Software for Fluid Power Technology

From Editor

Introduction - DYNAST Concept

DYNAST is easy-to-use for all users acquainted with MS Windows. To distract users from the system dynamics as little as possible, DYNAST does not assume any computer programming (and compilation). Yet it is sufficiently flexible and allows for communication with other software packages, even across the Internet. For example, instead of offering a choice of different integration routines like the other simulation packages, there is only one such routine, but very efficient and robust that it is capable of solving a wide class of problems without any user's intervention.

The input language of DYNAST was conceived as strongly problem oriented and, at the same time, as a user- rather than as a computer-friendly language. In fact, the average user does not need to learn the language at all thanks to the wizard dialogs. In addition, the submitted input data is checked continuously by a syntax analyzer and any errors in the data are promptly pointed out. On the other hand, more advanced users can develop sub model libraries of their own and play with the parameters of the computational algorithms.

Model Description

As an equation solver, DYNAST can be applied to systems of non-linear differential, algebraic or algebro-differential equations in the implicit form. DYNAST can be thus used not only for dynamic, but also for static and kinematic analysis. The equations can be submitted to DYNAST directly in a natural textual form without the need to convert them into a block diagram. Thanks to the implicit form of the equations and to their simultaneous solving, DYNAST imposes no restrictions on the equation structure and does not require their sorting. The order of differential equations may even change during their solution.

The equations can be defined by very flexible symbolic expressions using a rich variety of transcendent, polynomial, impulse, random, delay and piece-wise linear mathematical functions, which can be truncated, repeated periodically, controlled by logical conditions or by computed events, etc. Also measured data in a tabular form can used to specify a two- or three-dimensional function.

2. Mulipole Models

Unified physical-level modelling of mixed physical-domain systems is based in DYNAST on the multipole approach. The modelled systems are considered as decomposed into disjoint subsystems. Such a decomposition is similar to the idea of the free body diagrams in mechanics or control surfaces in thermodynamics. The multipole model of a subsystem is an approximation of the subsystem energy interactions with the rest of the system based on the assumptions that

• the interactions take place just in a limited number of interaction sites
• the interaction sites are formed by adjacent energy entries into the subsystem like electrical terminals, fluid inlets, shafts or other mechanical links, heat transferring surfaces, etc.
• the energy flow through each such entry can be expressed by a product of two complementary power variables

Examples of power-variable pairs in different physical domains make force - velocity, torque - angular velocity, volume flow rate - pressure, electrical current - voltage, magnetic flux rate - magnetic voltage, or entropy flow - temperature. The first quantity given in each of these pairs is a through variable whereas the second one is an across variable. These two groups of variables differ in the way they can be directly measured. A through variable is measured by an instrument included between entries, which must be disconnected first. On the other hand, an across variable is measured between distant entries without the need for any disconnection.

As an illustrative example, let us consider a copying lathe the cross-section of which is given in Fig. 1a. The cross-slide together with the cylinder and hydraulic servo system is travelling with constant speed along the bed of the lathe (in the direction perpendicular to the plane of the drawing). The stylus, which follows the variable contour of the rotating master, is fixed to the spool of the valve that controls the fluid flow into the cylinder. The cylinder carrying a tool shaping the manufactured work piece is movable while the piston is stationary.

In Fig. 1b, the lathe is decomposed into several subsystems that are sketched there as detached from each other. The sites of energy interaction between the subsystem energy entrances are denoted by small circles. The site A_x corresponds to the energy interaction between the stylus and the spool due to their translational motion along the x axis. Similarly, the site B_x represents the translational-energy interaction between the containers of both the spool valve and the cylinder as well as of the working tool. The sites C and D correspond to the fluid-energy interactions between fluid inlets of the valve, the cylinder and a fluid supply. The mutual energy interactions of several entries at a site are indicated in Fig. 1b by line segments placed between each site and the related entries.

A system can be decomposed into subsystems representing the components from which the real system is assembled, but a subsystem may be formed also by an aggregate of such components, or just by some physical effect. An example of the latter case gives the subsystem representing in Fig. 1b the friction between the contact surfaces of the cylinder container and the longitudinal slide.

Fig. 1: Copying lathe (a) assembled, (b) decomposed

3. Dynamic Diagrams

Once the decomposition of a system configuration is completed, the system dynamics can be easily represented by a dynamic diagram. The dynamic diagram of a system consists of graphical symbols representing the system submodels, i.e. models of the individual subsystems in the system. In DYNAST, a dynamic diagram can be set up from submodel symbols stored in submodel libraries using a schematic editor. A dynamic diagram corresponding to the copying lathe decomposition given in Fig. 1b is shown in Fig. 2. Each energy entry of a subsystem is represented in its submodel by a pole. The poles are denoted graphically by pins sticking out of the multipole symbols. The interaction sites in the real system are represented in the dynamic diagram by its nodes denoted by labels.

Fig. 2: Parameters for the CYLINDER submodel of the copying lathe

The incidence between nodes and multipole poles in a dynamic diagram is identical with the incidence between the interaction sites in the real system and the energy entrances of the subsystems. This incidence is denoted in the diagram by line segments called connects and interconnecting the nodes with the poles (compare the line segments in Fig. 1b and Fig. 2). The connects can be considered as ideal energy-transferring elements. In the mechanical domain they represent massless absolutely rigid links, in the fluid domain they behave as rigid conduits with ideal massless incompressible fluid, etc. The across variables at both ends of a connect are identical, while the through variable entering one end of the connect must leave the other end without any change.

The simplest multipoles in DYNAST submodel libraries are twopole physical elements. The elements are considered to be 'pure' in the sense that each of them exhibits a unique behaviour like energy dissipation (resistors and dampers), energy accumulation by the virtue of an across variable (capacitors or inertors), or energy accumulation by the virtue of a through variable (inductors and springs). In general, the pure elements can be non-linear, time-variable and controlled by external variables or parameters. (Ideal elements are those pure elements that are linear and time-invariant.) The kit of physical elements includes also pure sources of across and through variables. Energy conversion from one form to another can be modelled by pure transducers.

In Fig. 2, a pure damper is used to model friction between the cylinder and the slide, and the other damper models the dissipation of energy in the working process. The compliance of the workpiece is modelled by a pure spring. The velocity enforced by the rotating master on the stylus is imitated by the velocity actuator. The inertor models the inertial mass of the parts moving along x. A pure source of pressure stands for the fluid supply. The spool valve and the cylinder are modelled by more complex submodels stored in one of the DYNAST submodel libraries. Note also the symbols for the fluid drain and for the reference frame in the diagram.

In dynamic diagrams, multipoles may be combined with blocks. For example, in Fig. 2 integrating blocks are used to compute the x-positions of the stylus and of the tool. Blocks are also used in dynamic diagrams to model subsystems transferring energy predominantly in one direction only, like electronic controllers or sensors. Note the difference between connects and the line segments interconnecting block in a block diagram. In the latter case, only one variable is associated with each line segment, and this variable can propagate along the segment in one direction only. The energy flow associated with each connect can propagate along it in any direction.

4. Submodel Libraries

DYNAST is accompanied by libraries of submodels for electronic and fluid-power devices, electromechanical transducers, mechanical parts, control units, etc. As shown in the open dialog box for the CYLINDER submodel in Fig. 2, the default values of submodel parameters can be overridden by values specified manually one by one, or by a file with parameter values from a component catalogue. Each DYNAST submodel description is encapsulated in an independent file. The parameter values need not be constants, the can be specified by similar symbolic expressions like the equations.

Similar to system models, the submodels can be described by a combination of equations, pure twopoles, pure transducers and blocks as well as by other library submodels. Thus, the library submodels can be nested in a hierarchical way. The libraries are open for easy addition of user-defined submodels and symbols. There is no need for forming a special dialog box for each new submodel.

Using the multipole approach in DYNAST is of several important advantages:(2) the colors of these ports have to be same.

• dynamic submodels 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 (i.e., fluid power devices, electronic elements, electrical machines, mechanisms, etc.) by specialists in the field
• the submodels can be represented by different descriptions each of them suiting best to the related engineering discipline or application (by 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 rotational hydraulic one) can be taken into account without interfering with the rest of the system model

DYNAST Software System

The DYNAST system consists of several software packages. Fig. 3 shows the configuration of the DYNAST Solver composed from several sections. The section SYSTEM reads in problem descriptions submitted in a textual file as a set of algebro-differential equations and/or as the netlist of a dynamic diagram. In the latter case, this section formulates equations underlying the diagram.

The non-linear 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 sweeped 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 non-linear systems.

The DYNAST equation-solving routine 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 optimised during the integration to minimise 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 linearisation of the analysed non-linear equations. Thus the non-linear system models can be subjected to small-excitation analysis in the vicinity of their user-specified or computed quiescent operating point.

Operator functions representing transfer functions and transforms of initial-state responses for linearised system models can be computed by the PZ section. 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 semisymbolic-form 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 of fluid-lines) DYNAST analyses in the AC section.

Fig. 3: Data flow in DYNAST Solver

2. Access to DYNAST Solver

Thr DYNAST Solver can be installed either directly on the user's computer, or it can be installed on a server and then accessed across the Internet or Intranet. In both options, the access is enabled by software forming a DYNAST working environment. In the latter option, outlined in Fig. 4, DYNAST allows for collaboration of remote users working on a common project. It can be also utilised as a learning tool supporting a web-based course related to system dynamics. A special server-based software has been developed for the course tutors to monitor the students' performance, to correct their errors and to inspire them.

The DYNAST Solver can be accessed across the network in a web-based, on-line, and e-mail mode. The web-based mode allows for communication with the server without installing any special software (besides a browser enabling Java applets) on the client computer. There are two options for a graphical display of the computed responses on the client screen after they are computed on the server. The plots can be either generated on the server and sent in HTML to the client, or they can be visualised on the client computer by means of a Java applet.

The schematic editor DYNCAD in the form of a Java applet enables setting up dynamic diagrams directly on the Web. Besides symbols of pure two poles from different physical domains, pure transducers and blocks, also submodel libraries can be utilised and created using DYNCAD. It converts diagrams into the DYNAST input language and sends the data to DYNAST Solver across the Internet. Users can open their free private accounts in DYNCAD and store there their simulation problems. DYNCAD is also able to export the submitted diagrams to PostScript and to send them by e-mail. The e-mail access was designed for those with limited access to the Internet. After sending e-mail containing input data for DYNAST to the address dynast@virtual.cvut.cz, subject: compute, the computed results are sent back to the user's e-mail address automatically.

To utilise DYNAST in an even more comfortable and user-friendly way, working environment called DYNSHELL should download from the server and installed on the client PC with MS Windows. This allows for on-line access to DYNAST Solver. The same working environment is used also in connection with the single-user version of the DYNAST Solver installed on the same computer. Besides the context-sensitive help system, users of DYNSHELL are supported by the DYNSHELL tutorials, DYNAST users guide, libraries of submodels, collection of solved and resolvable examples, and a Web-based course on multipole modelling. DYNSHELL also provides access to a server-based software for documenting simulation experiments in PS, PDF and HTML formats.

The DYNAST Solver can communicate either directly, or across the Internet or Intranet with other software packages. DYNAST can be used as a Matlab modelling toolbox for control design or optimisation, it can communicate with Simulink via its S-function. Co-simulation with other packages is possible too. DYNAST is also used to drive animation of 3D objects visualized using VRML.

Fig. 4: Access to DYNAST Solver across the Internet or Intranet

Conclusion

References

Mann, H. and Sevcenko, M. 2001. Simulation and control design of fluid power systems across the Internet. Proc. 2nd Int. Workshop on Computer Software for Design, Analysis and Control of Fluid Power Systems, Ostrava, Czech Republic.

HM