Herman Mann and Lukas Waldmann
Czech Technical University, Zikova 4, CZ-166 35 Prague 6, Czech Republic
Keywords: engineering systems, modeling, simulation, analysis, Internet
The paper presents a unified approach to physical-level modeling and simulation of those systems the function of which is based on diverse physical phenomena treated traditionally by different engineering disciplines. Using examples, the paper attempts to show that the multipole approach to modeling of such systems is considerably more straightforward and efficient than the common block-diagram or bond-graph approaches. This has been verified well by developing and exploiting a simulation package DYNAST based on the unified appro-ach, which has been well tried also in control design. Now, DYNAST has been implemented on a super-computer and made accessible via the Internet to support cooperation of remote engineering teams and interactive learning of distance-education students.
It is well recognized that computer-based simulation is an indispensable engineering design tool as well as a learning tool. It helps engineers to develop products which are more competitive, and it gives students a better insight into system dynamics. However, to exploit the advantages of simulation to their full extent, both the engineers and students need simulation tools applicable across
Across Engineering Disciplines
The first requirement comes from the fact that most of the contemporary machines, instruments and other systems are of multidisciplinary nature. They utilize phenomena from more than one energy domains (mechanical, electrical, magnetic, fluid, thermal, thermodynamic, etc.) simultaneously. To simulate systems like this, we need unified modeling methods and versatile simulation tools applicable to different engineering disciplines at the same time. Introducing such methods into engineering study makes the curriculum more compact and efficient, and it gives students a more comprehensive view of the real world.
Across Design Levels
One might suggest that just the most popular software tools like MATLAB and SIMULINK, for example, are discipline independent. Yes, that is true, but they are well suited only for those applications where a high level of modeling abstraction and idealization is required. Such simplified functional models are commonly used in control synthesis, for example, due to the limitations of the existing control algorithms. These models, in the form of equations or block diagrams, are only concerned about the system input-state-output transformations, mostly linearized.
In many other phases of the system design and dynamic investigation engineers need, however, more realistic physical models of their systems. These models portray energetic interactions between the system components.
Across Geographical Distances
Simulation across distances is in demand for several reasons :
Physical models must respect
Using the common block diagrams to represent physical models is rather laborious as the diagrams display graphically sets of equations, not the actual structure of the modeled real systems. The underlying equations, and the corresponding block diagram for a system physical model, must be formed 'by hand' first, and only then a computer can be used to process it. Even if the constitutive relations characterizing the individual system components are encapsulated into blocks and stored in the computer memory already, the user still must form the equations and block configuration respecting the component energetic interactions by himself.
As the blocks are usually characterized by explicit equations, the 'causality problem' must be solved at the same time. Also some other specific phenomena, like 'algebraic loops', change-of-order of the underlying differential equations, etc., require special care. The bond-graph approach to the block-diagram construction, or the preprocessors to block-diagram oriented packages like DYMOLA are helpful, but do not remove the computational limitations of these packages.
To overcome these problems, we have genera-lized the multipole approach, known from electrical engineering, and adopted it to physical modeling of multidisciplinary systems. Each multipole models the energetic interaction between a component and the rest of the system assuming that the interactions take place just in a limited number of energy entrances like electrical terminals, pipe inlets, mechanical or thermal contacts, etc. The energy flow through each such entrance - represented by a multipole pole - is approximated by a product of two complementary physical quantities - a through variable and an across variable (e.g., force - velocity, torque - angular velocity, volume flow - pressure, electrical current - voltage, entropy flow - temperature, etc.).
The system physical models can be set up from the component multipole models in a kit-like fashion based on a mere inspection of the modeled real system in the same way as the system is assembled from the real components without forming any equations or graphs. Equation describing the system model can be formulated automatically using
Fig. 1a gives an example of a copying lathe. The cross-slide together with the hydraulic servosystem is traveling along the bed of the lathe (perpendicular to the plane of the drawing). The stylus follows the con-tour of the master (at the top) and the cylinder, con-trolled by the valve, drives the working tool.
In Fig. 1b, the lathe is decomposed into individual components, each of them is then replaced in Fig. 1c by a multipole model (Mann 1995a). The interactions between the real components are represented by line segments coalesced at nodes denoted by small circles. Node A represents motion of the valve spool as well as of the stylus following the master along the axis x.. Node B is representing motion along the axis x common to the valve and cylinder containers as well as to the tool. Nodes C and D correspond to the fluid inlet interconnections of the valve, cylinder and a supply.In Fig. 1c, a pure damper bf is used to model friction between the cylinder and the slide. The combination of pure damper bw and pure spring kw models dynamics of the working process. The ideal velocity actuator M imitates the velocity enforced by the rotating master to the stylus. Inertor m models the inertial mass of the moving parts. The ideal source of pressure S stands for the fluid supply.
Figure 1 (a) Copying lathe, (b) lathe decomposition, (c ) multipole
Like in the previous example, also in many other applications, it is
practical to utilize a kit of low-complexity two-pole physical models,
or physical elements, presented in Table 1. The elements are considered
to be 'pure' in the sense that each of them is characterized by
a simple but specific constitutive relationship and exhibits a unique physical
behavior complementing behavior of the other elements in the kit In general,
the constitutive relations of pure elements can be nonlinear and time-variable.
Ideal elements are pure elements, the constitutive relationship
of which is linear.
|Fluid or acoustic||
Transducers and couplings
Multipole models of transducers and couplings can be based on pure gyrators or pure transfor-mers. Besides the well known energy-transferring breed of these models, we also need their energy-storing modification when modeling electro-mechanical devices (Mann 1995b). Again, these pure models do not have to be ideal in DYNAST, their parameter can be nonlinear, controlled and time-variant. To show the need for pure energy-storing transducers, models of an electromagnetic relay are shown in Fig. 2.
The model shown in Fig. 2b utilizes an energy-storing transformer of ratio K(x,i) = i dL/dx where L(x) is the relay inductance which varies with the air-gap width x, i is the inductance current. Electrical resistance of the relay winding, mass of the movable part and friction is represented in the model by additional two-pole elements. Such a model, however, neglects saturation of the magnetic circuit which is assumed infinitely permeable, and ignores leakage and fringing fluxes.
Fig. 2c shows a relay model in which the magnetic circuit is represented in a more authentic way. Coupling between the electrical and magnetic circuits is modeled by an energy-transferring gyrator of ratio equal to the number of winding turns N. The elements Cf and Cg represent permeances of the ferromagnetic core and of the air-gap, respectively. The magneto-mechanical coupling is modeled by an energy-storing gyrator of the ratio factor K(x,w) which changes with the relay displacement x as well as with the magnetic voltage w across the gap. The element R f represents energy losses in the ferromagnetic core. Saturation or hysteresis of the ferromagnetic material can be taken into consideration within the element Cf, and also such effects like leakage and fringing could be respected in this model in a straightforward manner by additional two-pole elements.
Figure 2 (a) Electromagnetic relay, (b) electro- mechanical
and (c) electro-magneto-mechanical multipole model
More then ten years ago, we have developed a multipurpose simulation package DYNAST based on the ideas mentioned above. It has been well tried in many industrial enterprises, research institutes and university departments. DYNAST allows for unified modeling of multidisciplinary systems as well as for their seamless simulation on different levels of modeling abstraction. Using a very flexible object oriented input language, the systems under inves-tigation can be characterized
In the case of multipole models, nothing but the mutual incidences of their poles need to be specified in the input file. DYNAST then formulates all the equations respecting the physical laws governing the mutual energetic interactions between the components in terms of pole variables automatically.
DYNAST is accompanied by a library of models of many typical components. The library is open in the sense that the users can add their own models or model modifications. The component models can be characterized by sets of algebro-differential equations, by tables of measured data, by multipole and/or block configurations, or by a mixture of these.
DYNAST is accompanied by user's environ-ment with a graphical editor for displaying output data in different forms, and with a special input data editor analyzing syntax of the data conti-nuously during their preparation. Block and multipole diagrams can be submitted to DYNAST in their graphical form using a schematic capture editor, even in a hierarchical way.
To solve the resulting nonlinear algebro-differential equations, DYNAST uses a stiff-stable backward-differentiation formula. The length of the integration steps and, at the same time, the order of the method are varied during the integration to minimize the computation time while respecting the admissible computational error. The equation Jacobeans are evaluated using a symbolic differentiation procedure. Considerable savings of computation time and memory are achieved by exploiting the jacobian sparsity. Thanks to the implicit form of the equations and to their simultaneous solving, DYNAST imposes no restrictions on the system structure. There is no need for equation sorting to solve the causality or algebraic loop problem.
For nonlinear systems, DYNAST computes transient responses and also steady-state responses, either static or periodic. The static steady-states can be computed for a system- or ambient-parameter sweeps through an interval. The transient responses can start either from initial conditions specified by the user, or from initial conditions corresponding to a static or periodic steady-state. DYNAST also provides a linearized system model which can be subjected to small-excitation analysis in the vicinity of the user-specified or computed quiescent operating point. This analysis yields operator functions representing either system transfer functions or transforms of system initial-state responses. These operator functions are available in a semisymbolic form with the Laplace operator s as a symbol, and with the polynomial roots (poles and zeroes) and coefficients as numbers. For such operator functions, DYNAST can compute semisymbolic- and numeric-form time-domain characteristics.
DYNAST runs under MS DOS, MS Windows and UNIX. When compared with the most widespread simulation tools by solving the same set of problems, DYNAST was not only much easier to use for physical modeling, but also its computational methods appeared to be very efficient and robust (EUROSIM 1991).
DYNAST in Control Design
In control design, DYNAST can complement a control design package like MATLAB, for example, as a physical modeling toolbox. Models suitable for control synthesis using the MATLAB environment can be obtained by applying the MATLAB System Identification Toolbox to the responses of the plant physical model computed by DYNAST.
DYNAST is utilized as a physical modeling toolbox within the MATLAB environment in the following steps illustrated by Fig. 3 :
Figure 3. DYNAST as a physical modeling toolbox in the MATLAB
The aim of the TeleSimulation project developed in the Computing Centre of the Czech Technical University is to allow simulation across geographical distances. For this purpose, DYNAST was implemented on the CTU supercomputer IBM PS2. By interconnecting this computer with an Internet server a Web access to DYNAST has been arranged via the home page
with the graphical output generated by a Java script.
Users with a limited access to the Internet can utilize DYNAST via the e-mail at the address
email@example.com, Subject : compute
They will receive responses in a pseudo-graphical print-plot form. To try it, please, click here.
For an even more comfortable way of input data preparation and output data evaluation, user's environment can be downloaded from the server. Transfer of data between the server and clients is coded for security reasons. This environment can be also augmented by a schematic capture editor for submitting system models in a graphical form.
There are several other components developed and made accessible via WWW within the TeleSimulation project besides the DYNAST simulation engine :
Currently, these components are interconnected also with the TopClass virtual university environment. DYNAST allows there for interactive problem solving by submitting data directly from the Web pages with the problem assignments.
The next step should be linking the TeleSimulation project with the
Web pages of vendors publishing data sheets of their components, extracting
the component parameters from there and converting them into a format compatible
with DYNAST input language.
EUROSIM Simulation News 1, no. 3 (Nov.): 30~32 (back to citation).
Mann, H. 1995. Simulation of Fluid Systems Using Multipole Modelling. In Innovations in Fluid Power, C.R. Burrows and A.K. Edge, eds. John Wiley, New York, 116-132 (back to citation).
Mann, H. 1995. Circuit Model of Energy-Storing Transducers. Proceedings of the 1995 IEEE Int. Symposium on Circuits and Systems. (Seattle, WA, April 30 - May 3). IEEE, Piscataway, N.J., 1271-1274 (back to citation).