Methods of Virtual Engineering for Smart Systems Design · METHODS OF VIRTUAL ENGINEERING FOR SMART SYSTEMS DESIGN ... [email protected]/ ... with Matlab/Simulink

Paper

FUNDAÇÃO CALOUSTE GULBENKIAN

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METHODS OF VIRTUAL ENGINEERING FOR SMART SYSTEMS DESIGN

U. Gabbert, T. Nestorović, J. Wuchatsch

Institut für Mechanik Otto-von-Guericke-Universität Magdeburg

Universitätsplatz 2, 39106- Magdeburg, Germany e-mail: [email protected]/www.uni-magdeburg.de/ifme/numerik.html

Keywords: Virtual Engineering, Smart Systems, FEM, MBS, Overall Design

Abstract. The objective of this paper is to present an overall approach to a virtual design of smart systems such as high precision machines and smart structures for the vibration and noise control. The basis of this approach is an overall finite element model (FEM) or a MBS model of the smart system, where both models can be generated from a CAD model. The model includes the passive parts of the machine or structure as well as the actuators and sensors (e.g. piezoelectric patch actuators or stack actuators), joints and bearings (e.g. magnetic bearings), different types of excitations etc. It is very important to include also control into the design process, e.g. in order to study the controlled behavior of the system if different types of excitations, disturbances or environmental conditions are influencing the system. In the paper this approach is presented and applied to design two industrial problems – a smart funnel of a magnetic resonance tomograph and a circular table of a machine tool.

1 INTRODUCTION

The design in engineering usually starts with a preliminary computer model of the system under consideration which is extended and completed in next design steps until the final system is available as a virtual computer model. Such a virtual model is used to optimize the system until a first prototype is really built. The optimization usually includes the mechanical behavior, such as statics, strength of materials, dynamics, lifetime, safety etc. Electric and electronic components, control and several other components are usually developed separately and consequently, it is not possible to study the overall behavior of the system under realistic operating conditions. The future holistic design of a system requires the development and application of a new methodology, where it is important to

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extend the 3D product model of the system and its components by the most important physical models, such as mechanical, thermal, fluid, electric, magnetic models, the control electronics, the power supply as well as by models describing the general operating and environmental conditions of the system. But also the manufacturing process, the production logistics and even the recycling have an essential influence on the design process, which has to be taken into consideration. The holistic virtual development process also requires an integrated product data management system, which is able to create automatically and consistently the required user dependent partial models of the product. The product model in general covers the product geometry as well as functional, technological and other features.

Such an integrated development process has been partially realized at the chair of the authors, where besides the CAD software different analysis tools, such as the FEA software COSAR and ANSYS, the MBS software SIMPACK and the controller design tool Matlab/Simulink have been used. For coupling of different tools special data interfaces were created, which provide the required data exchange. But also a co-simulation of different tools is possible. Especially our finite element software COSAR (see: www.femcos.de), originally developed at the University of Magdeburg, has been extended to run multi-physics applications including control.

Our main objective is the development of smart machines and structures, which are designed to actively damp noise and vibration caused by unforeseen disturbances as well as to increase the accuracy of machines [4]. In smart structures design we are focused on thin lightweight structures, where we are mainly applying FEA tools. In smart machines, such as tool machines, large movements and rotations have to be taken into account. Different excitations and disturbances during operation cause vibration and noise, which may result in large inaccuracies of the manufacturing process. In order to model such behavior the MBS approach is sufficient, where sometimes the flexibility of parts of the system has to be taken into account, e.g. by including elastic sub-models generated by the finite element method.

Without control such smart systems cannot be developed properly. In the paper we are applying a model based optimal LQ controller, taking into account additional dynamics as a new design component. Therefore, a priori information about the type of disturbances (e.g. sinusoidal excitation) can be included into the controller design resulting in a better performance of the controlled behavior.

In the paper some details of the approach are presented first. Then two industrial applications are discussed – a funnel of a magnetic resonance tomograph (MRT) and the circular table of a machine tool with magnetic bearings and toque motor.

2 COUPLING OF CAD WITH MECHANICAL SIMULATION

It is generally accepted that the prerequisite for a continuous computer aided engineering is the integration of the product data throughout the product development. A suitable basis for modeling and integrating product data is offered by the product data technology, which is characterized by an explicit association with the product, and not by the process of planning


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and manufacturing. Since 1987, work has been in progress under the auspices of the International Standards Organization to develop a standardized product data model called STEP. Meanwhile STEP is general accepted, applicable and safe as numerous applications in industry have proved. The coupling of CAD systems with finite element analysis systems (FEA) or multi-body dynamics systems (MBS) as well as special preprocessor software via STEP is one of the favorite possibilities nowadays. Of course, there are several problems connected with such a data exchange between FEA, MBS and CAD and we are still far away from an integrated product data management system, which is required for future applications [2]. Whereas the preprocessors of FEA tools, e.g. FEMAP, have a good access to CAD software, this is in general not the case in MBS software. The reason is that the solution based on a MBS model only requires information about the mass and mass inertia for each body as well as the connections between the bodies and the fixed environment. The real geometry only helps to better understand the solution by applying an animation of the dynamic behavior of the system. There are many different MBS systems available on the market [16]. We are using the MBS software SIMPACK, which has been designed to simulate the nonlinear dynamic behavior of structures consisting of rigid and flexible parts. Due to its modular open structure it is well prepared to include control design software as well as other new features [9].

In our experiences the FEA software is well suited to design controlled smart structures especially in lightweight applications. Recently, the research group of the authors has extended a commercial FEA tool – COSAR (see: www.femcos.de) - to design smart structures including integrated piezoelectric actuators and sensors and control electronics [1], [5]. The MBS software taking into account also flexible parts is an excellent tool to design smart machine systems performing large movements (tool machines, robots etc.). In the following both approaches are discussed in more detail.

3 FEA BASED VIRTUAL DESIGN OF SMART STRUCTURES

Recently, a finite element based overall simulation and design tool for piezoelectric controlled smart structures has been developed, containing both a suitable controller design and the appropriate actuator/sensor placement [6], [12], [18]. The finite element semi-discrete form of the equations of motion can be derived using the well established approximation method of displacements and electric potential and following the standard finite element procedure [3], [7]. This approach has been used to develop a comprehensive library of multi-field finite elements (1D, 2D, 3D elements, thick and thin layered composite shell elements, etc.) to simulate the static and dynamic structural behaviour of smart structures (see Fig. 1).

The quality of a smart structure decisively depends on the amount, the shape and the distribution of the active material across the passive structure. The optimal design of the actuator/sensor configuration is a very complex problem, which has not yet been fully solved to date. A new methodology for an automatic placement of distributed patch actuators based on mathematical optimization methods including control has been developed First test examples demonstrate the functionality of the developed approach [18].


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Figure 1: Finite element library of COSAR for coupled electro-mechanical multi-field problems

The finite element package COSAR (see: http://www.femcos.de) has been extended by (i) multi-field finite elements (see Fig 1), (ii) special new preprocessors to automatically generate electro-mechanical coupled finite element models, (iii) numerical tools to solve the special types of coupled equations in the time domain, (iv) tools to modally reduce the number of equations, (v) data interfaces to connect bi-directionally the FEA tool COSAR with Matlab/Simulink for control design purposes and (vi) new postprocessors to prepare the results graphically.

4 MBS BASED VIRTUAL DESIGN

In the design of smart machine components, such as in tool machines, robots, measurement machines etc., the influence of large movements (e.g. rotations) on the dynamic behavior and the accuracy has to be taken into consideration. For this reason the application of a multi-body systems (MBS) approach is preferable. We are using the SIMPACK software as a basis for the virtual design developments, including elastic finite element models, control electronics, different types of active and passive joints, bearings, actuators and sensors, different types of excitation etc. Several of such extensions are not available in the standard MBS software, but can be added via special user defined interfaces.

An interesting field of smart structures concepts are machine tool systems, where vibrations caused by the manufacturing process can reduce the accuracy of work pieces. There are different kinds of additional actuators and sensors available, such as hydraulic, pneumatic, magnetic, electric, piezoelectric, optic etc. actuators, which can be integrated into the structure together with appropriate control electronics to fulfill special tasks. In the


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following special attention is paid to piezoelectric actuators as well as to magnetic actuators, which can be used to realize a high precision control of machine tools. The theoretical basis of modeling piezoelectric actuators and magnetic actuators in the frame of a finite element approach can be found in the literature (see e.g. [7], [8], [17]). Therefore, in the following only brief explanations regarding the implementation of such models in the MBS software are given.

Piezoelectric ceramics such as stack actuators or thin patch actuators can be described by the well known coupled electro-mechanical field equations. Based on these equations new force elements can be simply developed and integrated in MBS systems. In SIMPACK new force elements have been integrated by the authors using a Fortran user interface.

Magnetic actuators have also been included in SIMPACK based on the description of the user defined force elements [20]. Magnetic actuators, e.g. magnetic bearings, are highly nonlinear, where special attention has to be paid to creating a relatively simple but correct force element. The static magnetic force in the air gap can be described on the basis of the MAXWELL equations. In relation to MBS simulations it is often appropriate to describe magnetic actuators or magnetic bearings as one-dimensional magnetic force elements, which generally calculate the static forces beyond the magnetic saturation of the material. The input data of such a force element, which we have developed recently, are the geometry, the material data of the permanent magnet, the magnetic leakage flux and the B-H-graph or permeability of the material. A further input parameter is the electric current of the coil. Here a static parameter, a function or a controller output can be included [20].

5 CONTROLLER DEVELOPMENT AS A PART OF AN OVERALL VIRTUAL DESIGN PROCEDURE

Controller design represents an important part of an overall virtual design procedure. Actively controlled systems necessarily involve active components in terms of actuators and sensors, together with an appropriate control law, which enables adapting of the controlled system behaviour to desired requirements and environmental conditions. Regarding the possibilities for the controller design, numerous techniques are at disposal and application of an appropriate control law is closely related to requirements of the specific problem [3], [7], [10]. Virtual design techniques are based on appropriate models, which can be obtained in different ways. Model development for the controller design, based on FEA and MBS software represents a suitable basis for virtual investigations of the overall behaviour of an actively controlled system.

One approach to the controller design is a discrete-time control, based on the state-space model in a well known form [15]

][][][][

][][][]1[

kkkk

kkkk

FwDuCxy

εwΓuΦxx

++=

++=+ (1)


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where the appropriate state space matrices Φ, Γ, ε in the model are obtained by discretization of the continuous-time state space model, which e.g. results from the FE modelling and modal reduction [6]. Vector x represents the modal states, u is the vector of control inputs, y the vector of measured outputs and w represents excitations or disturbances. Especially for the vibration suppression purposes the optimal LQ tracking system with additional dynamics has been proven to be well suited for this purpose in cases when the external excitations or disturbances can cause resonant states [14]. With a priori knowledge about the type of the excitation or disturbance (periodic, exponential, or some other type which can be represented in the form of a rational transfer function) included in the form of additional dynamics in the design model, an optimal LQ controller can be designed. The control law ][][ kk dxLu −= obtained for the design model (realization (Φd, Γd)) minimizes the performance index

∑∞

=+=

0])[][][][(

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k

Td

Td kkkkJ RuuQxx (2)

Realization of the control system with the Kalman filter for estimation of the modal state variables is represented in Figure 2.

Controller design can be performed using some standard tools, like Matlab/Simulink, which is a convenient environment for the model based controller design and simulation. With an appropriate interface which has been developed in order to couple Matlab/Simulink with the finite element software COSAR [6] it is possible to perform not only simulations and virtual experiments in Matlab/Simulink, but also to investigate the behavior of the original structure influenced by the controller in the COSAR environment.

Considering the control principles, adaptive control can be used as an alternative to the optimal control of the linear time-invariant (LTI) systems in a sense that the state space model with the high accuracy requirements can be substituted by a reference model, which defines the desired properties of the controlled system in the case of the model reference adaptive control. Controller design is then predominantly based on the properties of the reference model as well as on the agreement between the reference and the system model. For the purpose of the virtual direct adaptive controller design, models obtained using the FE approach can be used to simulate the real behavior of the controlled structure in the closed-loop system [13].

Figure 3 represents an adaptive model reference control system with the implemented control law in the form:

)()()()()()()()()( ttttttttt rmm mmrKuKxKeKu uxyey

=++= (3)


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Figure 2: Discrete-time tracking system with additional dynamics and estimator

Figure 3: Model reference adaptive control system

As a connection between the virtual development and the final implementation, the real time behavior of actively controlled systems can also be investigated and tested using Hardware-in-the-Loop (HiL) systems. They offer the possibility to substitute parts or the complete virtual model of the investigated object by real components, while retaining the virtual environment and to investigate the behavior of the system under conditions which correspond to a great extent to real working conditions. One possibility for using such a system is a HiL system with dSPACE which integrates the control system with appropriate control laws realised in Matlab/Simulink environment, real object under investigation mainly with actuators and sensors included and a set of virtual auxiliary devices, which can simulate (among other functions) various data acquisition and monitoring tools, as well as AD and DA converters.


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Developed control laws can be implemented in the FEA software as well as in the MBS software. In MBS software this is a standard task, whereas such possibility is not available in standard FEA codes like ANSYS or ABAQUS. As mentioned above for our FEA software COSAR a bi-directional data interface was developed, which allows also to integrate developed time independent control laws in the FEA code by applying the control matrix K or the control law in form of a C code.

In the MBS software SIMPACK there are several possibilities available to implement a control strategy. The simplest ways are (i) the application of control elements, which are directly available in the software, (ii) the generation of the state space matrices (A, B, C and D) derived form a linearized MBS model, which can be transferred to Matlab/Simulink. But these control strategies are limited and often insufficient in special applications. In such cases SIMPACK offers an interface to different controller design tools, e.g. to Matlab/Simulink, to perform a co-simulation. If one sample time period is elapsed both solvers are forced to stop and interconnecting vectors are exchanged. A complex model can also be calculated in SIMPACK alone, if the control loop is imported via a data interface, which automatically creates a Simulink model by applying the REAL-TIME WORKSHOP using the supplied configuration files that can be incorporated fully within Simpack.

6 EXAMPLES

6.1 Vibration control of a funnel-shaped structure Active control in the sense of vibration suppression was developed for a funnel-shaped shell structure (see Fig. 4), the inlet part of the MRI tomograph produced by Siemens [13], [14]. The aim of the design was the reduction of transmitted vibrations from the cylindrical body of the tomograph to the funnel-shaped inlet using piezoelectric actuators and sensors. Six actuator-groups and six sensors attached to the surface of the funnel (Fig. 5) have be designed based on a finite element model of the funnel, which takes into account the coupled electro-mechanical behavior in the piezoelectric patches as well as the control electronic.

Figure 4: Funnel shaped part of a MRT Figure 5: Finite element model of the active funnel


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In the final optimized realization, the positions of actuators and sensors (see Fig 5) are denoted as 1L, 2L, 3L for the left-hand side actuators and sensors and 1R, 2R, 3R for the right-hand side ones. Applying described overall design procedure, control of the three selected eigenmodes (corresponding to the eigenfrequencies f1=9.573 Hz, f2=23.333 Hz, f3= 31.439 Hz) was performed in the sense of the vibration suppression in the presence of excitations.

Controller used for the vibration suppression is an optimal LQ tracking system with additional dynamics described in section 5 and in more detail in [14]. As a worst study case the excitations are selected as sine signals with frequencies corresponding to the eigenfrequencies of the funnel.

Figure 6: Sensor signal (left) and actuator signal (right).

(In the time interval from about one to eight seconds the controller was switched off.) The results of the optimal LQ controller design and implementation (response of the

sensor S1R and control signal of the actuator A2R in the presence of the sine excitation with the frequency equal to the first eigenfrequency) are represented in Fig. 6. The response in the absence of control is characterized by obviously greater vibration amplitudes in comparison with the controlled case. Several further design studies where performed, which demonstrate the advantage of an overall virtual design strategy.

6.2 Circular table with magnetic bearings as part of a machine tool

Figure 7 represents a circular table as a part of a machine tool system [19]. The table consists of two main parts: a support and a rotor. The support includes magnetic bearings to levitate the rotor for small translations along the main axis and the rotation about the horizontal axis and a torque engine for control of the large rotation about the vertical axis. On the upper side of the rotor a clamping plate is fixed by an angle change facility to permit lateral buckling. During high-precision machining with a required accuracy of some µm undesired deformations can considerably reduce the quality of the manufacturing process.

Such undesired deformation can occur due to the following reasons:

• Static deformations due to the mass (weight) of the work piece, the mass of the rotating table, the rotor, the clamping devices etc.;

• Dynamic deformations due to stochastic excitations of the magnetic bearings; • Dynamic deformations due to an asymmetric position of the work piece at the table;


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• Deformations due to the metal cutting operations, which induce high static and dynamic forces acting in horizontal and vertical direction at the work piece;

• Static deformations due to changing thermal influences during operation.

2

13

4

56

7 8

9

10

11

2

13

4

56

7 8

9

10

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Figure 6: Circular table as part of a machine tool system (1 rotor with flange, 2 clamping plate, 3 support, 4,5,6,7 stroke magnets, 8,9 torque magnets)

There are two different possibilities to increase the accuracy of the manufacturing

process in order to ensure a high quality of the work piece. The first possibility is to use active components of the machine system, such as electric

motors, magnetic bearings, hydraulic components etc., which are primary components of the system. These components can be additionally used as actuators for controlling undesired actions of the system. The second possibility is to add new smart components, such as piezoelectric stack actuators, which are additionally integrated into the machine system, e.g. to actively damp parts of the system.

Rundtisch - Transiente Rechnung

-2,00E-02

-1,50E-02

-1,00E-02

-5,00E-03

0,00E+00

5,00E-03

1,00E-02

1,50E-02

2,00E-02

0,00E+00 5,00E-03 1,00E-02 1,50E-02 2,00E-02 2,50E-02 3,00E-02 3,50E-02 4,00E-02 4,50E-02 5,00E-02

Zeit t [s]

Vers

chie

bung

u2

[mm

]

-6,00E+04

-4,00E+04

-2,00E+04

0,00E+00

2,00E+04

4,00E+04

6,00E+04

Elek

tr. P

oten

tial [

mV]

u2 Aktuatorknoten 15537 u2 Aktuatorknoten 15532 Elektr. Pot. Aktuatorknoten 15532 Figure 7: Vertical deflection of the upper plate exited by integrated piezoelectric stack actuators


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In order to demonstrate the active damping of undesired vibrations of the circular table during operation 12 additional piezoelectric stack actuators have been integrated into the upper part of the clamping plate (see Fig. 7). In Fig. 7 it is demonstrated that an excitation of the stack actuators with an admissible sinusoidal voltage close to the first eigenfrequency of the plate, the amplitudes of about 16µm can be achieved, which are large enough to damp undesired vibration amplitudes, which can occur during the operation.

7 CONCLUSION

In the paper an overall virtual design approach for smart structures and high precision machines to reduce vibration and noise and to increase the accuracy has been presented. The basis of this approach is an overall finite element model (FEM) or a MBS model of the smart system, where both models can be generated from a CAD model. The model includes the passive parts of the machine or structure as well as the actuators and sensors (e.g. piezoelectric patch actuators or stack actuators), joints and bearings (e.g. magnetic bearings), different types of excitations etc. It is very important to include also control into the design process, e.g. in order to study the controlled behaviour of the system if different types of excitations, disturbances or environmental conditions are influencing the system. To demonstrate the advantage and the potential of such an approach two industrial problems – a smart funnel of a MRT and a circular table of a machine tool – are discussed in the paper.

As conclusions of our investigation it can be stated, that in the moment, software and technology tools are not flexible enough for specific and economic deployment for industrial requirements. Contemporary general purpose software tools are mostly beyond what future technological developments really need. Especially the virtual holistic development process is still a future challenge. In the future the development process should be guided and supported by a virtual development platform, where e.g. modelling starts with the CAD data and virtual mock-ups to get geometry, kinematics and functionality descriptions, and a subdivision into domains and modules are generated. The domains will be discretized by applying a FEA and/or MBS approach, where the level of detail is automatically selected in accordance with the objectives of the approach. The overall model can be consistently extended by sub-models, such as electric, hydraulics, pneumatic and other parts, different types of actuators and sensors, control electronics etc. The assembly of structural members (domains and modules) will be programmed in a very simple way in a language chosen by the user applying an application programming interface. The precision of modelling and computation and necessary scaling should be to the greatest possible extend self-regulated.

Such a future holistic virtual design process for new products requires a considerable amount of interdisciplinary basic research, which will hopefully be financially supported by national science foundations, ministries and industrial concerns as well.


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Controlled Smart Structures. Journal of Theoretical and Applied Mechanics, 3, 38, pp. 475-498. [2] Gabbert, U., Wehner, P. (1998): The product data model as pool for CAD-FEA data, Engineering with

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developments. J. of Theoretical and Applied Mechanics, 3, 40, pp. 549-574. [5] Gabbert, U., Köppe, H., Seeger, F., Berger, H. (2002): Modeling of smart composite shell structures. J. of

Theoretical and Applied Mechanics, 3, 40, pp. 575-593. [6] Gabbert, U., Köppe, H., Nestorović Trajkov, T. (2002): Entwurf intelligenter Strukturen unter

Einbeziehung der Reglung. at – Atomatisierungstechnik 50 (9), 432-438. [7] Janocha, H. (Ed.) (1999): Adaptronics and Smart Structures – Basics, Materials, Design, and Applications,

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Anwendung, Teubner. [9] Kortüm, W., Sachau, D. and Schwertassek, R. (1996): Analysis and design of flexible and controlled

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Atomatisierungstechnik, Vol. 50 (9), pp. 422-431. [11] Lefevre, J., Gabbert, U. (2004): Simulation of piezoelectric smart lightweight structures by the finite

element method for acoustic control, PAMM, Vol. 4, pp. 340-341. [12] Nestorović Trajkov T., Köppe H., Gabbert U. (2003): Comparison of controller design approaches from a

vibration suppression point of view, Proceedings of SPIE, Vol. 5049, pp. 314-325. [13] Nestorović Trajkov, T., Gabbert, U., Köppe, H. (2003): Controller design for a funnel-shaped smart shell

structure, Facta Universitas, Series: Mechanics, Automatic Control and Robotics, Vol. 3, N° 15, pp. 1033-1038.

[14] Nestorović-Trajkov T., Köppe H., Gabbert U. (2005): Active vibration control using optimal LQ tracking system with additional dynamics, International Journal of Control (accepted for publication).

[15] Santina, M., Stubberud, A., Hostetter, G. (1994): Digital Control System Design, Saunders College Publishing, a Harcourt Brace College Publisher.

[16] Schiehlen, W. (1990): Multibody Systems Handbook, Springer. [17] Schweitzer, G., Traxler, A. and Bleuler, H. (1993): Magnetlager – Grundlagen, Eigenschaften und

Anwendungen berührungsfreier, elektromagnetischer Lager, Springer. [18] Seeger, F., Gabbert, U.: Optimal placement of distributed actuators for a controlled smart elastic plate,

PAMM, Volume 2, Issue 1, pp. 262-263. [19] Wuchatsch, J., Gabbert, U. (2003): Simulation eines Magnetrundtisches unter Nutzung elastischer

Mehrkörpermodelle, Tagungsband der 6. Magdeburger Maschinenbautage, Logos Verlag Berlin, pp. 133-138.

[20] Wuchatsch, J., Gabbert, U. (2004): Magnetic force elements for SIMPACK, Proceedings of SIMPACK User Meeting, 09.-10.11.2004 Eisenach, Germany, paper 30.

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Methods of Virtual Engineering for Smart Systems Design · METHODS OF VIRTUAL ENGINEERING FOR SMART SYSTEMS DESIGN ... [email protected]/ ... with Matlab/Simulink