Simulated Analog Computation

1
Simulated Analog Computation
July 16, 2002

• William McKay
• Dept of Electrical Engineering
• University of South Carolina

2
Outline

• Introduction / Motivation
• Simulated Analog Computation
• Architecture
• Integration Methods
• Ordering Problem
• Example
• VTB applications
• Conclusion

3
What is an Analog Computer?

• A computer for solving differential equations
• A block diagram solver (e.g. MathWorks Simulink)

4
Analog Computer History

• Analog computers were created shortly after
  Newton developed calculus
• Non-traditional computer
• Electronic analog computers are the latest
  incarnation
• Analog computers help put man on the moon

5
Electronic Analog Computers
6
Analog Computer Introduction

• 5 Basic blocks needed
• Integrator
• Gain
• Summer
• Multiplier
• Constant
• Various sources
• e.g. sine, ramp, impulse
• Math blocks
• e.g. trig functions, exponentials/logarithms

7
Motivation

• Elegant solution method for differential
  equations
• Linear Time Complexity
• Matrix techniques are polynomial time
• Handles nonlinear systems with ease
• Architecture handles distributed and
  hardware-in-the-loop naturally
• Architecture handles parallel solving

8
VTB Analog Computer

• Lean mean solving machine
• Main goal is speed
• GUI and command line

9
Linux Analog Computer

• Same code as Windows
• Same schematic files
• Same architecture
• Solver is a DLL
• Models are DLLs
• Command line

10
SAC Architecture

• Solver view of the system
• vector of blocks
• linear time complexity
• Block view of the system
• inputs and a step function
• necessary to have Step() and Update() functions

Model 1
Model 2
Model 3
Simulation Loop

11
Integration Methods

• Integration is the analog computer
• Pure/Streams integration
• Euler integration
• Adams-Bashforth integration
• Explicit multi-step startup problem

12
Adams-Bashforth

• Adams-Bashforth integration
• 1st order
• 2nd order
• Higher orders (6th Order)

13
Ordering Problem

• Example of the ordering problem
• Caused by pass through blocks (i.e. blocks that
  do not contain state)
• Gain blocks, sum blocks, etc
• Algebraic loops
• Feedback loops with no state blocks in the loop
• Petri Nets

14
Algebraic Loops
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Petri Nets

• Models become transitions
• Inputs become places
• State blocks generate tokens at the
  simulation start

16
Example - Second Order System
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Example - Solution
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Example - Solution
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VTB Uses

• Another solver available in the new version of
  VTB
• Can solve signal back-plane
• Natural for hardware-in-the-loop
• Natural for distributed computing
• Useful for less detailed models
• Should be able to quickly solve very large systems

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Conclusion

• Solver built for speed
• Theoretical linear time complexity
• Simple architecture of connected blocks
• Handles nonlinear systems with ease
• Solves a wide range of problems that can be
  modeled with differential equations
• Various uses for VTB