A Multi-Paradigm Modeling Approach for Hybrid Dynamic Systems Jin-Shyan Lee1,2, Meng-Chu Zhou2, and Pau-Lo Hsu1 1Dept. of Electrical & Control Engineering
National Chiao-Tung University, Hsinchu, Taiwan 2Dept. of Electrical & Computer Engineering
New Jersey Institute of Technology, Newark, USA
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Outline
I.
Introduction
II. Petri-Net Based Framework III. Example: A Rapid Thermal Process IV. Conclusion
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
I. Introduction
z
Why do we have modeling and simulation? –
Modeling is a way of representing our knowledge about structure and behavior of systems and further answering questions about them via the simulation (Mosterman and Vangheluwe, 2002).
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Traditional System Modeling ¾ Time-driven, continuous variable systems (CVS) z
Differential/Difference equations.
¾ Event-driven, discrete event systems (DES) z
Finite state automata or Petri nets (Cassandras and S. Lafortune, 1999; Zhou and Jeng, 1998)
¾ Both are to reduce the complexity for presenting real systems. 4
Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Issues in Traditional System Modeling ¾ Most practical systems have both the time-driven and event-driven dynamics and form the so-called hybrid dynamic systems (HDS).
¾ Relative literature (special issues) on HDS – Antsaklis and Nerode, “Hybrid control systems: An introductory discussion to the special issue,” IEEE Trans. Automat. Contr., 1998.
– Morse et al, “Introduction to the special issue on hybrid systems,” Automatica, 1999.
– Antsaklis and Lemmon, “Introduction to the special issue,” J. Discrete
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Event Dynamic Syst, 1998. Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Modeling Approaches for HDS ¾ Integrate Continuous and Discrete Models –
Extend CVS to include event-driven dynamics z
–
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Linear piece-wise systems (Branicky et al, 1998)
Extend DES to include time-driven dynamics z
Hybrid automata (Lygeros, 2003), Hybrid Petri nets (David and Alla, 1994), Hybrid Statechart (Lee and Hsu, 2002).
z
Commercial Software: MATLAB Simulink with Stateflow (Harman and Dabney, 2001), VHDL-AMS (Bakalar and Christen, 1999). Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Motivations ¾ Simultaneously dealing with the discrete and continuous variables is very difficult. ¾ Their mathematical backgrounds are completely different: event-driven vs. time-driven dynamics. ¾ Most of the existing HDS modeling approaches result in a unified, but more complicated and unnatural model. ¾ Design engineers cannot be allowed to use their preferred domain models.
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
II. Petri-Net Based Framework
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PN-Based Approach –
Use Petri net (PN) to model the event-driven dynamics
–
Use the Differential/Difference equations to model the time-driven dynamics
–
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Define the interfaces for model communications
Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Advantages of Using PN
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Graphic representation.
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More compact representation.
z
A structured model of DES dynamics.
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Mathematical support (reachability, invariant, reduction, siphon/trap, and simulation; Zhou and Jeng, 1998).
z
PN family (Stochastic PN, Colored PN, CTPN, Automation PN…etc)
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A large body of existent tools and software for PN analysis and design. http://www.daimi.au.dk/PetriNets/tools/ Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Multiple Models in Hybrid Control Systems Coordination Controller
Discrete Event Domain Signal Generator
Discrete Time Domain
Event Generator
Digital Controller
Holder (D/A)
Continuous Time Domain
…
Interface
Other Digital Controller
…
Sampler (A/D) Physical Plant
…
Other Physical Plant
…
Fig. 1. Multiple domains in hybrid control systems.
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
PN-Based Framework Command: start operation Working
Response: end operation
Completed
Exa mple : x1= f (x1, t) x2= f (x2, t) y= f (x1, x2, t)
s ta te e qua tions of unde r controlle d de vice s
Time dynamics
boundary interface Controllable Transition
Event dynamics
Hierarchical Hybrid Place
Fig. 2. Modeling the continuous dynamics within a Petri net via a hierarchical way.
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Comparison: Hybrid Petri Net (David & Alla, 1994) Discrete Petri nets start
end
Working
Completed
Self-loop
x1 x2
t
Continuous Transition
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y
Continuous Petri nets
Continuous Place
Fig. 3. Hybrid Petri net (with a net structure to model continuous dynamics). Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Discrete-Event & Discrete-Time Models Trigge r e ve nt
Digita l s igna l
Signal Generator (a )
Thre s hold-cros s ing
Eve nt
Event Generator (b)
Fig. 4. Interfacing devices in high level: (a) signal and (b)event generators.
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Discrete-Time & Continuous-Time Models
Ana log s igna l
Digita l s igna l
Sampler (A/D) (a )
Digita l s igna l
Ana log s igna l
Holder (D/A) (b)
Fig. 5. Interfacing devices in low level: (a) sampler and (b) holder.
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
III. Example: A Rapid Thermal Process Reaction Chamber
Exhaust
Temperature Controller
Pressure Controller-II
Flush Pump Heating Lamp
Bypass
Gas Supply Mass Flow Controller
Chamber Door
Pressure Controller-I Source Gases (e.g. H2, N2, O2)
Wafer
Fig. 6. A rapid thermal processor.
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Robot Arm
Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
A Hydrogen Baking Process Step 1) Step 2) Step 3)
Step 4) Step 5)
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Load the raw wafer. Close the chamber door. Open the gas valve to supply gases with a desired gas flow rate and pressure of 2.8 liters per minute (lpm) and 0.5 Torr, respectively. Close the gas valve. Turn on the heating lamp to bake the wafer with a desired baking temperature and time of 1000°C and 4 seconds, respectively. Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
A Hydrogen Baking Process (cont’d) Step 6)
Turn off the heating lamp.
Step 7)
Turn on the flush pump with a desired pressure of less than 0.05 Torr.
Step 8)
Turn off the flush pump.
Step 9)
Open the chamber door.
Step 10) Unload the processed wafer. 17
Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
PN Model p1
Load Wafer t1
t2
p2
Close Door t3
p3
Controllable transitions
t4
p4
Hierarchical Hybrid Places
p5
Supply Gas
Bake Wafer
p7
p14 p16
t12
t11
p13
p15
t9
t10
p11
t8
p10 t7
p9
t6
t5
p6
p12 p8
Flush Chamber p17
t14
p18
t15
Open Door p20
p21 t16
t13
p22
t18
Unload Wafer p23
t17
t19
p24
t20
p25 p26
p19
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Fig. 7. PN model of the RTP system. Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Table I. Notations for the PN model in Fig. 7
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Place p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 p23 p24 p25 p26
Description Raw wafer buffer Loading wafer Loading wafer completed Closing chamber door Closing chamber door completed Opening gas valve Mass flow controller ready Pressure controller-I ready Opening gas valve completed Closing gas valve Closing gas valve completed Turning on heating lamp Turning on heating lamp completed Temperature controller ready Turning off heating lamp Turning off heating lamp completed Turning on flush pump Turning on flush pump completed Pressure controller-II ready Turning off flush pump Turning off flush pump completed Opening chamber door Opening chamber door completed Unloading wafer Unloading wafer completed Processed wafer buffer
Transition t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20
Description Cmd: start loading wafer Re: end loading wafer Cmd: start closing chamber door Re: end closing chamber door Cmd: start opening gas valve Re: end opening gas valve Cmd: start closing gas valve Re: end closing gas valve Cmd: start turning on heating lamp Re: end turning on heating lamp Cmd: start turning off heating lamp Re: end turning off heating lamp Cmd: start turning on flush pump Re: end turning on flush pump Cmd: start turning off flush pump Re: end turning off flush pump Cmd: start opening chamber door Re: end opening chamber door Cmd: start unloading wafer Re: end unloading wafer
Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Fig. 8. Pressure and temperature in one cycle processing. Pressure in Chamber
Magnitude (torr)
0.8 Turn off ga s
0.6
Turn on pum p
0.4
0.2
0
Turn on ga s
0
Turn off pum p
10
20
loa d
30 Time (sec)
40
Temperature in Chamber
50
60
u nloa d
1200 ba king
Turn off la m p
Degree (centigrade)
1000 800 600 400 Turn on la m p
200 0
20
0
10
20
30 Time (sec)
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Session ThP09, Sept. 2. 2004
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IEEE CACSD, Taipei, Taiwan
IV. Conclusion ¾ We have presented a Petri net-based framework to model the hybrid dynamic systems.
¾ Future Work –
From a idea/concept, to a methodology, even to a theory…
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
Q&A Thanks for your time and attention! Jin-Shyan Lee Email:
[email protected] Tel: 886-3-5712121 ext. 54417
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Session ThP09, Sept. 2. 2004
IEEE CACSD, Taipei, Taiwan
