Implicit Integrators for Linear Dynamics Coupled to a Nonlinear Static Feedback and Application to Wind Turbine Control

In this paper, we propose a real-time nonlinear model predictive control (NMPC) strategy for stabilization of a vehicle near the limit of lateral acceleration using the rear axle electric torque vectoring configuration of an electric vehicle. A nonlinear four-wheel vehicle model that neglects the wheel dynamics is coupled with a nonlinear tire model to design three MPC strategies of different levels of complexity that are implementable online: one that uses a linearized version of the vehicle model and then solves the resulting quadratic program problem to compute the necessary longitudinal slips on the rear wheels, a second one that employs the real-time iteration scheme on the NMPC problem, and a third one that applies the primal dual interior point method on the NMPC problem instead until convergence. Then, a sliding mode slip controller is used to compute the necessary torques on the rear wheels based on the requested longitudinal slips. After analyzing the relative tradeoffs in performance and computational cost between the three MPC strategies by comparing them against the optimal solution in a series of simulation studies, we test the most promising solution in a high-fidelity environment.

The role of time integration in energy conservation in Smoothed Particle Hydrodynamics fluid dynamics simulations

In this study, a linearization approach is used to develop an implicit integration scheme for the high-temperature inelastic constitutive models based on non-linear kinematic hardening. A non-unified model is first considered in which inelastic strain rate is divided into the transient and steady parts driven, respectively, by effective stress and applied stress. By discretizing the constitutive relations using the backward Euler method, and by linearizing the resulting discretized relations, a tensor equation is derived to iteratively achieve the implicit integration of constitutive variables. The implicit integration scheme developed is shown to be applicable to a unified constitutive model in which back stress evolves due to static and dynamic recoveries in addition to strain hardening. The integration scheme is then programmed as a subroutine in a finite element code and applied to a lead-free solder joint analysis. It is thus demonstrated that the integration scheme affords the quadratic convergence of iteration even for considerably large increments, and that the non-unified and unified models give almost the same results as each other in the joint analysis.

Physics-Based Self-Learning Recurrent Neural Network enhanced time integration scheme for computing viscoplastic structural finite element response

For an efficient chemical reaction and a safe operation for both stationary and dynamic loads all values of anode and cathode gas pressures and stack temperature must fall within specific ranges. System error can result in values outside of these ranges, in turn causing serious damage to the fuel cell (FC). In addition the energy supply by the FC is at risk, because an emergency shutdown is possible. Therefore it is necessary to implement strategies for handling error cases in order to ensure safe operation. A common method for controlling the operation of PEM FC is a model predictive control, which allows for fault tolerance. In literature, error handling strategies are only considered for special parts of FC, but not for the whole system. This paper deals with real-time nonlinear model predictive control (NMPC) of electrical power with applied error handling strategies for a PEM FC system. Different types of errors are discussed in connection with various solution approaches. This fault tolerant NMPC handles all kinds of dynamic load changes and allows a safe operation of the FC in the event of errors, while maximizing power efficiency. Any emergency shutdown is not necessary and energy supply is still guaranteed. All experiments were verified on a test bench with a 4.4kW PEM FC.

This paper presents the implementation and experimental validation of a central control framework. The presented framework addresses the need for a controller, which provides high performance combined with a low-computational load while being on-line adaptable to changes in the control scenario. Examples for such scenarios are cooperative control, task-based control and fault-tolerant control, where the system's topology, dynamics, objectives and constraints are changing. The framework combines a fast Nonlinear Model Predictive Control (NMPC), a communication interface with the Robot Operating System (ROS) as well as a modularization that allows an event-based change of the NMPC scenario. To experimentally validate performance and event-based adaptability of the framework, this paper is using a cooperative control scenario of Unmanned Aerial Vehicles (UAVs).

Energy-efficient lane-change motion planning for personalized autonomous driving

Nonlinear Model Predictive Control for Ecological Driver Assistance Systems in Electric Vehicles

In the current work, a fully implicit numerical integration scheme is developed for modeling twinning-induced plasticity using a crystal plasticity framework. Firstly, the constitutive formulation of a twin-based micromechanical model is presented to estimate the deformation behavior of steels with low stacking fault energy. Secondly, a numerical integration scheme is developed for discretizing constitutive equations through a fully implicit time integration scheme using the backward Euler method. A time sub-stepping algorithm and the two-norm convergence criterion are used to regulate time step size and stopping criterion. Afterward, a numerical scheme is implemented in finite element software ABAQUS as a user-defined material subroutine. Finally, finite element simulations are executed for observing the validity, performance, and limitations of the numerical scheme. It is observed that the simulation results are in good agreement with the experimental observations with a maximum error of 16% in the case of equivalent stress and strain. It is also found that the developed model is able to estimate well the deformation behavior, magnitude of slip and twin shear strains, and twin volume fraction of three different TWIP steels where the material point is subjected to tension and compression.

Comparative studies on the performances of implicit and explicit integration schemes are conducted for a double structure hydro-mechanical coupling model of unsaturated expansive clays at an integration point level. The published constitutive model is built on the basis of two pore levels in expansive clay. In this paper, firstly, the implicit and explicit schemes based on the Euler backward and forward integration algorithms are proposed. These schemes can deal with multi-plastic mechanisms defined in the model and distinguish various cases in relation to the number of plastic mechanism active. Secondly, the performances of the integration schemes are demonstrated by comparisons of calculation results of a control-strain test with different strain increment sizes.

A finite element-peridynamic combined multiscale analysis strategy based on implicit integration scheme

Stress integration schemes for elastoplastic constitutive relations for homogeneous materials have been extensively proposed by several researchers during the last two decades. In this paper, a set of micromechanics equations are formulated based on the Transformation Field Analysis (TFA) method. When integrating the constitutive relation of fibrous composites, an implicit integration scheme, namely the Governing Parameter Method (GPM) is employed to provide the overall elastoplastic stress-strain relations for n-phase fiber-reinforced composites using the J 2-plasticity with strain hardening. This integration scheme is employed instead of the conventional explicit stress integration scheme because it only needs to solve a nonlinear algebraic equation instead of a 6 × (n + 1) system of differential-algebraic equations. The proposed integration scheme can accommodate other complex plasticity models as well. More importantly, the combined TFA and GPM approach can also be used as a constitutive model for use in nonlinear finite element method to analyze structural response.

Unlike steady-state optimization and linear model predictive control, dynamic optimization and nonlinear model predictive control is underway to industry application. This paper discusses the implementation issues of two-level control strategy integrated dynamic real-time optimization and nonlinear model predictive control of a heat-integrated distillation column system. To realize this scheme, four nonlinear programming problems: economic operation optimization, data reconciliation and state estimation, parameter estimation and nonlinear model predictive control, are considered based on system rigorous dynamic model. The economic operation optimization is to minimize the cost of the plant. The unmeasured states are estimated by measurements of temperatures, pressures and flow rates. Time-variant parameters such as tray efficiencies and feed composition are updated on-line. The sequential quadratic programming and orthogonal collocation are used to solve the dynamic nonlinear optimization problems.

A tendon-driven robot inspired from the bird neck is studied in this paper. The objective is to propose numerical integrations for this robot. The classical explicit and implicit Euler integration schemes can be used on this robot. When the elasticity in the tendons is not considered, these schemes are stable and give similar numerical integration results but the explicit implementation is faster. By considering the dynamics of the robot joints on one hand and the dynamics of the motors on the other hand, we propose two Euler integration schemes, explicit and implicit, that take into account the elasticity in the tendons. These schemes rely on the dynamics of the robot joints on the one hand, and on the dynamics of the motors on the other hand and it links them by the tendon elastic model. We observe that with the tendon elasticity model, the explicit integration becomes unstable, depending on the time step, while the implicit one stays stable. The numerical integration that uses this implicit scheme with tendon elasticity allows one to obtain more precise results, while the model of the system is more realistic. Moreover, the evolution of the tendon elongation during a desired motion can be obtained while they are computed in the integration scheme.

Finite element implementation of virtual internal bond model for simulating crack behavior