Simulation & ModellingSimulation & Modelling

Systems Engineering Training Programme for DRDO Systems Engineering Training Programme for DRDO Scientists at IAT, PuneScientists at IAT, Pune

11stst July 2003 July 2003

Lecture-1: Simulation & Modelling FundamentalsLecture-1: Simulation & Modelling Fundamentals

Lecture Outline

• What is Systems Modelling & why is it needed?

• Engineering Vs. Non-Engineering Systems.

• Modelling Techniques for Engg. Systems.

• What is Simulation?

• Offline Vs. Real-time Simulations.

• Simulation Methodology.

• Examples of Modelling.

• Examples of Offline Simulations.

Why is systems approach needed?

• “Need” for better products/services pushes technology into frontier areas. (e.g. Telecom, MEMS, Computers)

• “Cost” decides success or failure of innovations/ new developments. (e.g. Concorde)

• This puts pressure on design & development process.– Short Development Cycle; Long Product Life

– Small Development Cost; Large Benefits

– Environment Friendly; Socially Acceptable

• Multi-disciplinary nature of products makes the development process extremely complex & tough.

• Systems Approach is an important aid to this process.

What is systems approach?

• “Systems Approach” is a systematic tool for Integrated Technology and Product Development.

• “Systems Approach” is a methodology for looking at a complex product/ process as a single unit, composed of many sub-systems functionally related to each other.

• “Systems Approach” provides a mechanism for assessing the “performance” of System, against overall “design objectives”.

• “Systems Approach” is an extremely useful philosophy in the design and development process of Multi-disciplinary products.

What is the role of modelling?

• “Design” is a process of “repeated generation of responses to inputs”, to arrive at an acceptable product configuration, meeting stated requirements.

• “Concept” is usually what is available at early design stages, from which “responses to inputs” are generated.

• “Modelling” is a process by which a concept is translated into a more tangible form, quite often, but not necessarily, a mathematical one.

• “System Modelling” is a process of converting “Sub-Systems” into their corresponding tangible forms.

What is a system model?

• “System Model” is a specific assembly of “Sub-system” models, arrived at for meeting specified objectives.

• “Systems Modelling” is the process of determining (a) relationships of all “Sub-systems” and (b) quantitative features describing operations of all “Sub-systems”.

• “Relationships” among “Sub-systems is usually through ‘inputs’ to them and ‘outputs’ from them.

• “Quantitative Features” are usually derived from the laws governing the operation of “Sub-systems”.

Example of a system model

Input System Output

Sub - NSub - N-1Sub - 2Sub - 1

How is a system model created?

• Identify the system and its boundary.• Define the environment.• Decompose system into sub-systems till desired level of

details, and identify various interactions between them.• Define aspects of environment pertinent to the system. • Identify laws that govern the operation of each of the

sub-systems.• Decide the required complexity level of the model.• Choose a model philosophy. (Math./Physical/Hybrid)

Categories of systems & models

System Physical

Abstract

Engineering Non-Engg.

Continuous Vs. Discrete

Linear Vs. Nonlinear

Time Invariant Vs. Time Varying

Deterministic Vs. Stochastic

Causal Vs. Non-Causal

Engg. Vs. Non-Engg. Systems

Engg. Systems are both Deterministic and Stochastic (e.g. Mechanical, Electrical, Atmospheric etc.)

Non-Engg. Systems are usually Stochastic only (e.g. Biological, Social, political etc.)

Engg. Systems can be modeled using Mathematical relations

Non-Engg. Systems don’t have a sound Mathematical basis

Engg. Systems have well-defined universal laws

Non-Engg. Systems have no universal laws

Engg. Vs. Non-Engg. Systems

Generally, Engg. Systems exhibit Cause-Effect behaviour

Non-Engg. Systems don’t show Cause-Effect behaviour

Engg. Systems have a large range of modelling tools

Non-Engg. Systems have limited modeling options

Engg. System models can be evolved in good time

Non-Engg. System models take large time to evolve

Engineering System Model Types

• Purely Mathematical Models– Most commonly used in initial design stages

– Fairly inexpensive and usually less accurate

• Hybrid Models (Software-Hardware Models)– Used when some sub-systems are realized/frozen

– More expensive and more accurate

– Useful for modelling interfaces between sub-systems

• Scaled/Prototype Models– Used when actual system behaviour is needed

– Quite expensive, but close to real system

– Possible only towards end of the development process

How to choose a model type?

• Availability & Completeness of Modelling Information– Depends on the stage of product development

• Accuracy Required Vs. Accuracy Possible– Low fidelity models Vs. high fidelity models

– Multi-disciplinary modelling capability

– Essential physical effects to be included in model

• Availability of Resources for Response Generation– Available computational resources

– Available software tools & trained manpower

– Available infrastructure for testing & evaluation

Mathematical Modelling Procedure

• Definition & Characterization of Fundamental Variables– Mass, Momentum & Energy as basic quantities

• Idealized Element & Constitutive Relation Evolution– Known physical effects as idealized element

– Specific to each engineering discipline

– Mathematical relations describing energy exchange

• Continuity & Compatibility Condition Prescription– Translation of physical boundary conditions

– Prescription of interface behaviour

– Continuity on variables through an element

– Compatibility on variables defined on element boundaries

Discipline-wise Idealized Elements

Mechanical Systems Spring/Stiffness Element

Mass/Inertia Element

Damping Element

Electrical Systems Resistance Element

Inductance Element

Capacitance Element

Magnetic Element

Thermal Systems Conduction Element

Convection Element

Radiation Element

Fluidic Systems Tank Element

Pipe/Elbow Element

Piston Element

Miscellaneous Idealized Elements

Electro-Mechanical Systems Motor/Dynamo Element

Solenoid Element

Structural Systems Rod Element

Beam Element

Plate Element

Solid Element

Idealized Mechanical Elements

Idealized Electrical Elements

C

v

L

iR

Resistance Element

Capacitance Element

Inductance Element

v = i R

v = C i dt

v = L di/dt

Voltage Source

i

Current Source

L1

L2

Magnetic Element

i

Idealized Thermal Elements

Idealized Fluidic Elements

Idealized Fluidic Elements

Idealized Electro-Mechanical Elements

Mechanical System Modelling

• Spring-Mass-Damper System– Support Motion Excitation

M

K B

u(t)

y(t)

• Force Equilibrium– Newton’s Law

Md2y/dt2 + Bdy/dt + Ky

- Bdu/dt - Ku = 0• System (I/O) Form

y(t) = (Bd/dt+K) u(t)

(Md2/dt2+Bd/dt+K)

Electrical System Modelling

• Resistance-Inductance-Capacitance Circuit– Sinusoidal Voltage Excitation

R C

v(t)

• Charge, Potential Conservation– Kirchoff’s Laws

Ldi/dt + Cidt + Ri = v(t)• System (I/O) Form

i(t) = (d/dt) v(t)

(Ld2/dt2+Rd/dt+C)

L

i(t)

Fluidic System Modelling• Two-Tank Liquid Flow System

– Hydrostatics & Hydrodynamics

Q + q

q1

H1+h1H2+h2

q2

p1 = g h1; p2 = g h2

Tank1: q-q1= C1dp1/dt

Tank2: q1-q2 = C2 dp2/dt

Pipe-1: g(h1-h2)=R1 q1

Pipe-2: gh2 =R2 q2

R1C1C2 d2h2/dt2 + [C1(1+R1/R2)+C2]dh2/dt + h2/R2 = q/g

h1 = (1+R1/R2)h2 + R1C2dh2/dt

Modelling Aircraft FCSH

uman

Pil

ot

Servo

Auto-Pilot

Stick

Sensors

Cockpit Instruments

Pedal

Throttle

Servo

Servo

Fuel

Air

fram

e

Elevator

Ailerons

Rudder

Engine

Motion

Summary of Modelling

1. Modelling depends on knowledge base.

2. Type of model depends on resources.

3. Accuracy of model depends on technology.

4. Complexity of model depends on the overall objective.

What is simulation?

Physical SystemModelling Exercise

on a

Mathematical, Physical or

Hybrid Model

gives

Solution Exercise

acts on

System Response to Expected Inputs

Acceptable?

for

No

Yes

End

What is simulation?

Solution Exercise;

– Is a Process for generating information about the state of a system at any desired instant of time.

– Consists of impressing inputs on the system model and recording its behaviour as time progresses.

Solution Exercise can be Mathematical or Experimental

What is simulation?

Dictionary Definitions of Simulation;

– Appearing to be Something Else.

– Imitation of a Condition.

– Act or an Object that is Counterfeit or Feigned.

– Activity Producing Conditions Unreal but having Appearance of being Real.

Simulation is an activity which makes system model imitate the behaviour of actual system.

What is simulation?

Engg. Interpretation of Simulation;

– System model can be looked upon as an object expected to pretend to be the real Engg. system.

– Behaviour (or response of model to expected inputs), as time progresses, is expected to indicate how the actual system would have behaved under the same conditions.

– Therefore, “simulation” is a “step-by-step solution process” by which the behaviour (or response) of a model is generated as time progresses.

What is simulation?

Engg. Interpretation of Simulation;

– System model simulation gives an impression of an activated system, going through the various possible stages of response evolution.

– An important aspect of response evolution in system simulation is its “visual” representation.

Why simulation?

US Undersecretary of Defence Acquisition & Technology, “Study on Effectiveness of

Modelling & Simulation in the Weapon System Acquisition Process”, Oct. 1996.

Why simulation?

US Undersecretary of Defence Acquisition & Technology, “Study on Effectiveness of

Modelling & Simulation in the Weapon System Acquisition Process”, Oct. 1996.

Simulation as Visualization

RC (dv(t))/dt + v(t) = eo

v(t) = eo [ 1 – e-(t/RC) ]

RC

eo

i(t) v(t)

For Step-by-step approach;

N waypoints at t = T/N

v(k+1) = (1 - t/RC) v(k) +

eo t/RC

v(t)

t

Simulation Characteristics

– Simulation provides a “feel” for the system behaviour under differing inputs.

– In case of constraints on system response, simulation quickly provides the exceptions to be noted .

– Simulation methodology can mix software and hardware, to provide higher fidelity responses.

– However, simulation is highly problem specific and needs to be repeated as many number of times as there are test cases. This makes simulation a time consuming exercise.

Off-line Vs. Real-time Simulation

– In case of time scale mismatch between “simulation” and actual system, we get “offline simulation”.

– In case “simulation” proceeds at the same speed as the actual system, we get “real-time” simulation.

M

K B

u(t)

y(t)

Time scale of Spring-Mass-Damper System;

d = (1 - 2) . (K/m)

Time for solving the corresponding equation.

a few Milliseconds

Simulation Techniques

– Continuous simulation techniques are used when model is a set of differential equations (e.g. Analog Computer Simulation).

– Numerical simulation techniques are used when either system model is discrete or a powerful digital computer is available (e.g. Queueing Process).

– Hybrid simulation combines both Continuous and Numerical simulation techniques.

– Hardware-in-loop Simulation technique is used when both mathematical equations and hardware are part of the system model description. (e.g. Iron Bird).

Monte’ Carlo Simulation

– System “simulation” with Random Nos.

– Developed at Los Alamos Lab. For Nuclear Research.

– Random Nos., satisfying constraints, used in very large trials. (Name borrowed from famous gaming city).

(xp,yp): a < xp < b; 0 < yp < ymax

A large No. of Points Chosen &

Tested for the conditions

Area fraction; ratio of selected

points to total points used.

y

xa b

ymax

Summary of Simulation

– Simulation is tool to improve team cohesiveness.

– Simplified models are easier to simulate.

– Development/Life Cycle are evaluated quickly.

– Simulation accelerates IPPD Process.

– Verification & Validation issues are handled adequately in simulation.