Numerical Challenges in continuous-time Co-Simulation

Transcription

1 Numerical Challenges in continuous-time Co-Simulation AVL German Simulation Conference, Ulm, Dr. Martin Benedikt VIRTUAL VEHICLE Research Center Graz, Austria COMET K2 Competence Center - Initiated by the Federal Ministry of Transport, Innovation & Technology (BMVIT) and the Federal Ministry of Science, Research & Economics (BMWFW). Funded by FFG, Land Steiermark and Steirische Wirtschaftsförderung (SFG)

2 ViF/AVL Strategic Cooperation Co-Simulation Seed Action Innovation VIRTUAL VEHICLE / Benedikt AVL German Simulation Conference / Ulm 2

3 Why Co-Simulation? Many sub-systems impact energy efficiency of aggregate system Higher integration levels of multiple mechatronic systems required Integration on controls and physics Sub-systems modelled in a plurality of legacy authoring tools Co-simulation supports the use of legacy tools with its dedicated solvers Co-simulation supports the use of IP sensitive simulation solutions Co-simulation environment must be based on least common denominator Non-iterative co-simulation is the viable industrial solution! 2018 / Benedikt AVL German Simulation Conference / Ulm 3

4 Two perspectives 2018 / Benedikt AVL German Simulation Conference / Ulm 5

5 Continuous-time Co-Simulation Challenge ABS Scenario: Full braking after acceleration to 100 km/h Significantly shorter braking distance by accurate coupling! 2018 / Benedikt AVL German Simulation Conference / Ulm 6

6 Non-iterative Co-Simulation aliasing effects due to sampling estimation error due to extrapolation discontinuities at coupling time instants 2018 / Benedikt AVL German Simulation Conference / Ulm 7

7 Problem: Aliasing Effect of sampling a continuous signal in frequency domain sampling time (macro step size) 2018 / Benedikt AVL German Simulation Conference / Ulm 8

8 Problem: Estimation Error Modelling of the transfer behaviour of the coupling process time-delay introduced 2018 / Benedikt AVL German Simulation Conference / Ulm 9

9 Solution Approach - NEPCE effective bandwidth 2018 / Benedikt AVL German Simulation Conference / Ulm 10

10 Non-iterative Co-Simulation Embedding of anti-aliasing filter effective bandwidth Embedding of smoothing filter 2018 / Benedikt AVL German Simulation Conference / Ulm 11

11 Frequency consideration & stiffness Bandwidth of couling signal (system dynamic) determines of both, stepsize of the underlying solver as well as the macro-step-size fast dynamics towards stiff dynamics macro-step filtering 2018 / Benedikt AVL German Simulation Conference / Ulm 12

12 NEPCE - Relaxing numerical stiffness 2018 / Benedikt AVL German Simulation Conference / Ulm 13

13 Simple but realistic demo example Motivation Hidden co-simulation functionality within available tools FMUs generated for integration into 3rd party tools, e.g. GT, Cosimate, etc. Demonstration of Model.CONNECT benefits Example: Stiff Spring Damper Mass Cascade* (decomposed rotational shaft) acceleration torque Mass speed torque Spring Damper Mass speed torque Spring Damper Mass speed brake torque * M. Benedikt, E. Drenth; Relaxing Stiff System Integration by Smoothing Techniques for Non-Iterative Co- Simulation, IUTAM Symposium 2018, Darmstadt Benedikt 2018 NEPCE Evaluation Example 14

14 Reference Simulation and FMU integration 1) Reference Model in Simulink Matlab 2) Exported as FMU (via FMI.Lab) 3) Integration of FMU s Matlab R2017b FMU FMU FMU Model.CONNECT Matlab FMU FMU FMU Model.CONNECT FMU FMU FMU Benedikt 2018 NEPCE Evaluation Example 15

15 Reference Simulation and FMU integration Coupling Error Exact steady state result Benedikt 2018 NEPCE Evaluation Example 16

16 Outlook / up-coming approaches FMI for Co-Simulation (10/2010) Tool FMU Model Solver 2018 / Benedikt AVL German Simulation Conference / Ulm 21

17 Directional Derivatives Utilization utilization of linearized subsystems (!) by master algorithms enables linearly-implizit (explizit) master algorithms (internal states needed) enables interface-jacobian-based master algorithms (pre-step stab.) NEPCE-ll 2018 / Benedikt AVL German Simulation Conference / Ulm 22

18 Directional Derivatives Utilization Directional Derivatives improve stability behaviour in general! Model.CONNECT s pre-step algorithm outperforms linear-implicit schemes! 2018 / Benedikt AVL German Simulation Conference / Ulm 23

19 Conclusion Co-simulation is performed because of rather complex subsystems simulations, inherently representing stiff system simulations and, iterating over macro-steps and extracting model-information is pratical (almost and till now) impossible. Model.CONNECT solutions relaxing stiffness for (model-free) non-iterative schemes out performs classical linear-implicit non-iterative schemes 2018 / Benedikt AVL German Simulation Conference / Ulm 24

20 Thanks for your attention! Dr. Martin Benedikt Head of Co-Simulation and Software VIRTUAL VEHICLE Research Center, Graz, Austria 2018 / Benedikt AVL German Simulation Conference / Ulm 25