SciCADE 95: International conference on scientific computation and differential equations

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included

A direct method for trajectory optimization of rigid bodies through contact

Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform.United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation Program (Grant W91CRB-11-1-0001)National Science Foundation (U.S.) (Grant IIS-0746194)National Science Foundation (U.S.) (Grant IIS-1161909)National Science Foundation (U.S.) (Grant IIS-0915148

Control and Simulation of Photovoltaic Power Plants in OpenModelica

As solar generation increases globally, there exists a need for innovation and increased operational flexibility. In Photovoltaic Power Plants (PVPPs) and Large Scale Photovoltaic Power Plants (LS-PVPPs) the challenges increase due to the necessity to integrate them into the electrical system. To ensure the stability and reliability in the electricity supply, power systems require complex dynamic analysis. Therefore, to carry out these analysis, modelling and simulation tools are needed. This thesis focuses on the control and operation of PVPPs in OpenModelica, a free and open-source modelling and simulation environment based on Modelica language. In the later part, OpenModelica potential in large-scale power systemoriented models is investigated. These issues are addressed by a literature review concerning photovoltaic power systems and OpenModelica functionality, a theoretical analysis of a photovoltaic inverter and a LS-PVPP, and detailed simulations. The models are tested under variations in the active and reactive power requirements. The results show an optimal dynamic response and the capacity to perform independent active and reactive power controls. As an outcome, OpenModelica is a promising tool for power system modelling and simulation even though existing barriers and difficulties must be overcome

On the Statics, Dynamics, and Stability of Continuum Robots: Model Formulations and Efficient Computational Schemes

This dissertation presents advances in continuum-robotic mathematical-modeling techniques. Specifically, problems of statics, dynamics, and stability are studied for robots with slender elastic links. The general procedure within each topic is to develop a continuous theory describing robot behavior, develop a discretization strategy to enable simulation and control, and to validate simulation predictions against experimental results.Chapter 1 introduces the basic concept of continuum robotics and reviews progress in the field. It also introduces the mathematical modeling used to describe continuum robots and explains some notation used throughout the dissertation.The derivation of Cosserat rod statics, the coupling of rods to form a parallel continuum robot (PCR), and solution of the kinematics problem are reviewed in Chapter 2. With this foundation, soft real-time teleoperation of a PCR is demonstrated and a miniature prototype robot with a grasper is controlled.Chapter 3 reviews the derivation of Cosserat rod dynamics and presents a discretization strategy having several desirable features, such as generality, accuracy, and potential for good computational efficiency. The discretized rod model is validated experimentally using high speed camera footage of a cantilevered rod. The discretization strategy is then applied to simulate continuum robot dynamics for several classes of robot, including PCRs, tendon-driven robots, fluidic actuators, and concentric tube robots.In Chapter 4, the stability of a PCR is analyzed using optimal control theory. Conditions of stability are gradually developed starting from a single planar rod and finally arriving at a stability test for parallel continuum robots. The approach is experimentally validated using a camera tracking system.Chapter 5 provides closing discussion and proposes potential future work

Efficient Trajectory Optimization for Curved Running Using a 3D Musculoskeletal Model With Implicit Dynamics

Trajectory optimization with musculoskeletal models can be used to reconstruct measured movements and to predict changes in movements in response to environmental changes. It enables an exhaustive analysis of joint angles, joint moments, ground reaction forces, and muscle forces, among others. However, its application is still limited to simplified problems in two dimensional space or straight motions. The simulation of movements with directional changes, e.g. curved running, requires detailed three dimensional models which lead to a high-dimensional solution space. Weextended a full-body three dimensional musculoskeletal model to be specialized for running with directional changes. Model dynamics were implemented implicitly and trajectory optimization problems were solved with direct collocation to enable efficient computation. Standing, straight running, and curved running were simulated starting from a random initial guess to confirm the capabilities of our model and approach: efficacy, tracking and predictive power. Altogether the simulations required 1 h 17 min and corresponded well to the reference data. The prediction of curved running using straight running as tracking data revealed the necessity of avoiding interpenetration of body segments. In summary, the proposed formulation is able to efficiently predict a new motion task while preserving dynamic consistency. Hence, labor-intensive and thus costly experimental studies could be replaced by simulations for movement analysis and virtual product design

ReMKiT1D -- A framework for building reactive multi-fluid models of the tokamak Scrape-Off Layer with coupled electron kinetics in 1D

In this manuscript we present the recently developed flexible framework for building both fluid and electron kinetic models of the tokamak Scrape-Off Layer in 1D - ReMKiT1D (Reactive Multi-fluid and Kinetic Transport in 1D). The framework can handle systems of non-linear ODEs, various 1D PDEs arising in fluid modelling, as well as PDEs arising from the treatment of the electron kinetic equation. As such, the framework allows for flexibility in fluid models of the Scrape-Off Layer while allowing the easy addition of kinetic electron effects. We focus on presenting both the high-level design decisions that allow for model flexibility, as well as the most important implementation aspects. A significant number of verification and performance tests are presented, as well as a step-by-step walkthrough of a simple example for setting up models using the Python interface

Dynamic analysis of astronaut motions in microgravity: Applications for Extravehicular Activity (EVA)

Simulations of astronaut motions during extravehicular activity (EVA) tasks were performed using computational multibody dynamics methods. The application of computational dynamic simulation to EVA was prompted by the realization that physical microgravity simulators have inherent limitations: viscosity in neutral buoyancy tanks; friction in air bearing floors; short duration for parabolic aircraft; and inertia and friction in suspension mechanisms. These limitations can mask critical dynamic effects that later cause problems during actual EVA's performed in space. Methods of formulating dynamic equations of motion for multibody systems are discussed with emphasis on Kane's method, which forms the basis of the simulations presented herein. Formulation of the equations of motion for a two degree of freedom arm is presented as an explicit example. The four basic steps in creating the computational simulations were: system description, in which the geometry, mass properties, and interconnection of system bodies are input to the computer; equation formulation based on the system description; inverse kinematics, in which the angles, velocities, and accelerations of joints are calculated for prescribed motion of the endpoint (hand) of the arm; and inverse dynamics, in which joint torques are calculated for a prescribed motion. A graphical animation and data plotting program, EVADS (EVA Dynamics Simulation), was developed and used to analyze the results of the simulations that were performed on a Silicon Graphics Indigo2 computer. EVA tasks involving manipulation of the Spartan 204 free flying astronomy payload, as performed during Space Shuttle mission STS-63 (February 1995), served as the subject for two dynamic simulations. An EVA crewmember was modeled as a seven segment system with an eighth segment representing the massive payload attached to the hand. For both simulations, the initial configuration of the lower body (trunk, upper leg, and lower leg) was a neutral microgravity posture. In the first simulation, the payload was manipulated around a circular trajectory of 0.15 m radius in 10 seconds. It was found that the wrist joint theoretically exceeded its ulnal deviation limit by as much as 49. 8 deg and was required to exert torques as high as 26 N-m to accomplish the task, well in excess of the wrist physiological limit of 12 N-m. The largest torque in the first simulation, 52 N-m, occurred in the ankle joint. To avoid these problems, the second simulation placed the arm in a more comfortable initial position and the radius and speed of the circular trajectory were reduced by half. As a result, the joint angles and torques were reduced to values well within their physiological limits. In particular, the maximum wrist torque for the second simulation was only 3 N-m and the maximum ankle torque was only 6 N-m

A preconditioned Krylov subspace approach to a tightly coupled aeromechanical system

A tightly coupled approach is attempted to compute a modest fluid-structure interaction for high subsonic flow through a converging nozzle with deformable walls. A globally convergent Newton statement and a matrix-free GMRES linear equation solver are used to linearize and solve the coupled system of equations without explicitly forming the left hand side jacobian matrix associated with the Newton method. A variable forcing function term is successfully incorporated into the Newton statement to balance inner (linear) and outer (nonlinear) iterations. The fluid-structure system is solved for comparison purposes using a loosely coupled approach. Residual convergence stagnated in the tightly coupled system approach but converged successfully in the loosely coupled approach using the same coding for domain calculations. A novel approach using time derivative preconditioning is incorporated to speed convergence of the GMRES linear equation solver. No algebraic preconditioning is used. The fluid flow equations showed significant improvements using the time derivative preconditioning method but the error term generated in the structural equations overwhelmed the physical solution increment. The Taylor Weak Statement derivation of the finite element form of the fluid flow equations with time derivative preconditioning shows a strong connection to the Streamwise Upwind Petrov Galerkin (SUPG) method. This connection is exploited to develop a theoretical basis for the damping term and the time scale parameter common to the SUPG method

A High-Power Medium-Voltage Open-Loop Induction Motor Drive for Industry Applications: Stability Analysis and Implementation

Due to their several advantages, induction motors are widely used for industrial applications today. The present study focuses on developing a robust high-power induction motor variable frequency drive. In order to test the algorithms of the motor control on an actual induction motor, it is important to first carry out simulation tests to verify and troubleshoot the control strategy. One of the most common software used for such a need is MATLAB/Simulink. To run such experiments requires a significant simulation time and at the same time must satisfy a certain level of accuracy. Therefore, one of the objectives of the thesis is to carry out a study on some of the ODE solvers of MATLAB/Simulink to choose the most efficient solver for the simulation tests of the motor control strategy. The fixed step solvers ode1, ode2 and ode4 and the variable step solvers ode45, ode113 and ode23 are studied in terms of the actual time taken to complete the simulations and the relative tolerance of each solver. Comparing the performance of the fixed step and variable step solvers it is evident that the variable step solvers outperformed the fixed step solvers in terms of both speed and accuracy. One of the most famous speed control strategies is the open loop V/Hz control. In this control method two modulation techniques were studied. This was the asynchronous modulation technique and the synchronous modulation technique. With the use of the asynchronous modulation technique subharmonics are introduced. To avoid the introduction of such harmful subharmonics the synchronous modulation technique is proposed. The synchronous modulation technique is implemented with the open loop V/Hz control strategy and simulation tests were carried out to verify the problem of subharmonics being removed. Another problem encountered with the open loop V/Hz control strategy is the presence of large current and torque oscillations of the motor at low to medium frequencies. This is due to the nonlinear interactions between the electrical and mechanical subsystems. To mitigate these unwanted oscillations a stability analysis of the open loop V/Hz control is carried out and a region of instability is determined. Two mitigation techniques are proposed in this thesis namely varying slope V/Hz control strategy and the active damping control strategy. The proposed techniques are verified and validated through simulation tests on a 7 MW medium voltage (MV) induction motor in MATLAB/Simulink and on a low voltage (LV) induction motor in laboratory without a mechanical load. Moreover, in this thesis it has been examined that with the consideration of the magnetic saturation of the motor, more stable operations are achieved. This is firstly verified in simulation where considering the magnetic saturation allowed the use of higher flux values providing more stable machine operations while at the same time allowing for a larger torque. With the experimental test on a 10-kW induction motor it was proved that the results obtained through simulations where more stable operations were seen as the value of the flux were increased were correct. In the power applications such as the ac-dc conversion for the above mentioned 7 MW medium voltage induction motor, a high total harmonic distortion (THD) can be seen in the primary currents with the use of the conventional diode-based ac-dc conversion. In addition, such a conversion does not permit the control of the dc link voltage and has not power factor correction. To overcome these shortcomings the Active Front End rectifier which uses IGBTs that can be electronically controlled is used. In the AFE, the waveform of the input current is monitored and is shaped to be sinusoidal as a result decreasing the THD. Another significant advantage of the AFE rectifier is its capability to handle regenerative power. In this thesis, two configurations of the AFE rectifier are studied. These two configurations include firstly the development of the AFE rectifier using a two-level three-phase inverter and secondly the development of the AFE rectifier with single phase H-bridge cells. From the comparison of the performance of the two configurations of the AFE it is seen that the AFE realised with the H Bridge cells and phase shifted secondary was the best in terms of the THD and the dc link voltage ripple. From these results the AFE realised with H Bridge circuits and phase shifted secondary is chosen for the operation of a real high-power induction motor controlled with the open loop V/Hz control strategy and equipped with the active damping technique for mitigating the current and torque oscillations