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Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

Abstract Real-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the gradient-based optimization methodology for multibody dynamic systems with joint friction using a direct sensitivity approach. The Brown–McPhee model has been used to characterize the joint friction in the system. This model is suitable for the study due to its accuracy for dynamic simulation and its compatibility with sensitivity analysis. This novel methodology supports codesign of the multibody system and its controller, which is especially relevant for applications like robotics and servo-mechanical systems, where the actuation and design are highly dependent on each other. Numerical results are obtained using a software package written in Julia with state-of-the-art libraries for automatic differentiation and differential equations. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applications.

Verulkar, Adwait

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER

Applications of Multibody for Everybody (M4E) in Marine Energy

Multibody for Everybody (M4E) is an open-source symbolic dynamics modeling framework designed to automate the derivation of equations of motion and simulation of constrained multibody systems using the joint coordinate formulation.

16 TIDAL AND WAVE POWER

Hydrodynamic characterization of the coastal pioneer array ocean observing system

Ocean observation buoys require relatively small amounts of power, yet traditionally necessitate costly resupply trips for battery replacement. With the offshore location of the buoys and small power requirements, wave energy may be an effective solution for providing consistent and reliable power to support the buoy instrumentation. The US National Science Foundation Ocean Observatories Initiative (OOI) includes arrays of point absorber-like buoy systems used for ocean observation that have been deployed at multiple locations including the Southern Mid-Atlantic Bight. A study is currently underway to design a pitch resonator wave energy converter to supplement existing renewable energy generation for powering observation instrumentation. This paper details field measurements from surface moorings of the OOI Coastal Pioneer Array, which informs the subsequent development of a numerical model for the moored observation system. The model is developed in Wave Energy Converter Simulator (WEC-Sim), which leverages the Simscape multibody solver within the MATLAB/Simulink framework and linear potential flow theory to simulate the hydrodynamic interactions and multibody dynamics in 6 degrees of freedom. Multiple tuning variables are considered to produce a model for the system that matches well with empirical data (about 8% error). In conclusion, the WEC-Sim model will serve as a platform for integrating the pitch resonator wave energy converter concept and deployment preparation (detailed design including power take-off and control systems, response evaluation, etc.).

hydrodynamic modeling

Numerical Modeling & Optimization of the iProTech Pitching Inertial Pump (PIP) Wave Energy Converter (WEC) (CRADA Final Report)

This project represents a continuation of the collaboration between iProTech and NLR to simulate, optimize and design the iProTech Pitching Inertial Pump (PIP) device. The objectives of this TEAMER project are twofold: 1. Refining the physical characteristics of the existing iProTech PIP WEC-Sim model to enhance the model’s fidelity and include controllable components. Key model enhancements target the inclusion of Coulomb friction, the introduction of a controllable bypass valve, and the replacement of traditional check valves with advanced motorized ones. 2. Exploring traditional and advanced control algorithms. From traditional methods like latching control to cutting-edge reinforcement learning (RL) algorithms, the goal is to ensure the PIP device's adaptability and optimal performance across a range of ocean conditions. NLR is tasked with augmenting the WEC-Sim model and implementing the control algorithms, culminating in performance comparison analyses. iProTech will update their existing 3D models, advise on model improvements, and determine crucial system metrics. WEC-Sim, developed in MATLAB/SIMULINK with Simscape Multibody, is the main piece of software that will be used in this project. Coupled with the MATLAB RL Toolbox, it offers a robust platform for in-depth simulation and optimization of the iProTech PIP device. Building on previous work to explore the PIP design space and optimize its geometry, mass distribution, center of gravity and other key parameters, this project aims to refine iProTech’s existing numerical models and develop effective control algorithms that can seamlessly integrate into their future hardware testing campaigns.

16 TIDAL AND WAVE POWER

Introducing Kynema, an Open-Source Performance-Portable Flexible-Multibody-Dynamics Solver

In this talk we introduce Kynema, an open-source general flexible-multibody-dynamics solver that is well suited for simulating wind turbine structural dynamics. Kynema uses a Lie-group time integrator for constrained systems and runs on both CPUs and GPUs. Timing results for simulations are presented for the IEA 15-MW turbine with and without aerodynamic forces.

17 WIND ENERGY

Investigation of Main Bearing Fatigue Estimate Sensitivity to Synthetic Turbulence Models Using a Novel Drivetrain Model Implemented in OpenFAST

ABSTRACT A coupled medium‐fidelity drivetrain model is developed and implemented in OpenFAST for a 10‐MW land‐based reference turbine. The implementation is verified against a fully coupled multibody wind turbine model, including a detailed drivetrain. The new model can simultaneously and accurately estimate main bearing loads and represent elastic bending of the drivetrain. It has low computational cost and is useful for early design phases, sensitivity analyses and complex systems like wind farms (where computational expense must be expended elsewhere). Here, the model is implemented for a monopile offshore wind turbine and used to investigate the sensitivity of main bearing basic rating life to different synthetic turbulence models. Large‐eddy simulations (LES) targeting stable, neutral, and unstable atmospheric conditions at below‐, near‐ and above‐rated wind speeds are used as a reference. The turbulence models recommended by the International Electrotechnical Commission, the Mann spectral tensor model, and the Kaimal spectral model with exponential coherence are fitted to the LES data. Additionally, a constrained turbulence generator, PyConTurb (short for Python Constrained Turbulence ), based on LES data, is applied in the aero‐hydro‐servo‐elastic simulations. Taking PyConTurb as the baseline, the Kaimal model significantly underestimates fatigue of the downwind main bearing, with between 10% and 40% less damage. The Mann model also underestimates the downwind main bearing fatigue by up to 30%. The upwind main bearing damage is driven by mean loads, and differences between models are less significant, although the trends are similar. Reasons for these discrepancies are investigated and attributed to differences in spatial and temporal variations among the turbulence models.

17 WIND ENERGY

A Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet‐Neumann Schwarz Alternating Method

Contact phenomena are crucial for understanding the behavior of mechanical systems. However, existing computational approaches for simulating mechanical contact often face numerical challenges, such as inaccurate physical predictions, energy conservation errors, and unwanted oscillations. Here, we introduce an alternative technique for simulating dynamic contact based on the non‐overlapping Schwarz alternating method, originally developed for domain decomposition. In multibody contact scenarios, this method treats each body as a separate, non‐overlapping domain and prevents interpenetration using an alternating Dirichlet–Neumann iterative process. This approach has a strong theoretical foundation, eliminates the need for contact constraints, and offers flexibility, making it ideal for multiscale and multiphysics applications. We conducted a numerical comparison between the Schwarz method and traditional methods, such as the Lagrange multiplier and penalty methods, focusing on a benchmark impact problem. Our results indicate that the Schwarz alternating method outperforms traditional methods in several key areas: it provides more accurate predictions for various measurable quantities and demonstrates exceptional energy conservation capabilities. To address unwanted oscillations in contact velocities and forces, we explored various algorithms and stabilization techniques, ultimately opting for the naïve‐stabilized Newmark scheme for its simplicity and effectiveness. Additionally, we validated the efficiency of the Schwarz method in a three‐dimensional impact problem, highlighting its inherent capacity to accommodate different mesh topologies, time‐integration schemes, and time steps for each interacting body.

Schwarz alternating method

Multibody for Everybody (M4E) - A Linearization Approach to Enable Frequency Domain Analysis, Time Integration and Control Co-Design

1.1 Background/Objectives: Marine energy represents a promising yet underexploited source of power. To increase the harvested power, significant efforts have been made to improve wave energy converter (WEC) modeling capabilities and optimize power take-off (PTO) performance; however, these efforts have often treated WEC dynamics, PTO design, and controller development sequentially. In contrast, control co-design (CCD) is emerging as a promising strategy to address these issues directly, creating a growing need for fast analysis tools suitable for repeated simulation and parametric studies [1]. To support this need, this work presents the Multibody for Everybody (M4E) [2] linearization module, which employs a symbolic toolbox to provide deeper insight of WEC design parameters. The objective is to demonstrate that a minimal-coordinate linearization of articulated WEC dynamics can provide accurate wave response predictions and substantial computational savings relative to nonlinear time-domain simulation, while preserving compatibility with broader wave-energy analysis workflows, enabling CCD. 1.2 Approach/Activities: The proposed approach linearizes the equations of motion, generated by M4E, in minimal coordinates about a selected operating point and combines the resulting system with frequencydomain hydrodynamic terms to incorporate the reduced mass, damping, stiffness, and forcing operators. The linearized model is used for both impedance-based response amplitude operator (RAO) prediction and rapid regular-wave time integration. The methodology is demonstrated on a single-flap device and a FOSWEC configuration, with linearized M4E responses compared against the corresponding nonlinear M4E simulations and WEC-Sim results. Regular-wave time histories, RAO trends, and runtime differences are assessed. The framework is also compatible with broader wave-energy workflows, including coupling to WecOptTool, although that capability is not the focus of this work [3]. 1.3 Results/Lessons: The linearized M4E model reproduces key regularwave response characteristics such as integration and Response Amplitude over multiple frequencies. This module matches nonlinear M4E and WEC-Sim results while substantially reducing integration cost. Thus, the proposed framework can serve as a rapid analysis layer for articulated WEC design, parameter studies, and controls-oriented workflows. The analysis is most appropriate in the near-equilibrium regime, about the linearization point.

16 TIDAL AND WAVE POWER

Tunable Collective Excitations in Epitaxial Perovskite Nickelates

The formation of plasmons through the collective excitation of charge density has generated intense discussions, offering insights to fundamental sciences and potential applications. While the underlying physical principles have been well-established, the effects of multibody interactions and orbital hybridization on plasmonic dynamics remain understudied. Here, in this work, we present the observation of conventional metallic and correlated plasmons in epitaxial La 1-x Sr x NiO 3 (LSNO) films with varying Sr doping concentrations (x = 0, 0.125, 0.25), unveiling their intriguing evolution. Unlike samples at other doping concentrations, the x = 0.125 intermediate doping sample does not exhibit the correlated plasmons despite showing high optical conductivity. Through experimental investigation using spectroscopic ellipsometry and X-ray absorption spectroscopy, that is further supported by theoretical calculations, the O2p-Ni3d orbital hybridization for x = 0.125 is found to be significantly enhanced, alongside a considerable weakening of its effective interaction comprising long-range Coulomb and variable interaction, U*. These factors account for the absence of correlated plasmons and the high optical conductivity observed in LSNO(0.125). Our findings highlight the significant impact of orbital hybridization on the electronic structures and the formation of quasiparticles in strongly correlated systems, opening new paths for plasmonic-based engineering research.

36 MATERIALS SCIENCE

Multilevel Conditional Disturbance Rejection Control for Satellite Attitude Tracking

Recently, the conditional disturbance rejection controller (CDRC) was proposed to improve control performance by leveraging disturbances that have beneficial effects on the system. However, it only considers disturbances acting on the state variable directly influenced by them. Although fast convergence of this state can be achieved with the CDRC, it may unintentionally affect the convergence of the output (i.e., the primary state). Here, in this article, a multilevel CDRC is proposed to enhance satellite attitude control performance by accounting for the effect of disturbances on both attitude (output) and angular velocity. The extended state observer is employed to estimate the lumped disturbance, including the modeling errors and external disturbances. Then, a backstepping-based controller with the multilevel disturbance rejection law (ML-DRL) is designed for attitude tracking. The ML-DRL is developed to improve the control performance by using a disturbance with a damping effect on both attitude and velocity. Faster convergence of attitude and velocity can be achieved by conditionally compensating for the disturbance. The stability of the proposed control method is analyzed by demonstrating that the errors are bounded as time tends to infinity. The attitude control performance of the proposed method is evaluated through numerical examples conducted using the MATLAB/Simulink Multibody tool.

Active disturbance rejection control (ADRC)