An α-Model Parametrization Algorithm for Optimization with Differential-Algebraic Equations

An optimization task with nonlinear differential-algebraic equations (DAEs) was approached. In special cases in heat and mass transfer engineering, a classical direct shooting approach cannot provide a solution of the DAE system, even in a relatively small range. Moreover, available computational procedures for numerical optimization, as well as differential- algebraic systems solvers are characterized by their limitations, such as the problem scale, for which the algorithms can work efficiently, and requirements for appropriate initial conditions. Therefore, an αDAE model optimization algorithm based on an α-model parametrization approach was designed and implemented. The main steps of the proposed methodology are: (1) task discretization by a multiple-shooting approach, (2) the design of an α-parametrized system of the differential-algebraic model, and (3) the numerical optimization of the α-parametrized system. The computations can be performed by a chosen iterative optimization algorithm, which can cooperate with an outer numerical procedure for solving DAE systems. The implemented algorithm was applied to solve a counter-flow exchanger design task, which was modeled by the highly nonlinear differential-algebraic equations. Finally, the new approach enabled the numerical simulations for the higher values of parameters denoting the rate of changes in the state variables of the system. The new approach can carry out accurate simulation tests for systems operating in a wide range of configurations and created from new materials.

Development of Dynamics for Design Procedure of Novel Grating Tiling Device with Experimental Validation

The article proposes a dynamic for design (DFD) procedure for a novel aperture grating tiling device using the multibody system (MBS) approach. The grating device is considered as a rigid-flexible MBS that is built primarily based totally at the load assumptions because of grating movement. This movement is utilized in many industrial applications, such as the compression of laser pulse, precision measuring instruments, and optical communication. A new design procedure of tiling grating device frame is introduced in order to optimize its design parameters and enhance the system stability. The dynamic loads are estimated based on the Lagrange multipliers that are obtained from the solution of the MBS model. This model is fully non-linear and moves in the three-dimensional space, and the relative movement of its bodies is restricted by the description of the constraints function in the motion manifold. The mechanism of the grating device is structurally analyzed in keeping with the dynamic conduct and therefore the generated forces. The symbolic manipulation as well as the computational work of solving the obtained differential-algebraic equations (DAEs) is carried out using MATLAB Symbolic Toolbox. Once the preliminary design has been attained, the stress behavior of the grating device is examined using the MATLAB FEATool Multiphysics toolkit, regarding system stability and design aspects. Moreover, the design was constructed in real life, and the movement has been verified experimentally, which confirms the effectiveness of the proposed procedure. In conclusion, the DFD procedure with trade-off optimization is utilized successfully to design the grating unit for maximum ranges of grating movements.

Computer simulation of boronizing kinetics for a TB2 alloy

The boron diffusion at the surface of a TB2 alloy was simulated via two mathematical models relying on the numerical resolutions of the system of differential algebraic equations (DAE) for the integral method and ordinary differential equations for the mean diffusion coefficient (MDC) method. Both approaches allowed us to compute the boron diffusion coefficients in TiB2 and TiB for a maximum boron content of 31.10 wt.-% in TiB2 at 1223, 1273, 1323 and 1373 K. The boron activation energies in TiB2 and TiB were evaluated and compared with the data published in the literature. Finally, an experimental validation of both models was made through a comparison of the thicknesses of the experimental layers with the predicted values. Consequently, the simulated thicknesses were in line with the experimental values.

Evaluation of Linear Implicit Quantized State System method for analyzing mission performance of power systems

The Linear Implicit Quantized State System (LIQSS) method has been evaluated for suitability in modeling and simulation of long duration mission profiles of Naval power systems which are typically characterized by stiff, non-linear, differential algebraic equations. A reference electromechanical system consists of an electric machine connected to a torque source on the shaft end and to an electric grid at its electrical terminals. The system is highly non-linear and has widely varying rate constants; at a typical steady state operating point, the electrical and electromechanical time constants differ by three orders of magnitude—being 3.2 ms and 2.7 s respectively. Two important characteristics of the simulation—accuracy and computational intensity—both depend on quantization size of the system state variables. At a quantization size of about 1% of a variable’s maximum value, results from the LIQSS1 method differed by less than 1% from results computed by well-known continuous-system state-space methods. The computational efficiency of the LIQSS1 method increased logarithmically with increasing quantization size, without significant loss of accuracy, up to some particular quantization size, beyond which the error increased rapidly. For the particular system under study, a “sweet spot” was found at a particular quantum size that yielded both high computational efficiency and good accuracy.

Mixed-mode oscillations for slow-fast perturbed systems

This article concerns the dynamics of mixed-mode oscillations (MMOs) emerging from the calcium-based inner hair cells (IHCs) model in the auditory cortex. The paper captures the MMOs generation mechanism based on the geometric singular perturbation theory (GSPT) after exploiting the average analysis for reducing the full model. Our analysis also finds that the critical manifold and folded surface are central to the mechanism of the existence of MMOs at the folded saddle for the perturbed system. The system parameters, such like the maximal calcium channels conductance, controls the firing patterns, and many new oscillations occur for the IHCs model. Tentatively, we conduct dynamic analysis combined with dynamic method based on GSPT by giving slow-fast analysis for the singular perturbed models and bifurcation analysis. In particular, we explore the two-slow-two-fast and three-slow-one-fast IHCs perturbed systems with layer and reduced problems so that differential-algebraic equations are obtained. This paper reveals the underlying dynamic properties of perturbed systems under singular perturbation theory.

Advanced Controller Development Based on eFMI with Applications to Automotive Vertical Dynamics Control

High-level modeling languages facilitate system modeling and the development of control systems. This is mainly achieved by the automated handling of differential algebraic equations which describe the dynamics of the modeled systems across different physical domains. A wide selection of model libraries provides additional support to the modeling process. Nevertheless, deployment on embedded targets poses a challenge and usually requires manual modification and reimplementation of the control system. The novel proposed eFMI Standard (Functional Mock-up Interface for embedded systems) introduces a workflow and an automated toolchain to simplify the deployment of model-based control systems on embedded targets. This contribution describes the application and verification of the eFMI workflow using a vertical dynamics control problem with an automotive application as an example. The workflow is exemplified by a control system design process which is supported by the a-causal, multi-physical, high-level modeling language Modelica. In this process, the eFMI toolchain is applied to a model-based controller for semi-active dampers and demonstrated using an eFMI-based nonlinear prediction model within a nonlinear Kalman filter. The generated code was successfully tested in different validation steps on the dedicated embedded system. Additionally, tests with a low-volume production electronic control unit (ECU) in a series-produced car demonstrated the correct execution of the controller code under real-world conditions. The novelty of our approach is that it automatically derives an embedded software solution from a high-level multi-physical model with standardized eFMI methodology and tooling. We present one of the first full application scenarios (covering all aspects ranging from multi-physical modeling up to embedded target deployment) of the new eFMI tooling.

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential–algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.