System Modeling and Simulation

Mechatronic products are formed by combining subsystems that perform different functions.

To examine such complex products, physical modeling is generally performed first, followed by mathematical modeling.

In a mathematical model, each element is commonly represented with symbols and block diagrams.

Simulation is the process of running and observing a system virtually after its mathematical model has been prepared.

Visual software packages are available for modeling and simulating dynamic systems.

Simulation can be performed, for example, with Simulink, which operates on MATLAB.

The system can therefore be studied at low cost before a physical system or prototype is built.

A system is a collection of interacting or related elements with functional connections directed toward a particular purpose.

A system can also be defined as a structure that performs a function on input values and produces output values.

It can be represented mathematically as `f(x)=y`.

The boundaries of a system depend on the purpose of the analysis.

The area outside those boundaries is the system environment.

A system is affected by its environment through its boundaries and also affects that environment through the same boundaries.

Systems are named according to their function and subsystems, such as a power-transmission system.

A system is often represented as a rectangle with incoming and outgoing arrows.

An electric motor, for example, converts electrical power as input into rotary motion as output.

A thermometer converts measured temperature as input into a numeric indication as output.

A control system performs the control actions required to direct system behavior toward a desired state.

Models are simplified representations of real mechatronic systems.

Physical modeling is used when working directly on the real mechatronic system is impractical.

Mathematical modeling is then performed using the physical model and relevant laws.

A mathematical model represents the system abstractly.

The model is analyzed with computer assistance.

The closer the model is to reality, the closer the obtained results are to actual behavior.

The model is improved iteratively until the solution reaches the desired state.

Example Simulation Software

MATLAB and Simulink by MathWorks

LabVIEW by National Instruments

MATRIXx SystemBuild by Integrated Systems

Easy5 by Boeing

VisSim by Visual Solutions

Functions of Simulation Software

Create the model

Edit the model

Run the simulation

Obtain simulation results

A graphically constructed model is generally expressed through block diagrams.

Simulation Stages

Preparation: derive the equations of the blocks in the model

Iteration: solve the equations with numerical methods

Termination: obtain, record and animate the results

Basic System Elements

Physical-system elements operate according to the principles of energy flow, conversion and storage.

Physical relations among simple mechanical, electrical, hydraulic and thermal elements are comparable.

Energy flow requires a potential difference between terminals.

Energy flows from high potential to low potential.

System Variables

Effort Variable

A variable measured as a difference between the two terminals of an element.

Examples include voltage, velocity, pressure and temperature difference.

Flow Variable

A variable that remains continuous through the system.

Examples include current, force, volumetric flow and thermal flow.

Element Groups in Physical Systems

Resistance: the element opposes flow.

Inductance: the element stores energy.

Capacitance: the element stores charge or an analogous physical quantity.