TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the ever-growing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed.

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Modeling and control of an Euler-Bernoulli beam under unknown spatiotemporally varying disturbance

Proceedings of the 2011 American Control Conference ◽

10.1109/acc.2011.5991312 ◽

2011 ◽

Author(s):

Shuzhi Sam Ge ◽

Shuang Zhang ◽

Wei He

Keyword(s):

Bernoulli Beam ◽

Modeling And Control ◽

And Control ◽

Euler Bernoulli Beam

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Modeling and Control of a Nonlinear Beam

14th Biennial Conference on Mechanical Vibration and Noise: Vibration and Control of Mechanical Systems ◽

10.1115/detc1993-0218 ◽

1993 ◽

Author(s):

H. T. Banks ◽

Belinda B. King

Keyword(s):

Linear Problem ◽

Nonlinear Stiffness ◽

Bernoulli Beam ◽

Nonlinear Beam ◽

Modeling And Control ◽

Stiffness Properties ◽

Linear Damping ◽

And Control ◽

Euler Bernoulli Beam ◽

Nonlinear Analog

Abstract In this paper we develop a mathematical model for a nonlinear analog of the Euler-Bernoulli beam which possesses linear damping and nonlinear stiffness properties. This nonlinear model is used as a basis for approximation and linearization. Feedback design for the linear problem is applied to compute gains which are then used in the nonlinear system.

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Integrated Toolkit for Closed-Loop Flow Control: Flow Simulation, Reduced-Order Modeling, and Control Design (Invited)

38th Fluid Dynamics Conference and Exhibit ◽

10.2514/6.2008-3980 ◽

2008 ◽

Author(s):

Tim Colonius ◽

Kunihiko Taira ◽

Won Joe ◽

Clancy Rowley ◽

Sunil Ahuja

Keyword(s):

Flow Control ◽

Closed Loop ◽

Control Design ◽

Flow Simulation ◽

Reduced Order Modeling ◽

Control Flow ◽

Modeling And Control ◽

Reduced Order ◽

And Control

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Asymmetric Bifurcation of Initially Curved Nanobeam

Journal of Applied Mechanics ◽

10.1115/1.4030647 ◽

2015 ◽

Vol 82 (9) ◽

Cited By ~ 7

Author(s):

X. Chen ◽

S. A. Meguid

Keyword(s):

Symmetry Breaking ◽

Degrees Of Freedom ◽

Surface Elasticity ◽

Beam Theory ◽

Surface Effects ◽

Beam Model ◽

Bernoulli Beam ◽

Reduced Order ◽

Euler Bernoulli Beam ◽

Bifurcation Behavior

In this paper, we investigate the asymmetric bifurcation behavior of an initially curved nanobeam accounting for Lorentz and electrostatic forces. The beam model was developed in the framework of Euler–Bernoulli beam theory, and the surface effects at the nanoscale were taken into account in the model by including the surface elasticity and the residual surface tension. Based on the Galerkin decomposition method, the model was simplified as two degrees of freedom reduced order model, from which the symmetry breaking criterion was derived. The results of our work reveal the significant surface effects on the symmetry breaking criterion for the considered nanobeam.

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Decentralized Control of a Tower Crane

Volume 6: International Symposium on Motion and Vibration Control ◽

10.1115/detc99/movic-8402 ◽

1999 ◽

Author(s):

Kiyoshi Takagi ◽

Hidekazu Nishimura

Keyword(s):

Decentralized Control ◽

Three Dimensional ◽

Reduced Order Model ◽

Flexible Structure ◽

Order Model ◽

Modeling And Control ◽

Reduced Order ◽

Tower Crane ◽

Three Dimensional Models ◽

And Control

Abstract This paper deals with modeling and control of a crane mounted on a tower-like flexible structure. A fast transfer of the load causes the sway of the load rope and the vibration of the flexible structure. Our object is to control both the sway and the vibration by the inherent capability of the tower crane. This paper makes its three-dimensional models for simulation and reduced-order-model in order to design the decentralized control system. Then, we design the decentralized H∞ compensator and verify the efficiency by simulations and experiments.

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Model Reduction Methods for Complex Network Systems

Annual Review of Control Robotics and Autonomous Systems ◽

10.1146/annurev-control-061820-083817 ◽

2020 ◽

Vol 4 (1) ◽

Author(s):

X. Cheng ◽

J.M.A. Scherpen

Keyword(s):

Autonomous Systems ◽

High Dimensional ◽

Annual Review ◽

Publication Date ◽

Network Systems ◽

Modeling And Control ◽

Reduced Order ◽

Reduction Methods ◽

The Stability ◽

And Control

Network systems consist of subsystems and their interconnections and provide a powerful framework for the analysis, modeling, and control of complex systems. However, subsystems may have high-dimensional dynamics and a large number of complex interconnections, and it is therefore relevant to study reduction methods for network systems. Here, we provide an overview of reduction methods for both the topological (interconnection) structure of a network and the dynamics of the nodes while preserving structural properties of the network. We first review topological complexity reduction methods based on graph clustering and aggregation, producing a reduced-order network model. Next, we consider reduction of the nodal dynamics using extensions of classical methods while preserving the stability and synchronization properties. Finally, we present a structure-preserving generalized balancing method for simultaneously simplifying the topological structure and the order of the nodal dynamics. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 3, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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An Energy Closure Criterion for Model Reduction of a Kicked Euler–Bernoulli Beam

Journal of Vibration and Acoustics ◽

10.1115/1.4048663 ◽

2020 ◽

Vol 143 (4) ◽

Author(s):

Suparno Bhattacharyya ◽

Joseph P. Cusumano

Keyword(s):

Model Reduction ◽

Mode Selection ◽

Computational Cost ◽

Impulsive Loading ◽

Bernoulli Beam ◽

Full System ◽

Fixed Amount ◽

Reduced Order ◽

Proper Orthogonal ◽

Euler Bernoulli Beam

Abstract Reduced order models (ROMs) can be simulated with lower computational cost while being more amenable to theoretical analysis. Here, we examine the performance of the proper orthogonal decomposition (POD), a data-driven model reduction technique. We show that the accuracy of ROMs obtained using POD depends on the type of data used and, more crucially, on the criterion used to select the number of proper orthogonal modes (POMs) used for the model. Simulations of a simply supported Euler–Bernoulli beam subjected to periodic impulsive loads are used to generate ROMs via POD, which are then simulated for comparison with the full system. We assess the accuracy of ROMs obtained using steady-state displacement, velocity, and strain fields, tuning the spatiotemporal localization of applied impulses to control the number of excited modes in, and hence the dimensionality of, the system’s response. We show that conventional variance-based mode selection leads to inaccurate models for sufficiently impulsive loading and that this poor performance is explained by the energy imbalance on the reduced subspace. Specifically, the subspace of POMs capturing a fixed amount (say, 99.9%) of the total variance underestimates the energy input and dissipated in the ROM, yielding inaccurate reduced-order simulations. This problem becomes more acute as the loading becomes more spatio-temporally localized (more impulsive). Thus, energy closure analysis provides an improved method for generating ROMs with energetics that properly reflect that of the full system, resulting in simulations that accurately represent the system’s true behavior.

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