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Structured Modeling of Mechatronic Systems
in which you meet the modest but talented multiport component
Characterization of Modern Engineering SystemsFeatures of modern engineering systems:• multiple physical domains• energy transfer processes (thermodynamic
networks, first-law principle)• energy conversion processes (transducers)• information transfer (signals)• increasingly larger and more complex
Engineering modeling is an art, not a science.
Models should be “designed” to answer certain questions of the product development team.
• Under-modeling may cause the team to miss certain critical behaviors.
• Over-modeling may obscure insight into causes of behavior.
• Over-modeling leads to excessive costs during optimization and sensitivity testing.
Basic Concepts in Multiport Modeling
• A multiport component interacts through a set of ports.
• Two port types - power ports for energy, signalports for information interaction.
• Connectors join same port types in pairs.• Models can be organized hierarchically (e.g., to
control density of information display).• Models can be organized for re-use (libraries).
Some multiport components• Permanent-magnet motor: a 2-port
electrical port, shaft port• Positive-displacement pump: a 3-port
shaft, high-P fluid, low-P fluid ports• Hydraulic cylinder: a 3-port
ram port, fluid port A, fluid port B• Op-amp integrating circuit: a 2-port
electrical input, output ports• Solenoid valve: a 2-port
slider port, electrical port
Permanent-magnet motor
ia
ea
+ > τ, ω
PMMOTORea
ia
τ
ω
Electrical port
Rotational port
Hydraulic cylinder
Q1Q2
VL
FL
P1
P2
A1 A2
HCYLINDERFL
VL
P1 Q1P2 Q2
Common power port types
• mechanical translation: force, velocity• mechanical rotation: torque, angular velocity• electrical terminal-pair: voltage, current• fluid power: pressure, volume flow• magnetic power: mmf, flux rate• thermal power: temperature, entropy rate
Note that power is the product of the port variable pair.
Units for common power port types
• translation: force [N], velocity [m/s]• rotation: torque [Nm], angular velocity [rad/s]• electrical: voltage [v], current [A]• fluid power: pressure [N/m2], volume flow
[m3/s]
Note that power is the product of the port variable pair. In the units given above, the power is Watts for all port types.
Some common power connectors
• translation: rod {force, velocity}• rotation: shaft {torque, angular velocity}• electrical: wire pair {voltage, current}• fluid power: pipe, hose {pressure, volume flow}
An ideal connector has no material properties of importance (e.g., inertia, compliance, resistance, friction, etc.) It conveys the energy instantly from one port to the other port without losses or delays.
Multiport modeling is useful because ...
• it applies to mechatronics systems. (both power and signal types; transducers)
• it is effective at both simple and complex levels. (easy to learn; extendible)
• it is graphical in nature. (good visualization properties; hierarchical)
• it lends itself to computer implementation. (good user interface; object-oriented)
Multiport modeling is compatible with existing modeling methods.
• Mechanics: Newton’s laws, free-body diagrams.
• Mechanics: Lagrange’s method - energy• Electrical circuits: Kirchoff’s laws• Electronic components: representation as
ported devices (i.e., circuit elements)• Transducers: consistent modeling approach
based on power/energy across domains
Multiport modeling is compatible with existing modeling methods. (cont.)
It can represent more abstract modeling forms. • Finite-element representation (M,C,K
matrices)• Modal representation of vibratory systems
(normal modes)• Power-conserving transformations
(e.g., xyz to spherical coordinate mapping)• Transfer functions and impedance methods
Multiport modeling can help your career
• You can demonstrate awareness of the “big picture” and the details of a project.
• You can demonstrate control over the level of model complexity suitable for the project.
• You can organize models for re-use.• You can communicate effectively with co-workers
and with management.
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