A unified finite element framework for the dynamic analysis of controlled flexible mechanisms

in Proceedings of the ECCOMAS Conference on Advances in Computational Multibody Dynamics (2005, June)

This paper proposes a unified formalism for the simulation of mechatronic systems with complex flexible mechanisms. The equations of motion are formulated using a nonlinear Finite Element approach for the ... [more ▼]

This paper proposes a unified formalism for the simulation of mechatronic systems with complex flexible mechanisms. The equations of motion are formulated using a nonlinear Finite Element approach for the mechanism, and the block diagram language for the control system. The set of strongly coupled equations of motion is constructed numerically, and integrated in the time domain using the generalized-alpha method. Convergence and stability properties are thus guaranteed for the simulation algorithm. Two illustrative examples are treated in the fields of vehicle dynamics and robotics respectively. [less ▲]

Optimization of mechatronic systems: application to a modern car equipped with a semi-active suspension

in Herskowitz, José (Ed.) Proceedings of the 6th World Congress of Structural and Multidisciplinary Optimization (WCSMO6) (2005, May)

The research aims at developing a global mechatronic approach to model, simulate and optimize complex industrial applications. The approach is illustrated with the simulation and the optimization of a ... [more ▼]

The research aims at developing a global mechatronic approach to model, simulate and optimize complex industrial applications. The approach is illustrated with the simulation and the optimization of a modern car (an Audi A6) equipped with a controlled semi-active suspension. An optimization procedure is used to find the best sub-system parameters in order to improve the comfort of the passengers while preserving the car ride and handling performances. Two different modeling and optimization approaches are used and compared. The first one is realized in the MATLAB-SIMULINK environment and is based on a symbolic multibody model of the chassis while the hydraulic actuators, and the controller are integrated using S-functions. Optimization is also carried out in MATLAB using algorithms available in MATLAB libraries, especially a genetic algorithm (GA). On the other hand, the second approach relies on a multibody model based on the Finite Element method whereas the optimization can be realized with an industrial open optimization tool. [less ▲]

Two competing linear models for flexible robots: Comparison, experimental validation, and refinement

in Proceedings of the American Control Conference (2005)

The modeling of a rigid robot attached to a flexible base is addressed in this work. Two approaches are compared: the Finite Element Method (FEM) and the Transfer Matrix Method (TMM). Initially, idealized ... [more ▼]

The modeling of a rigid robot attached to a flexible base is addressed in this work. Two approaches are compared: the Finite Element Method (FEM) and the Transfer Matrix Method (TMM). Initially, idealized models of the hydraulic actuators are used that do not include flexible effects in the joints. Those models greatly overestimate the second natural frequency of the system, therefore the identification of local flexibilities in the joints is pursued to improve the results. The very good agreement between both approaches, and their ability to represent the physical system (once joint flexibility is included), confirms their efficiency and relevance in this context. [less ▲]

Generation of closed-form models for the control of flexible mechanisms: a numerical approach

in Proc. of the 7th Int. Conf. on Motion and Vibration Control (MOVIC) (2004, August)

In robotics, most high performances control strategies require a closed-form representation of the mechanical dynamic behaviour. This is even more critical when significant flexible effects are to be ... [more ▼]

In robotics, most high performances control strategies require a closed-form representation of the mechanical dynamic behaviour. This is even more critical when significant flexible effects are to be considered in the control algorithm. This paper presents a method to build closed-form dynamic equations for flexible multibody systems in terms of minimal coordinates. Relying on the Finite Element (FE) formulation, the method is able to tackle complex topologies with closed-loops in a systematic way. The method is based on an interpolation strategy. For a number of selected points in the configuration space, a full Finite Element model is built and reduced according to a component mode synthesis. Then, a piecewise polynomial model is adjusted to match the collected data. In order to guarantee the continuity of the model, a mode tracking strategy is implemented. After the presentation of the reduction procedure and of the interpolation strategy, a four-bar mechanism is analyzed as an illustrative example. [less ▲]

Model reduction of flexible mechanisms: A numerical approach

Scientific conference (2004, May)

A model reduction method for the control of rigid mechanisms

in Proceedings of the ECCOMAS Conference on Advances in Computational Multibody Systems (2003, July)

This paper proposes a control strategy for flexible mechanisms. Our starting-point is a classical collocated PID control of the joint actuators designed for the equivalent rigid mechanism. An additional ... [more ▼]

This paper proposes a control strategy for flexible mechanisms. Our starting-point is a classical collocated PID control of the joint actuators designed for the equivalent rigid mechanism. An additional state feedback is implemented to control the flexible modes. On the basis of a few vibration measurements, it generates an additional command for the joint actuators. This non-collocated control scheme is designed according to the H procedure in order to have robust performances and stability with respect to configuration changes. In this paper, a new reduction methodology is presented to build a linear low-order and sufficiently accurate model of the mechanism with the PID feedback, which is suitable for the design of the H controller. First, a detailed Finite Element model of the mechanism is elaborated including the initial PID compensator. This set of nonlinear differential and algebraic equations is then linearized around a chosen reference configuration and a reduction technique is developed to extract a compact set of ordinaray differential equations. The retained degrees of freedom are the joint coordinates and a few modal coordinates representing the deformation of the whole mechanism. The kinematic description is thus decomposed into two parts, a rigid body motion described by the joint coordinates and a flexible motion for which shape functions have to be selected. For this selection, a modal analysis of the controlled mechanism is performed and the first few modes are kept, as in the Craig-Bampton or McNeal-Rubin reduction techniques. For robust performance specifications, the variations of the model with respect to the configuration changes should be estimated. Thus, the reduction procedure is realized for a few values of the joint coordinates, and the reduced models are compared. As the set of shape functions changes with the configuration, the physical meaning of the modal coordinates should be reinterpreted in each model, which is one difficulty of the approach. To illustrate the method, the case of a two-link flexible manipulator is presented. Simulation of the complete nonlinear Finite-Element model with the global control scheme is performed in order to assess the final performances of the closed-loop system. [less ▲]

Simulation of an Active Control System in a Hot-Dip Galvanizing Line, Virtual Nonlinear Multibody Systems

in NATO Review (2003), 103

Simulation of an Active Control System in a Hot-Dip Galvanizing Line

in Preprints of the NATO Advanced Study Institute on Virtual Nonlinear Multibody Systems (2002, June)

This paper concerns the modeling and the integrated numerical simulation of a flexible mechanism subject to the action of a digital control system. A general method is proposed, based on the formalism of ... [more ▼]

This paper concerns the modeling and the integrated numerical simulation of a flexible mechanism subject to the action of a digital control system. A general method is proposed, based on the formalism of flexible multibody systems (MBS) using the Finite Element Method (FEM). Nonlinear effects in the mechanical structure or in the control system can be taken into account. The numerical simulation tool is applied to design an active control system in a hot-dip galvanizing line, which aims at reducing the vibrations of the steel strip. [less ▲]

Active Control of the Steel Strip in a Hot-Dip Galvanizing Line

Conference (2002, March)

This paper concerns the design of an active control system for a hot dip galvanizing line. The control system aims at reducing the vibrations of the steel strip in order to improve the quality of the ... [more ▼]

This paper concerns the design of an active control system for a hot dip galvanizing line. The control system aims at reducing the vibrations of the steel strip in order to improve the quality of the product. The mechanical structure is quite flexible and many vibration modes need to be controlled. The actuators and the sensors are collocated and the control law is a direct velocity feedback, which doesn't require any model of the plant. This control law adds damping on all the vibration modes and it guarantees the stability of the system. The position of the actuators is chosen to maximize the controllability and the observability. The relevance of this strategy is discussed. The natural frequencies of the mechanical system are evaluated using the Finite Element Method. In this particular example, it was found that the frequencies of the flexion vibration modes almost match the frequencies of the torsion modes. The corresponding pole/zero pattern leads to very small root loci where the damping increment is strongly limited. A simulation of the closed loop system is required to evaluate the performance of the active control and to choose the feedback gain. The time-domain evolution of the mechanical structure is computed using the Finite Element Method and an implicit integration scheme. Assuming that the control system is digital and neglecting the dynamics of the actuators, the control system is introduced into the mechanical simulation as a users' routine called at each sampling time of the digital controller. This quite general approach allows to deal with nonlinear eff ects either in the mechanical structure or in the control system, what opens new perspectives in integrated simulation of controlled flexible mechanisms. The simulation shows that a single actuator is not able to control the whole steel strip. Even if the gain increases, the controlled point becomes quickly a fixed point, and the vibration of the rest of the structure is not significantly attenuated. At least three actuators are necessary to get the expected performance. [less ▲]