DLR FF-DR-ER, Technical Report TR R101-93, March

Transcription

1 DLR FF-DR-ER, Technical Report TR R101-93, March The ANDECS Simulation Environment DSSIM Martin Otter Institute for Robotics and System Dynamics German Aerospace Research Establishment (DLR), Oberpfaenhofen Abstract DSSIM is a general purpose simulator for dynamic systems. It is part of the ANDECS R environment, a software package for the analysis and design of controlled systems. DSSIM solves initial value problems of explicit ordinary dierential equations and of dierential-algebraic equations. A unique feature is the close interaction with an engineering database system, e.g. to automatically store all simulation results together with the input data on database. 1 Introduction In this paper the ANDECS R simulation environment DSSIM and the modelling environments for DSSIM are presented. ANDECS R1 [6] is a powerful and exible software package for the analysis and design of controlled dynamic systems. It is developed at the DLR on the basis of the engineering database system RSYST [9] of the University of Stuttgart and consists of the following components: Basic Methods: Basic mathematical methods like matrix computation using the Matlab syntax, interpolation of signals or root nding of nonlinear functions. Linear Methods: Analysis and design methods for linear dynamic systems like linear simulation, calculation of poles and zeros, pole placement, LQG or H1. Simulation: Simulation environment for DSblocks (see below), including linearization and calculation of stationary points. Optimization: Multi-objective parameter and trajectory optimization. The design history is recorded on an automatically evolving database, allowing new design directions to be started from the actual or from past design steps. Visualization: Standard diagrams like 2-D line, Bode, Nyquist and root locus diagrams. Special diagrams like parallel coordinates to visualize optimization criterias. DSSIM 2 [5] is the run time environment of ANDECS R to simulate dynamic systems. It is not a special purpose simulator for robots, but a general purpose one with emphasis on the modelling and simulation of controlled mechanical systems. 1 ANDECS stands for Analysis and Design of Controlled Systems and is a registered trademark of DLR. 2 DSSIM stands for Dynamic System Simulation.

2 DLR FF-DR-ER, Technical Report TR R101-93, March The ANDECS Modelling Environments Modelling and Simulation in ANDECS are separated into two distinct parts as shown in Figure 1. The interface between these two parts is dened by a neutral description of input/output blocks, which are realized as Fortran- or C-subroutines with dened formal arguments. A block of this type is called DSblock (= Dynamic System block) [8]. domain specific model libraries for Dymola mechanics electronics... ACSL multibody modelling environments model export a model is described by upto 11 FORTRAN or C subroutines with the neutral DSblock interface neutral model bus model import... DSSIM... simulation environments Figure 1: Separation of modelling and simulation by DSblock interface A DSblock allows the description of generic, time-delayed, time-, state-, and step-event dependent explicit ordinary dierential equations (ODE), dierential-algebraic equations (DAE), and overdetermined dierential algebraic equations (ODAE). The latter equations appear, if a higher index dierential algebraic equation is transformed to an index 1 equation, e.g. in multibody systems with closed kinematic loops or in transistor models of electronic circuits. The event-handling feature is used to treat discontinuous equations or equations with varying structure, e.g. impact, friction, backlash, sampled data systems. Modelling is not performed in module DSSIM. Existing modelling environments are enhanced by a code generator, which generates a standardized DSblock. Numerical programs are enhanced by a subroutine layer in DSblock format, which allows the calling of the software package at specic time instants to calculate the right hand side of the dierential equation. Presently, the following modelling environments have been enhanced by DSblock code generators: ACSL A general purpose simulation language [7]. ACSL is the de facto industrial standard for simulation languages. Dymola A new, very powerful, object oriented modelling language [2, 1, 3]. Simpack A general purpose multibody program [10]. Dymola is the prefered modelling environment for ANDECS. It supports the building of

3 DLR FF-DR-ER, Technical Report TR R101-93, March domain specic model libraries. Models are hierarchically decomposed into submodels and can be connected together according to the physical coupling of the components. The multibody part of the Manutec r3 benchmark models [4] are for example dened in the following way in the Dymola {use multibody library mbsdir.lib; O(n) algorithm} model dlr1_mbs submodel (Inertial) i (ng3=-1) submodel (Revolute) r1 (n3=1), r2 (n1=1), r3(n1=1, r3=0.5) submodel (Revolute) r4 (n3=1, nrot3=1, Jrot=1.6e-4, irot=-99) submodel (Revolute) r5 (n1=1, nrot3=1, Jrot=1.8e-4, irot= 79.2, r3=0.73) submodel (Revolute) r6 (n3=1, nrot3=1, Jrot=4.3e-5, irot=-99) submodel (Body) m1 (I33= 1.16) submodel (Body) m2 (m =56.5, r1 = 0.172, r3 = 0.205, I11= 2.58, I22= 2.73, I33= 0.64, I31= -0.46) submodel (Body) m3 (m =26.4, r1 = 0.064, r3 =-0.034, I11= 0.279, I22= 0.413, I33= 0.245, I31=-0.070) submodel (Body) m4 (m =28.7, r3 = 0.32, I11= 1.67, I22= 1.67, I33= 0.081) submodel (Body) m5 (m = 5.2, r3 = 0.023, I11= 1.25, I22= 1.53, I33= 0.81 ) submodel (Body) m6 (I33=0.0001) input t1, t2, t3, t4, t5, t6 { Connection structure of robot } connect i to r1 to r2 to r3 to r4 to r5 to r6 connect m1 at r1, m2 at r2, m3 at r3, m4 at r4, m5 at r5, m6 at r6

4 DLR FF-DR-ER, Technical Report TR R101-93, March { The torques in the joints are the input signals, e.g. from other submodel} r1.f = t1 r2.f = t2 r3.f = t3 r4.f = t4 r5.f = t5 r6.f = t6 end 3 The ANDECS Simulation Environment DSSIM Before simulations of DSblocks can be carried out by DSSIM, the desired DSblocks must be introduced to the system by a conguration module. This module generates a le, which has to be compiled together with the corresponding DSblock subroutines. After a new binding run, the dened DSblocks are available within ANDECS and can be simulated by DSSIM. Since any number of DSblocks can be kept in the executable image simultaneously, online switching between design alternatives or system representations of various complexity is possible. The result of a simulation experiment is a set of computed signals, which are automatically stored on a RSYST-database and visualized with any available graphics module. All input data of an experiment, e.g. integration method or length of communication interval, are stored on database as well. Therefore every simulation run is completely documented and reproducible. Figure 2 shows a screen-hardcopy of a typical DSSIM session. In the lower left part, the input window is shown. In the right part, the RSYST database browser is present and in the upper left part the online graphics of DSSIM can be seen. The DSSIM simulation environment uses well-tested numerical integration routines from various sources. Presently the following solvers are provided: Deabm Lsode Lsodar Rk45/78 Grk4t Dassl/rt Multistep solver of Shampine/Watts for non-sti and moderately sti ODEs. Multistep solver of Hindmarsh for sti and non-sti ODEs. Multistep solver of Petzold/Hindmarsh, which switches automatically between a non-sti and a sti integration algorithm along the solution. Lsodar also provides a root nder. Runge-Kutta-Fehlberg solvers of Kraft/Fuhrer of xed orders 5 and 8 with variable stepsize using the Prince-Dormand coecients. A(89.3)-stable linearly-implicit Rosenbrock type single-step solver of xed order 4 for sti and oscillating ODEs of Arnold. Multistep solvers of Petzold for DAEs and for DAEs with root nder.

5 DLR FF-DR-ER, Technical Report TR R101-93, March Figure 2: Simulation Environment DSSIM Odassl/rt Multistep solvers of Fuhrer based on Dassl/rt of Petzold for ODAEs and for ODAEs with root nder. Mexx Extrapolation solver of Lubich for a restricted class of index-2 ODAEs. There are a wide variety of options available to dene a simulation experiment. For example, the communication time grid can be dened as an equidistant grid, as an arbitrary user dened grid or as an automatic grid. Based on the RSYST module concept and its macro facility DSSIM can be combined with other RSYST and ANDECS modules. This allows customized realizations of analysis and design tools which use nonlinear time simulation in combination with e.g. active online monitoring, parameter variation, multi-criteria parameter and trajectory optimization or Monte Carlo experimentation. 4 Software and Hardware Requirements Presently (= December 1992) ANDECS is available for IBM RS6000 and HP/Apollo workstations. ANDECS will become available for Unix workstations of other vendors as well. ANDECS is written in Fortran 77 and C and requires the following software products as basis: Unix System V.3, X-Window 11.4, Motif 1.1, Phigs. It is planned to reimplement the graphics of ANDECS directly on X-Window. In this case Phigs is no longer needed. ANDECS and the ANDECS simulation environment DSSIM are available from: Prof. G. Grubel, Institute for Robotics and System Dynamics, German Aerospace Research

6 DLR FF-DR-ER, Technical Report TR R101-93, March Establishment (DLR), D-8031 Oberpfaenhofen, Germany. Phone: 08153/28-484, df12@vm.op.dlr.de References [1] Cellier F.E.: Continuous System Modeling. Springer-Verlag, New York, [2] Cellier F.E., and Elmqvist H.: The Need for Automated Formula Manipulation in Object- Oriented Continuous-System Modeling. IEEE Symposium on Computer-Aided Control System Design, CACSD'92, March 17{19, 1992, Napa, California. [3] Elmqvist H.: A Structured Model Language for Large Continuous Systems. Ph.D. dissertation. Report CODEN:LUTFD2/(TFRT{1015), Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, [4] Franke J. and Otter M.: The Manutec r3 Benchmark Models for the Dynamic Simulation of Robots. Separate contribution in Volume I of \The International Handbook on Robot Simulation Systems", editor D. Wloka. [5] Gaus N., Otter M.: Dynamic Simulation in Concurrent Control Engineering. IFAC Symposium on Computer Aided Design in Control Systems, Swansea, UK, Preprints pp. 123{126, July, [6] Grubel G., Bals H., Finsterwalder R., Gramlich G., Joos H.-D. and Otter M.: Computer-Integrated Control-Dynamics-Design Experimentation by ANDECS. ESA Workshop Spacecraft Guidance Navigation and Control Systems Software for Design and Implementation, Noordwijk, 29. Sep - 1. Oct, [7] Mitchell E.E.L., and Gauthier J.S.: ACSL: Advanced Continuous Simulation Language { Reference Manual. Edition 10.0, MGS, Concord., Mass., [8] Otter M.: DSblock: A neutral description of dynamic systems. Version 3.2. Technical Report TR R81-92, Institute for Robotics and Systemdynamics, German Aerospace Research Establishment (DLR), Oberpfaenhofen, May [9] Ruhle R.: Rsyst - Ein Softwaresystem zur Integration von Daten und Programmen zur Simulation wissenschaftlich-technischer Systeme. Rechenzentrum der Universitat Stuttgart, RUS-5, Marz [10] Rulka W.: SIMPACK { A Computer Program for Simulation of Large-motion Multibody Systems. Multibody Systems Handbook, edited by W. Schiehlen, Springer-Verlag, 1990.