Dynamical system simulation: Difference between revisions

Revision as of 01:15, 1 June 2020

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'''Dynamic simulation''' (or dynamic system simulation) is the use of a computer program to model the time-varying behavior of a [[dynamical system]]. The systems are typically described by [[ordinary differential equations]] or [[partial differential equations]]. A simulation run solves the state-equation system to find the behavior of the state variables over a specified period of time. The equation is solved through numerical integration methods to produce the transient behavior of the state variables. Simulation of dynamic systems predicts the values of model-system state variables, as they are determined the past state values. This relationship is found by creating a model of the system. <ref> Korn, Granino A. Advanced dynamic-system simulation: model-replication techniques and Monte Carlo simulation. John Wiley & Sons, 2007. p. 2.</ref>

==Overview==

Simulation models are commonly obtained from discrete-time approximations of continuous-time mathematical models. <ref>Klee, Harold, and Randal Allen. Simulation of dynamic systems with MATLAB and Simulink. Crc Press, 2016. p. 3.</ref>

As [[mathematical model]]s incorporate real-world constraints, like gear [[backlash (engineering)|backlash]] and rebound from a hard stop, equations become nonlinear. This requires numerical methods to solve the equations. <ref>Klee, Harold, and Randal Allen. Simulation of dynamic systems with MATLAB and Simulink. Crc Press, 2016. p. 93.</ref>.

A [[numerical simulation]] is done by stepping through a time interval and calculating the integral of the derivatives through [[numerical integration]].

Some methods use a fixed step through the interval, and others use an adaptive step that can shrink or grow automatically to maintain an acceptable error tolerance. Some methods can use different time steps in different parts of the simulation model.

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==Applications==

The first applications of computer simulations for dynamic systems was in the aerospace industry.<ref>Klee, Harold, and Randal Allen. Simulation of dynamic systems with MATLAB and Simulink. Crc Press, 2016. p. xiii.</ref>. Commercial uses of dynamic simulation are many and range from nuclear power, steam turbines, 6 degrees of freedom vehicle modeling, electric motors, econometric models, biological systems, robot arms, mass-spring-damper systems, hydraulic systems, and drug dose migration through the human body to name a few. These models can often be run in [[real-time simulation|real time]] to give a virtual response close to the actual system. This is useful in [[process control]] and [[mechatronic]] systems for tuning the [[automatic control]] systems before they are connected to the real system, or for human training before they control the real system.

Simulation is also used in computer games and animation and can be accelerated by using a [[physics engine]], the technology used in many powerful [[computer graphics]] [[software]] [[computer program|programs]], like [[3ds Max]], [[Maya (software)|Maya]], [[Lightwave]], and many others to simulate physical characteristics. In computer animation, things like [[hair]], [[cloth]], [[liquid]], [[fire]], and [[wiktionary:particles|particles]] can be easily modeled, while the human [[animator]] animates simpler objects. Computer-based dynamic animation was first used at a very simple level in the 1989 [[Pixar]] [[short film]] ''Knick Knack'' to move the fake snow in the snowglobe and pebbles in a fish tank.

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*[[PottersWheel]] — A Matlab toolbox to calibrate parameters of dynamic systems

*[[Simcad Pro]] — A dynamic and interactive discrete event simulation software

== External links ==

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==References==

{{Reflist}}

[[Category:Computer physics engines]]