal control theory based on linear quadratic regulator technology with the specified flying qualities. With the iteration of proposed guardian maps approach, the set of controller gain vector within the flight envelope is obtained. The results of nonlinear simulation show that the proposed approach of control system design has the ability to ensure the global stability through the flight envelope and to maintain the flying qualities.

Understanding the impact of insulating and conducting endplate boundary conditions on turbulence in CSDX through nonlocal simulations

The Controlled Shear Decorrelation Experiment (CSDX) linear plasma device provides a unique platform for investigating the underlying physics of self-regulating drift-wave turbulence/zonal flow dynamics. A minimal model of 3D drift-reduced nonlocal cold ion fluid equations which evolves density, vorticity, and electron temperature fluctuations, with proper sheath boundary conditions, is used to simulate dynamics of the turbulence in CSDX and its response to changes in parallel boundary conditions. These simulations are carried out using the BOUndary Turbulence (BOUT++) framework and use equilibrium electron density and temperature profiles taken from experimental measurements. The results show that density gradient-driven drift-waves are the dominant instability in CSDX. However, the choice of insulating or conducting endplate boundary conditions affects the linear growth rates and energy balance of the system due to the absence or addition of Kelvin-Helmholtz modes generated by the sheath-driven equilibrium E × B shear and sheath-driven temperature gradient instability. Moreover, nonlinear simulation results show that the boundary conditions impact the turbulence structure and zonal flow formation, resulting in less broadband (more quasi-coherent) turbulence and weaker zonal flow in conducting boundary condition case. These results are qualitatively consistent with earlier experimental observations.

Nonlinear simulations of beam-driven compressional Alfvén eigenmodes in NSTX

Results of 3D nonlinear simulations of neutral-beam-driven compressional Alfvén eigenmodes (CAEs) in the National Spherical Torus Experiment (NSTX) are presented. Hybrid MHD-particle simulations for the H-mode NSTX discharge (shot 141398) using the HYM code show unstable CAE modes for a range of toroidal mode numbers, n=4−9, and frequencies below the ion cyclotron frequency. It is found that the essential feature of CAEs is their coupling to kinetic Alfvén wave (KAW) that occurs on the high-field side at the Alfvén resonance location. High-frequency Alfvén eigenmodes are frequently observed in beam-heated NSTX plasmas, and have been linked to flattening of the electron temperature profiles at high beam power. Coupling between CAE and KAW suggests an energy channeling mechanism to explain these observations, in which beam-driven CAEs dissipate their energy at the resonance location, therefore significantly modifying the energy deposition profile. Nonlinear simulations demonstrate that CAEs can channel the energy of the beam ions from the injection region near the magnetic axis to the location of the resonant mode conversion at the edge of the beam density profile. A set of nonlinear simulations show that the CAE instability saturates due to nonlinear particle trapping, and a large fraction of beam energy can be transferred to several unstable CAEs of relatively large amplitudes and absorbed at the resonant location. Absorption rate shows a strong scaling with the beam power.

Adaptive Control Within a Flight Envelope Protection System

An adaptive control augmentation is presented for desired systems containing a feedforward term and is applied to a controller within a flight envelope protection system for a transport-class aircraft. By recovering the baseline controller’s nominal performance in the presence of failures and disturbances, the proposed controller is able to improve aircraft performance, reducing pilot workload and allowing pilots to focus their attention on determining a course of action to prevent the offnominal condition from propagating into a loss-of-control sequence. Combined with the flight envelope protection system and other technologies, the proposed algorithm can form an integrated system for preventing aircraft loss of control. Nonlinear simulation results show the efficacy of the proposed control law.

Analysis and Performance Enhancement of Vector-Controlled VSC in HVDC Links Connected to Very Weak Grids

Voltage source converter (VSC)-based high-voltage direct current (HVDC) transmission systems have been employed widely in recent years. However, connecting a VSC-HVDC link to a very weak grid (a high-impedance grid) is challenging. A vector-controlled VSC is incapable of injecting/absorbing its maximum theoretical active power in such grids. A simple yet effective control system for a standard vector-controlled VSC in a very weak grid condition has not been reported in the literature. This paper, benefiting from a comprehensive small-signal model, presents a detailed analysis of the VSC dynamics and shows how the assumptions made for designing VSC regulators in strong grids are no longer valid in very weak grids. The paper then proposes and compares two straightforward solutions: retuning the control parameters and using an artificial bus for converter-grid synchronization. Both methods enable the VSC to operate at the maximum theoretical active power at a very weak grid condition (i.e., at unity short-circuit ratio) by minimal modification in the widely accepted vector control method. The advantages and disadvantages of each method are discussed. The analytical results are verified by detailed nonlinear time-domain simulation results.