Structured Modeling of Mechatronic Systems in which you meet the modest but talented multiport component

Characterization of Modern Engineering Systems Features 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, signal ports 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 + τ, ω > ea Electrical port Rotational port ea τ PMMOTOR ia ω

Hydraulic cylinder Q1 Q2 VL FL P1 P2 A1 A2 HCYLINDER FL VL P1 Q1 P2 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.