lect 11: hybrid system modeling and simulation

Lect 11: Hybrid System Modeling and Simulation

2 of 31

© 2014 Tag Gon Kim

EE612: Lect. 11 Hybrid System M&S

Hybrid (combined) Modeling Framework

Systems Taxonomy: State vs observation time CS, SDS, DS, DES

Combination of more than two systems in different types listed above

To specify different level of abstraction

Most common in EE: CS (analog) + DS (digital) system

Required is interface between different type (eg. ADC or DAC)

Top-down design/step-wise refinement

Hybrid System in combination of DES + CS

DES Specification of what to do high level behavior of system

CS Specification of how to do lower level detailed behavior

Interface between two

E/A converter: event-to-analog converter

A/E converter: analogy-to-event converter

Application of DES+CS hybrid system

Electro-Mechanical System (CS: Mechanical; DES: Electronics)

Hybrid Control System (CS: PID Controller; DES: Planning/scheduling)

Manufacturing System (CS: Machines; DES: Scheduler)

Mixed Mode Circuit (CS: Analog Circuit; DES: Digital Circuit)

Defense Modeling (CS: Engineering(H/W) Model, DES: Engagement(Process) Model)

Hybrid System Modeling

참고 문헌

JD-18(2001)

JD-19(2001)

CF-70(2001)

© 2014 Tag Gon Kim

3 of 31


Continuous System

Modeling: Differential Equation

Simulation Method: Numerical Analysis with uniform/non-uniform time steps

Representative M&S Tool: MATLAB

Discrete Event System

Modeling: DEVS Equation

Simulation Method: Event scheduling with time advances in a random interval

Representative M&S Tool: DEVSim++

dQ/dt = f(Q, X) = AQ + BX Y = g(Q, X) = CQ + DX

Co

nti

nu

ou

s S

yst

em

Dis

cre

te E

ven

t

Syst

em

Input State Output System Model

Differential Equation

DEVS Equation

q’ = dint(q) dext (q, x )

y = l(q)

time(t)

state(Q)

t

X(t) Y(t)

t

time(t)

state( Q)

t

Xe Ye

t

x3 x2 x3 x4 x5

e1 e2 ek

s1

s2

sk

y2 y4 y3

Simulator

Equation Solver

(eg: MATLAB)

Execution algorithm

for DEVS model

(eg: DEVSim++)

Systems M&S: Continuous vs Discrete Event System

© 2014 Tag Gon Kim

4 of 31


(I) Combined one Formalism (II) Two Formalisms

State Transition

Function

Output Function

Discrete

OUTPUT

Continuous

OUTPUT

Discrete

INPUT

Continuous

INPUT

disc contS S

Discrete

OUTPUT

Continuous

OUTPUT

Discrete

INPUT

Continuous

INPUT

DES

Model

Conti.

Model

E/S S/E

Feature

No use of existing M&S Tools

and Models Use of existing M&S Tools and Model Reuse

New M&S Tools Required Existing M&S Tools

New M&S Theory Existing M&S Theory and Interface Theory

Hybrid M&S Methods

5 of 31

© 2014 Tag Gon Kim


DEVSim++ Engine MATLAB Engine

DEVS Models Differential

Equations

MATLAB DEVSim++

HLA/RTI

HLA/RTI Based Distributed Simulation Environment

KHLAAdaptor KHLAAdaptor

© 2014 Tag Gon Kim

6 of 31


PlusSim Architecture for Hybrid System M&S

Use of existing continuous and discrete event M&S Tools

Distributed simulation using well-defined I/F between CS and DES

Pug-and-Play for both CS and DES in a Single Processor Environment

MATLAB Engine

Differential Equations

MATLAB

DEVSim++ Engine

DEVS Model

DEVSim++

PlugSim

Interface Interface

Time synchronization

Data Exchange

DES M&S Env. CS M&S Env.

Interoperation

Object Model

(IOM)

PlugSim Based Centralized Simulation Environment

Process Communication

Using shared memory

Or TCP

참고 문헌

CF-112(2011)

© 2014 Tag Gon Kim

7 of 31


IOM

Input/Output Data Declaration for Models to be plugged in

Data Mapping Table for Interface in Hybrid Simulation

Use of a pre-define template

Plug-in CS/DES simulators

DEVS Model MATLAB Model

Interface Interface Data1

Data1

Data2

Data3

Data2

Data3

IOM

Name of Data From To

Data1 DEVS MATLAB

Data2 MATLAB DEVS

Data3 MATLAB DEVS

Time Synch Data Exchange PlugSim

Interoperation Object Model (IOM)

8 of 31

© 2014 Tag Gon Kim EE612: Lect. 11 Hybrid System M&S

Issues in hybrid simulation engine

Data exchange S/E, E/S conversion function

Data type mismatch needs type conversion

How do we convert the mismatched data?

Time synchronization Presimulation

Time advance needs the minimum next simulation time between CS and DES models

How do we know the minimum?

output : Event

output: Signal(time function)

input: Signal(time function)

Discrete Event

Model Continuous Model

Hybrid Model

input : Event

I/O Type Mismatch between CS and DES

9 of 31

© 2014 Tag Gon Kim


Interface Between CS and DES: Conversion Function

2:SEf

:ESg

ESSE gfcf ,

: Event-to-(Analog)Signal conversion function (E/S Converter)

: (Analog)Signal-to-Event conversion function (S/E Converter)

gES CS DES

t1

e4

t t3

e2

t2 t1 t3 t4

e1

e3 e2

e6

t t2 t1 t4 t3 t

fSE CS DES

t2 t1 t3 t4 t

Conversion Function: cf

Transformation between Analog and Event

∑: a set of events (input and output of DES)

Ω: a set of time segmented functions (input and output of CS in time interval)

© 2014 Tag Gon Kim

10 of 31


Next Time Schedule in Hybrid Simulation

DES Model CS Model

Next event time

(known from model)

Next event time

(No knowledge before

Execution of CS model)

Pre-Simulation

Identification of

a next event

time in CS model

Next event time

(computed from simulation of CS model)

Time synch module

- Find the minimum

event time between

the two

- Execution of one

with the minimum

Time synch algorithm

© 2014 Tag Gon Kim

11 of 31


Time advance for hybrid simulation

tN = min{tNcs, tNDES}, tNcs is computed by pre-simulation

Pre-Simulation: Identification of a next event time in CS

Time Synch by Pre-Simulation (1/2)

DES DES

CS CS

Sdisc Sdisc

Scont Scont

t

t t

t

Scheduler Scheduler

tNDES tNDES

t2

tNDES t2

threshold

tNDES

© 2014 Tag Gon Kim

12 of 31


Time synch by Pre-Simulation (2/2)

DES Model PlugSim CS Model

time advance request (tN, done)

time adv. grant (*, tN)

time advance request(tN1, done)

Output

Pre-Simulation(tN)

tN

Pre-Simulation(tN1)

tN1

No output(tN)

Output(t2)

13 of 31

© 2014 Tag Gon Kim


Example 1 using HLA/RTI: Target Tracking System (TTS)

missile

HDM

environment

controller

CCM

missile position event

target

fSE

gES

hitting event

DAM

HM

HDM: High level Decision Model

14 of 31

© 2014 Tag Gon Kim


Example 1: CS(CCM) Model of TTS Using MATLAB

Controller Model:

control equations

max

0

ff

f

y

x

mg

mgf

f

f

y

x22

max )(

mgvszk

vszk

f

f

yyyy

xxxx

y

x

)(

)(

g

f

f

m

m

v

v

s

s

m

km

k

v

v

s

s

y

x

y

x

y

x

y

x

y

x

0

0

0

10

01

00

00

000

000

1000

0100

20

10

50

0

0

0

0

0

y

x

y

x

v

v

s

s

Missile model: missile kinetic behavior equations

15 of 31

© 2014 Tag Gon Kim


Example1: Simulation Result

Processor 1:

DEVSim++

RTI Exec Processor 2:

MATLAB

Missile

Position

Trajectory

16 of 31

© 2014 Tag Gon Kim


Example 2 using HLA/RTI : Mobile Robot System (MRS) W

landmark

Human

Operator Joystick

Environments Mobile

Robot

x, y, Φ

landmarks

message vd, wd

handling

events

fSE

gES

DES CS

fx, fy

landmarks

events

17 of 31

© 2014 Tag Gon Kim


Example 2: Continuous System in MRS

PID

Controller Motors

PWS

kinematics

Vehicle

kinematics

Inverse

PWS

Kinematics

u1

u2

v w

θd1

Continuous Systems

vd, wd

x, y, Φ

θd2

θ1

θ2

Joystick fx, fy

18 of 31

© 2014 Tag Gon Kim


Example 2: MATLAB Model of CS in MRS

Joystick

Two Motors

19 of 31

© 2014 Tag Gon Kim


Example 2: Environment of landmarks points

W

landmarks

right turn point

crossroad point

point

straight point

end point

straight point

straight point

left turn point

20 of 31

© 2014 Tag Gon Kim


Example 2: Simulation of MRS

W

right turn point crossroad point

straight point

end point

straight point

straight point

left turn point

21 of 31

© 2014 Tag Gon Kim


어뢰 탐색

회피 기동

어뢰 발사

투하 후

탐색

Example 3 using PlugSim: AntiTorpedo Simulation

22 of 31

© 2014 Tag Gon Kim


Simulation

Result

Plug-in Simulator

• change of dynamics of torpedo

Example 3: AntiTorpedo Model

Discrete Event System (DEVS Model)

Continuous System (MATLAB + Algorithm)

© 2014 Tag Gon Kim

24 of 31


PlugSim

Interoperation Environment for A Single Computer Environment

Case Study 목적

이산 사건 모델과 연속 모델을 이용한 하이브리드 시뮬레이션 실험

Example 4 using PlugSim : 시나리오 (1/ 2)

표적 확인

표적 탐지/획득

발사통제

표적 요격

임무 종료

아군 함정

목표 진지

Alarm1

: Missile 속도(빠르게)

조절

Alarm2

: Missile 속도(느리게)

조절

© 2014 Tag Gon Kim

25 of 31


Example 4: 시나리오 (2/ 2)

Case Study 상세 시나리오

아군 함정이 (100,100,0)에서 목표(0,0,0)를 향해서 이동

아군 함정의 탐지 거리 (35.5km) 이내에 적군이 탐지 되면 Missile 발사

Missile은 3차원 운동 방정식을 이용해 포물선 형태로 목표를 향해 접근

Missile 모델은 목표와의 거리를 판단하여 특정 조건이 만족 되면(물체와의 거리) 경보(Alrarm)를 울려 Missile Control 모델에게 알려 Missile 속도를 제어

Alarm1(원거리) : Missile의 속도 증가

Alarm2(근거리) : Missile의 속도 감소

미사일이 목표에 근접하면 명중 판단 이후, 시뮬레이션 종료

하이브리드 모델

Missile 모델(연속 모델) + 전함 모델(이산 사건 모델)로 구성

하이브리드 시뮬레이션 환경

PlugSim기반의 하이브리드 시뮬레이션 환경

© 2014 Tag Gon Kim

26 of 31


Example 4: 연속 시스템 모델 설계

Missile 모델 (연속 모델)

Missile의 운동 모델을 3차원 방정식으로 표현

MATLAB/SIMULINK를 이용하여 구현

Missile의 3차원 운동 방정식을

MATLAB/Simulink로 구현

© 2014 Tag Gon Kim

27 of 31


Example 4: 이산사건 시스템 모델 설계 (1/5)

전함 모델 – Coupled Model (DEVS)

alarm1

alarm2

Destroy

Adjust

C2 Model

Missile Control Model

Maneuver Model

Detect Model

alarm1

alarm2

Destroy

Detected

Adjust

Adjust

Position

Destroy

Destroy

© 2014 Tag Gon Kim

28 of 31


C2 모델 – Atomic model

내,외부 전황 상황을 판단해 전함 제어

Example 4: 이산사건 시스템 모델 (2/5)

alarm1

alarm2

Destroy

adjust

WAIT @Infinity

COMMAND @tc

?alarm1 || ?alarm2 || ?detected

!adjust

?Destroy

Detected

Destroyed @0

!destroy

destroy

© 2014 Tag Gon Kim

29 of 31


Example 4: 하이브리드 시뮬레이션 구조

Warship Model

(DEVS 모델)

Missile Model

(MATLAB 모델)

PlugSim

하이브리드 시뮬레이션 구조

PlugSim : 하이브리드 시뮬레이션의 데이터 교환 및 시간 동기화

Interface Interface adjust

adjust

alarm1

alarm2

destroy

alarm1

alarm2

destroy

공유 객체

모델

데이터 이름 데이터 타입 From To

adjust double, double, double Warship Missile

alarm1 Event Missile Warship

alarm2 Event Missile Warship

destroy Event Missile Warship

모델들의 IOM 참조

IOM

© 2014 Tag Gon Kim

30 of 31


Example 4: S/E, E/S 변환기

Warship Model

(DEVS 모델)

Missile Model

(MATLAB 모델)

Interface Interface

ZPos

XPos t

Adjust

(Detect)

Alarm1

:ESg

E/S Converter

2:SEf

S/E Converter

Adjust

(Alarm1)

Alarm2

Adjust

(Alarm2)

Destroy

Alarm1

Alarm2

Destroy

© 2014 Tag Gon Kim

31 of 31


Example 4: 시뮬레이션 결과

하이브리드 시뮬레이션 결과 비교

하이브리드 시뮬레이션을 통해서 이산사건 모델에서 연속 시스템의 제어 가능

연속 모델의 이산사건 기반 제어는 Run-time 에서 연속 모델(Missile Model)이 일정한

조건(ex. 거리, 환경변수 값)을 만족하면 이산사건 모델(Missile Control Model)에 보고.

보고를 받은 이산사건 모델은 미사일 운동방정식(파라미터) 변경을 명령 함

새로운 형태의 무기체계 개발을 위한 M&S 기술

< Missile Control Model이 있는 경우> < Missile Control Model이 없는 경우>

Alarm1 : 거리 22km

Alarm2 : 거리 3km

연속시스템의 이벤트

식별 지점

하이브리드 모델 시뮬레이션 연속 시간 모델 시뮬레이션

lect 11: hybrid system modeling and simulation

Documents