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Continuous simulation

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Continuous Simulation refers to a computer model of a physical system that continuously tracks system response over time according to a set of equations typically involving differential equations.[1][2]

History

It is notable as one of the first uses ever put to computers, dating back to the Eniac in 1946. Continuous simulation allows prediction of

Established in 1952, The Society for Modeling & Simulation (SCS) is a nonprofit, volunteer-driven corporation dedicated to advancing the use of modeling & simulation to solve real-world problems. Their first publication strongly suggested that the Navy was wasting a lot of money through the inconclusive flight-testing of missiles, but that the Simulation Council's analog computer could provide better information through the simulation of flights. Since that time continuous simulation has been proven invaluable in military and private endeavors with complex systems. No Apollo moon shot would have been possible without it.

Dissociation

Discrete event simulation
Continuous simulation

Continuous simulation must be clearly differentiated from discrete event simulation. While a discrete event simulation is based on a system which changes its behaviour only at discrete points in time, the system of a continuous simulation changes its behaviour at countless points in time. Even though, the execution of the simulation itself is totally different in this matter, in some cases one can simulate the same issue with both types of simulation.
In this example the sales of a certain product over time is shown. Using a discrete event simulation makes it necessary to have an occurring event to change the number of sales. In contrast to this the continuous simulation has a smooth and steady development in its number of sales. [5]

Conceptual model

Continuous simulations are based on a set of differential equations. These equations define the peculiarity of the state variables, the environment factors so to speak, of a system. These parameters of a system change in a continuous way and thus change the state of the entire system.[6]

The set of differential equations can be formulated in a conceptual model representing the system on an abstract level. In order to develop the conceptual model 2 approaches are feasible:

  • The deductive approach: The behaviour of the system arises from physical laws that can be applied
  • The inductive approach: The behaviour of the system arises from observed behaviour of an actual example[7]

A widely known example for a continuous simulation conceptual model is the “predator/prey model”.

The predator/prey model

The predator/prey model

This model is typical for revealing the dynamics of populations. As long as the population of the prey is on the rise, the predators population also rises, since they have enough to eat. But very soon the population of the predators becomes to large so that the hunting exceeds the recreation of the prey. This leads to a decrease in the prey’s population and as a consequence of this also to a decrease of predators population as they do not have enough food to feed the entire population.[8]

Mathematical theory

In continuous simulation, the continuous time response of a physical system is modeled using ODEs, embedded in a conceptual model.

In very few cases these ODEs can be solved in a simple analytic way. More common are ODEs, which do not contain enough information for a direct solution. In these cases one has to use numerical approximation procedures. This problem of solving the ODEs is called the initial value problem.

The main solution methods for the intivial value problem can be categorized into two groups:

Using these solution methods makes it necessary to take especially care of

  • the stability of the method
  • the method property of stiffness
  • the discontinuity of the method
  • Concluding remarks contained in the method and available to the user

These points are crucial to the success of the usage of one method.[10]

Mathematical examples

Newton's 2nd law, F = ma, is a good example of a single ODE continuous system. Numerical integration methods such as Runge Kutta, or Bulirsch-Stoer could be used to solve this partictular system of ODEs.

By coupling the ODE solver with other numerical operators and methods a continuous simulator can be used to model many different physical phenomena such as

  • flight dynamics
  • robotics
  • automotive suspensions
  • hydraulics
  • electric power
  • electric motors
  • human respiration
  • polar ice cap melting
  • steam power plants
  • etc.

There is virtually no limit to the kinds of physical phenomena that can be modeled by a system of ODE's. Some systems though can not have all derivative terms specified explicitly from known inputs and other ODE outputs. Those derivative terms are defined implicitly by other system constraints such as Kirchhoff's law that the flow of charge into a junction must equal the flow out. To solve these implicit ODE systems a converging iterative scheme such as Newton-Raphson must be employed.

Simulation software

In order to execute the continuous simulation in an efficient and comfortable way, one has to use appropriate simulation software like Simcad Pro. Simcad Pro offers a GUI to model the continuous simulation gaphically. Thus, no coding is necessary. The software provides a bunch of parameters to add like "lead time", "resource wait" or "utilization". As the created models are compatible to other systems (RFID, ERP, etc.) it is easy to monitor ongoing processes and to reveal problems early. Additionally, Simcad Pro can be used as a training software for managers and operators.[11]

Modern applications

Continuous simulation is found

  • inside Wii stations
  • commercial flight simulators
  • jet plane auto pilots[12]
  • advanced engineering design tools[13]

Indeed, much of modern technology that we enjoy today would not be possible without continuous simulation.

Other types of simulation

References

  1. ^ Continuous Simulation description from University of Utrecht
  2. ^ Definition of Simulation with reference to "continuous simulation" at Encyclopedia.com
  3. ^ Electric circuit simulation from Memorial University Canada
  4. ^ "Intelligent Robotic Systems", pub. Springer Link ISBN 978-0-306-46062-3
  5. ^ "'' Developments in Business Simulation & Experiential Exercises, Volume 13, 1986''" (PDF). http://sbaweb.wayne.edu. Retrieved 2012-01-23. {{cite web}}: External link in |publisher= (help)
  6. ^ "'' Continuous Simulation''". http://www.scribd.com. Retrieved 2012-01-23. {{cite web}}: External link in |publisher= (help)
  7. ^ Louis G. Birta, Gilbert Arbez (2007). Modelling and Simulation, p. 249. Springer.
  8. ^ Louis G. Birta, Gilbert Arbez (2007). Modelling and Simulation, p. 255. Springer.
  9. ^ Louis G. Birta, Gilbert Arbez (2007). Modelling and Simulation, p. 282. Springer.
  10. ^ Louis G. Birta, Gilbert Arbez (2007). Modelling and Simulation, p. 288. Springer.
  11. ^ "'' "On–the-fly" Continuous simulation software for the continuous flow modeling – Liquid and Gas simulation technology built into Simcad Pro''". http://www.createasoft.com. Retrieved 2012-01-26. {{cite web}}: External link in |publisher= (help)
  12. ^ http://dx.doi.org/10.1016/S0967-0661(99)00202-6 Robust sampled-data H∞-flight-controller design for high α stability-axis roll maneuver
  13. ^ VisSim Visual Simulation Language for Continuous Simulation and Model Based Development
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