Authors:
Heřman Mann and Michal Ševčenko, Computing and Information Centre, Czech Technical University in Prague
Zikova Street 4, CZ-166 35 Prague 6, Czech Republic, {mann,sevcenko}@vc.cvut.cz
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A software system for efficient modeling and simulation distributed across the Internet has been made freely accessible at http://virtual.cvut.cz/dyn/. The system supports collaboration of remote engineering teams as well as hands-on training of Web-based course learners. The kernel of the system – DYNAST Solver – solves nonlinear algebro-differential equations. For multipole models characterizing configuration of dynamic systems the equations are not only solved, but also formed automatically. DYNAST Solver is also able to linearize the models and to provide their semisymbolic analysis in time- and frequency-domains. Clients can submit their problems via a graphical user interface of two different forms in a very easy and efficient way. In control design, DYNAST modeling a plant to be controlled can communicate across the Internet with the
MATLAB toolset installed on the client’s computer. The simulation results can be animated by means of a 3D visualization tool. A server-based documentation package supports publishing reports on simulation experiments. An accompanying Webbased course on systematic modeling is enhanced by a knowledge-sharing system with interactively resolvable examples.
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Dynamic systems, modeling, simulation, virtual experiments.
I NTRODUCTION
When designing complex contemporary systems, engineers usually proceed through several modeling levels. While they start from the conceptual level of the highest modeling abstraction and continue down up to the most concrete manufacturing level, they pass through two important intermediate levels: functional and physical. The functional-level model apply typically to the control-design phase when engineers are concerned about either analog or digital input and output signals, states, disturbances etc.
Physical-level models are less abstract than the conceptual- or functional-level ones as they portray energy interactions between real system components. Very often, energy interactions in several different physical domains must be considered in these models simultaneously. The physical-level models are called also virtual prototypes as they are used in a growing number of applications to replace to some extent the time consuming and costly experimenting with real prototypes.
The conceptual- and functional-level models of dynamic systems are represented quite conveniently by block diagrams submitted for simulation to one of the available block-oriented software packages like Simulink. Using such a package for physical-level modeling, however, is a cumbersome and error prone task. It requires involved manual formulation of the underlying equations and, in addition, manual conversion of the equations into a block diagram.
In the past, the efficiency of a computation was evaluated from the point of view of its demand on computer time only.
Nowadays, however, expenses related to computation are dominated by the cost of personnel required to prepare the input data and to interpret the results. This cost is proportional to the amount of time these two operations require as well as to the their demands on personnel qualification. Fortunately, modern computers can be exploited not only to solve equations, but also to formulate them for a given configuration of the modeled real system. At the same time, modern computational algorithms require much less operator’s experience and intervention then the old ones.
A software package for efficient modeling and simulation across the Internet called DYNAST has been developed
 to give to distance or continuous education students a hands-on opportunity to solve real world problems
 to provide an easy access to a powerful simulation engine for engineers even in small enterprises
 to support cooperation of remote teams involved in common research or design projects
The DYNAST package respects the fact that most of the contemporary machines, instruments and other engineering systems are of multidisciplinary nature, as their design requires integration of several traditional engineering disciplines. To simulate such systems, the package was made applicable in a unified way to different
 physical domains (mechanical, electrical, magnetic, fluid, or thermal)
 levels of modeling abstraction and idealization (conceptul, control-design or virtual-prototyping level)
 model descriptions (equations, block diagrams, input and output signal waveforms, etc.)
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M
ODEL DESCRIPTIONS
DYNAST allows for models of system dynamics characterized by
 sets of nonlinear algebraic, differential or algebro-differential equations submitted in a natural textual and implicit form
 block diagrams submitted in a graphical form with any algebraic loops
 multipole diagrams representing graphically the actual configuration of the modeled real systems
 combinations of the descriptions mentioned above
For multipole diagrams the underlying equations are formed by DYNAST automatically.
Principles of multipole modeling
The automatic formulation of equations for physical-level modeling of multidisciplinary systems is based in DYNAST on the multipole modeling approach well established in the electrical engineering domain. Thanks to the similarity of dynamic effects in different physical domains, this approach can be generalized and applied to all the domains in a unified way. The multipole modeling procedure starts with an imaginary decomposition of the modeled systems into disjoint subsystems. (This idea is similar to the free body diagrams in mechanics or control surfaces in thermodynamics.)
The subsystem multipole models are approximations of the subsystem mutual energy interactions assuming that
 the interactions take place just in a limited number of interaction sites formed by adjacent energy entries into the subsystems (like fluid inlets, electrical terminals, translating or rotating mechanical connections, heat-transferring contact surfaces, etc.)
 the energy flow through each such entry can be expressed by a product of two complementary power variables (like force – velocity, torque – angular velocity, volume flow rate – pressure, electrical current – voltage, magnetic flux rate – magnetic voltage, or entropy flow – temperature)
Each energy entry into a subsystem is represented in its multipole model by a pole associated with a pair of the power variables. In graphical symbols of individual multipoles, the poles are denoted by pins , i.e. by short line segments sticking out of the symbol outlines.
Dynamics of a complete system can be easily represented graphically by a multipole diagram consisting from symbols of subsystem multipole models. Figure 1 shows an example of the multipole diagram of a rolling mill for metal strips. The sites of energy interaction between adjacent energy entries are portrayed in the multipole diagram by the diagram nodes . The incidence between the subsystem energy entries interacting at the same site is indicated in the diagram by line segments interconnecting the node standing for the site with pins symbolizing the involved entries. Each of these line segments, called connectors , can be viewed as ideal elements capable of transferring energy in both directions without any dissipation, accumulation or delay. (They behave like an ideal shaft, rigid conduit with an ideal fluid, ideal electrical conductor, etc.) To simplify the diagrams, several connectors can be combined into the bus connector denoted by a thick line segment.
The simplest multipoles are twopole elements considered as pure models in the sense that each of them exhibits a unique dynamic behavior like energy dissipation (resistors and dampers), energy accumulation, (capacitors, inertors, inductors and springs), and pure sources of across and through variables. In general, these elements can be nonlinear, time-variable or controlled. The multipoles can be combined also with blocks like integrators, summators, etc. Energy conversion from one form to another is modeled by pure transducers. Only four different pure transducers are needed to model all kinds of electro-magnetic, electro-mechanical, magneto-mechanical, fluid-mechanical, rotary-rotary, rotary-linear, linear-linear, and energy conversions.
DYNAST is accompanied by libraries of submodels for electronic and fluid-power devices, electromechanical transducers, mechanical parts, control units, etc. Multipole models of real subsystems like electronic or fluid devices, various mechanisms, motors or sensors, heating or cooling units, etc., can be set up from the pure multipoles. Similarly to system models, the subsystem dynamics can be described by a combination of multipoles, blocks, and equations, which can be nested in a hierarchical way. The libraries are open for easy addition of user-defined submodels and their graphical symbols.
Special editors for creating the symbols have been developed. Each DYNAST submodel description is encapsulated in an independent file. The default values of submodel parameters can be overridden by values specified manually one by one, or by a file with parameter values read in from component catalogues. The parameter values can be specified by constants as well as by symbolic expressions.
In Figure 1 showing the multipole diagram of a rolling mill, the three DC motors, the two coilers and the set of rollers are represented by symbols of library models of these subsystems. The multipole symbols are combined with symbols of block forming the electronic feedbacks controlling the DC motors. During the simulation, the thickness of the incoming metal strip is varied randomly, the rolling process is modeled as strongly nonlinear, and the considerable transportation lag between gage measurements and rolling is respected.
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Advantages of multipole modeling
The most important advantage of multipole diagrams over block diagrams or bond graphs is in the isomorphism between their structure and the geometric configuration of the modeled real system. In fact, multipole diagrams represent a mapping of real systems from the geometric onto the topological space. (Recollect that a block diagram is just a graphical representation of a set of equations. The line segments interconnecting block diagrams are associated with just one variable that can propagate in one direction only. Though bond graphs represent energy flow between subsystems, their structure is not at all isomorphic with the geometric configuration of real systems.)
The practical consequence of the isomorphism is that the multipole diagram can be set up in a kit-like fashion in the same way in which the real system is assembled from its subsystems. This modeling procedure can be thus based on mere inspection of the modeled system without forming any equations. Equations underlying the multipole diagrams are then formed by a computer automatically utilizing
 constitutive relations of the individual multipoles
 physical laws governing the balance of energy, mass, and electric or magnetic charge in the individual sites of interaction
 laws respecting the geometric connectedness of real systems.
The multipole approach is also of several other important advantages:
 multipole models can be developed, debugged, tuned up and validated once for ever for the individual subsystems independently of the rest of the system, and once they are formed they can be stored in submodel libraries to be used any time later
 this job can be done for different types of subsystems (e.g., fluid power devices, electronic elements, electrical machines, mechanisms, etc.) by specialists in the field
 inside, the submodels can be represented by different descriptions each of them suiting best to the related engineering discipline or application (lagrangian equations in mechanics, circuit diagrams in fluid power or electronics, block diagrams in control, etc.)
 the submodel refinement or subsystem replacement (e.g., replacement of an electrical motor by a hydraulic one) can be taken into account without interfering with the rest of the system model
 it allows for mixed-level modeling of real systems, i.e. for modeling a system part on the conceptual or functional level by blocks, and at the same time, some other part on the physical level by multipoles
D ISTRIBUTED S IMULATION S OFTWARE
DYNAST Solver
DYNAST Solver that has been developed for efficient modeling, simulation and analysis of multidisciplinary engineering systems forms the kernel of the distributed simulation system. DYNAST Solver is capable of
 solving implicit sets of nonlinear algebro-differential equations submitted in a natural textual form
 simulating nonlinear modeled by multipole and/or block diagrams submitted in a graphical form (the underlying equations are then formed automatically)
 linearizing the diagrams and providing their semisymbolic analysis in time- and frequency-domains
Figure 2 shows the flow of data in the DYNAST Solver. The section SYSTEM reads in files with problem descriptions in a textual form representing equations and/or diagram netlists. In the latter case, this section forms equations underlying the diagram. The input data is interpreted, so there is no compilation delay when processing them. The DYNAST input language was design to be user oriented rather than computer oriented, yet it is ‘object oriented’. It has been implemented already in the first version of DYNAST more than 15 years ago.
Nonlinear systems of equations are solved in the TR section. Besides transient responses , this section computes also system steady states after converting the differential equations into algebraic ones. The algebraic equations can be solved also for a parameter swept through an interval. The transient responses can start either from initial conditions specified by the user, or from those corresponding to the system steady state. Even if the user-specified initial conditions are inconsistent,
DYNAST is able to find the nearest consistent initial conditions just in few iterations. There is also the fast Fourier transformation available in this section for frequency-spectrum analysis of steady-state periodic solutions of nonlinear systems.
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The nonlinear equation-solving routine in DYNAST is based on a stiff-stable implicit multistep backward-differentiation integration formula. The length of integration steps and, at the same time, the order of the formula is continuously optimized continuously to minimize the computation time while respecting the admissible computational error. Jacobians of the equations are evaluated using a symbolic differentiation procedure. Considerable savings of computational time and memory are also achieved by exploiting the jacobian sparsity. The integration provides also automatic liberalization of the analyzed nonlinear equations. Thus, the nonlinear system models can be subjected to small-excitation analysis in the vicinity of a userspecified or computed quiescent operating point.
The PZ section can compute operator functions representing transfer functions and transforms of initial-state responses for lineralized system models. The operator functions are provided in a semisymbolic form with the Laplace operator s as a symbol and polynomial roots or coefficients as numbers. For such operator functions, DYNAST can compute semisymbolicform time-domain characteristics in the TRA section; the FRE section evaluates the corresponding frequency characteristics numerically. Linear frequency-dependent models (like those with parameter-distributed submodels) DYNAST analyses in the
AC section.
The server supports also DYNAST Publisher, i.e. a LaTeX based documentation system for automated publishing of reports on simulation experiments and descriptions of library submodels. The system extracts automatically the relevant parts of the input data and captures the submitted multipole or block diagrams as well as the resulting output plots and includes them into the documents. DYNAST Publisher can also convert the documents into PostScript, PDF and HTML formats.
Graphical user interfaces
The server-based DYNAST Solver can be accessed across the Internet in a Web-based, on-line and e-mail modes [1]. Setting up the multipole and block diagrams directly on a Web page is enabled by the schematic editor DYNCAD formed by a Java applet. DYNCAD converts diagrams into the DYNAST input language and sends the data to the DYNAST Solver across the
Internet. After the computational results are sent back, they can be plotted on the client-computer screen.
Even more comfortable and user-friendly mode of access to DYNAST Solver provides DYNAST Shell as shown in
Figure 3. This mode requires, however, downloading and installing this software on client computers with MS Windows.
DYNAST Shell has been designed to for a wide variety of tasks in a way suitable to users of different levels of qualification and experience. All operations are supported by a context sensitive help system. There is a built-in syntax analyzer continuously checking the submitted data. Dialog windows (wizards) allow for submitting data without knowledge of the
DYNAST input language. DYNAST Shell includes graphical editors for multipole and block diagrams as well as for submodel symbols. A special dialog box for each new submodel is formed automatically as shown in the screenshot of the
DYNAST Shell graphical interface in Figure 4. DYNAST Shell can also communicate with the server-based LaTeX documentation system.
The simulation results can be used for animation of 3D-space models formed using VRML- and Java-based visualization tools developed for the purpose. The motion scripts for the virtual experiments are generated by DYNAST Solver. The users need to download and install only the free CORTONA software on their PCs. Figure 5 shows examples of four movable 3D virtual experiments: a gyroscope, robot, carriage with a double pendulum, and mixing of two different liquids.
Another very useful tool communicating with the server is the software package called DYNAST Monitor. It allows design managers or tutors to observe from any site on the Internet the data files and diagrams the server users are submitting to DYNAST Solver from their client computers. They can communicate with the users across the Internet and help them to solve their problems.
DYNAST
IN CONTROL DESIGN
Modeling toolbox for MATLAB
The server-based DYNAST Solver can communicate with the MATLAB control-design toolsets installed on the client computer across the Internet. Using either DYNCAD or DYNAST Shell, a model of the plant to be controlled can be easily set up in a graphical form. DYNAST Solver can be then used to validate the open-loop model. At the same time, DYNAST
Solver is able to compute the required plant transfer-function poles and zeros, and to export them to MATLAB in an M-file.
After designing analog control within the MATLAB environment, the DYNAST model of the plant can be augmented by the designed control structure and verified by DYNAST.
In the case of a digital control design, there is another option. After designing the digital control using the MATLAB toolset, the resulting control structure is implemented in Simulink while the controlled plant model remains in DYNAST.
Simulink installed on the client computer can then communicate with the remote DYNAST Solver at each time step across the Internet while exploiting the Simulink S-function. The following examples demonstrate the efficiency enhancement of control design when using DYNAST as a modeling toolbox for MATLAB.
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The procedure for the design of PID control for the plant in the form of the inverted pendulum shown in Figure 6 a using
MATLAB is well described in [2]. After a free-body diagram is constructed for the plant and the corresponding differential equations are formulated, these equations are linearized, reduced to their normal form, and converted to transfer functions.
Only then the results of these tedious and error prone manual operations can be submitted to MATLAB.
DYNAST allows avoiding all these manual operations. Figure 6 b shows a multipole model of the inverted pendulum set up using the Web-based schematic editor DYNCAD. The horizontal motion of the cart, identified with the x -motion of point
B , is represented in the multipole model by node B x
. After opening the DYNCAD menu for the rectilinear mechanical domain, the cart dynamics can be represented by the symbols for mass inertia, for damping and for the source of force F acted on the cart by an actuator .
The pendulum dynamics is modeled by a library model for the planar motion of a body with the rotational joint B . The x - and y -motions of the point A are represented by nodes A x
and A y
in the multipole model, while the rotational motion of the pendulum represents node A
φ
. Line segments interconnect nodes related to the same motion, either rectilinear or angular. The integrating blocks are added to compute positions, and the ideal measuring instruments identify variables that should be exported by DYNAST.
After validating the plant model by computing its responses, DYNCAD (or DYNAST Shell) can be used to export an Mfile with the plant transfer functions across the Internet to MATLAB installed on a client computer. After this step, the control design can proceed using the MATLAB toolset as shown in [2]. The feedback loop resulting from the control design can be then added to the plant model as shown in Figure 7. The complete controlled system is finally verified using
DYNAST. Note, that any manual equation formulation or manipulation was avoided in this procedure.
Example of digital control
After exporting the transfer-function data of the plant model by DYNAST, the digital-control design can proceed again within the MATLAB environment as shown in [2]. To verify the design outcome in this case, the digital feedback loop can be implemented in SIMULINK as shown in Figure 8. The large square block represents there the plant multipole model from
Figure 6 b , which remains in DYNAST. Communication between SIMULINK and DYNAST along the lines interconnecting this block with the rest of the diagram exploits the SIMULINK S-function. This time, the resulting responses are observed in
SIMULINK.
Example of mixed analogue-digital control
Figure 1 shows a more complex plant controlled across the Internet. The two DC motors driving the coilers with a metal strip are controlled for a constant tension in the strip and the third DC motor driving the rollers milling the strip is controlled for a constant strip velocity. The three analog PID controllers are included in the multipole model. An external digital adaptive controller respecting data coming across the Internet from the model controls the gap between the rollers.
C
ONCLUSIONS
Capabilities of the distributed simulation system have been well proven by many of its academic and industrial users already.
Automated statistic analysis of the server access indicates that people from all over the world utilize the system for solving a large number of problems each month. A large collection of solved and interactively resolvable examples is available at [1].
The system is also exploited in a course on modeling, simulation and control design [4] that is currently under development.
A
CKNOWLEDGMENT
This paper describes an outcome partly developed within the frame of the following projects supported by EU grants:

RichODL – Enriching ODL by knowledge sharing for collaborative computer-based modeling and simulation, Socrates
ODL Transnational Cooperation Project No. 56057-CP-2-99-1-CZ-ODL-ODL

DynLAB – Course on dynamics of multidisciplinary and controlled systems in a virtual lab, Leonardo da Vinci
Programme Pilot Project No: CZ/02/B/F/PP/134001
 eMerge – Educational Network Structure for Dissemination of Real Laboratory Experiments to Support Engineering
Education, Socrates Transnational Cooperation Project No. 100671-CP-1-2002-1-FR-MINERVA-M
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R
EFERENCES
[1] Website of the “Virtual Action Group for Multidisciplinary System Simulation”, a part of the Technical Committee on Computer Aided Control
System Design of the IEEE Control Systems Society at http://icosym.cvut.cz/cacsd/dyn/
[2]
Messner, B. Tilbury, D., “Control Tutorials for MATLAB”, University of Michigan/ Prentice Hall, at http://www.engin.umich.edu/group/ctm/.
[3] Website of the DynLAB project within the EU Leonardo da Vinci Programme at http://icosym.cvut.cz/dynlab/.
[4] Mann, H., Ševčenko, M., “Innovative Didactic Concepts and Tools for Systems Dynamics and Control”, in these ICEE 2003 Proceedings .
FIGURES
F IGURE 1
( A ) R OLL MILL FOR METAL SHEETS .
M ULTIPOLE MODELS OF ( B ) DC MOTOR , ( C ) STRIP COILER , ( D ) ROLLING PROCESS .
FIGURE 2
D ATA FLOW IN DYNAST S OLVER
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FIGURE 3
D ISTRIBUTED ENVIRONMENT FOR SIMULATION , VIRTUAL EXPERIMENTS AND CONTROL DESIGN .
FIGURE 4
D IALOG BOX FOR THE CYLINDER SUBMODEL IN A COPYING LATHE MODEL IN DYNAST S HELL .
FIGURE 5
E XAMPLES OF VIRTUAL EXPERIMENTS DRIVEN BY DYNAST IN C ORTONA .
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Figure 8 Inverted pendulum.
FIGURE 6
INVERTED PENDULUM AND ITS MODEL IN DYNCAD.
(a) (b)
FIGURE 7
A NALOG PID CONTROL OF THE INVERTED PENDULUM IN DYNCAD.
FIGURE 8
D IGITAL PID CONTROL OF THE INVERTED PENDULUM IN S IMULINK WITH DYNAST MODEL OF THE PLANT .
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