Page 43 - DCAP601_SIMULATION_AND_MODELING

Unit 2: Simulation of Continuous System (I)

Notes
3.00 58.57 8.57 82.86
3.10 58.19 8.19 83.63
3.20 57.82 7.82 84.36
3.30 57.48 7.48 85.05
3.40 57.15 7.15 85.70
3.50 56.84 6.84 86.32
3.60 56.55 6.55 86.91
3.70 56.27 6.27 87.46
3.80 56.00 6.00 87.99
3.90 55.75 5.75 88.50
4.00 55.51 5.51 88.97
4.10 55.29 5.29 89.43
4.20 55.07 5.07 89.86
4.30 54.86 4.86 90.27
4.40 54.67 4.67 90.66
4.50 54.48 4.48 91.03
4.60 54.31 4.31 91. 39
4.70 54.14 4.14 91.73
4.80 53.98 3.98 92.0'
4.90 53.82 3.82 92.35

5.00 53.68 3.68 92.65

2.1.2 Numerical Integration vs Continuous System Simulation

Continuous Simulation points to a computer model of a physical system that endlessly tracks
system response over time as per the set of equations usually including differential equations.
In continuous simulation, the continuous time reply of a physical system is modeled using
ODEs.
Newton’s 2nd law, F = ma, is a superior example of a single ODE continuous system. Numerical
integration methods like Runge Kutta, or Bulirsch-Stoer are used to elucidate the system of
ODEs. By integrating the ODE solver with other numerical operators and techniques a continuous
simulator can be used to model many different physical phenomena like flight dynamics, robotics,
automotive suspensions, hydraulics, electric power, electric motors, human respiration, polar
ice cap melting, steam power plants etc. There is practically no limit to the classes of physical
incident that can be modeled by a system of ODE’s. Some systems although can not have all
derivative terms mentioned explicitly from known inputs and other ODE outputs. Those
derivative terms are defined completely by other system constraints like Kirchoff’s law that the
flow of charge into a joint must equal the flow out.

Notes To resolve these implicit ODE systems a congregating iterative scheme like
Newton-Rapson must be employed.

LOVELY PROFESSIONAL UNIVERSITY 37