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.