Page 669 - The Mechatronics Handbook

FIGURE 21.6 Iconic diagram of the simple servo system.

FIGURE 21.7 Icon of the motor expanded to ideal physical elements.
In the next step we can detail the description of the DC motor. One solution could be the description
given in Fig. 21.7. The motor is now described by a number of ideal physical elements, each representing
a basic physical relation. The motor has an electrical (EL) as well as a mechanical port (MECH).
Each of the elements in this figure can be described as an element with an electrical and/or mechanical
port. The idea of ports is made more explicit in so-called bond graphs. 9–12 For the electrical elements
these are the voltage difference over the element and the current through the element. For the mechanical
elements these are the torque and the (angular) velocity. The products of these conjugated variables (P = ui
or P = Tω) represent power.
If we go down a step further into the hierarchy, we arrive at the level of equations. For instance, an
electrical resistor can be described by the equation:
.
.
p u R*p i (21.1)
=

.
.
where the variables p u and p i indicate the conjugated variables u and i of the electrical port p. Note
that this is an equation and not an assignment statement. It could have been written equally well in the
form:
.
.
=
p i 1/R * p u (21.2)
In a similar way the inductance can be described by the equations:
.
.
.
.
p u L*ddt pi )or p i) = 1/L * int p u) (21.3)
(
(
(
=
.
.
where ddt(p i) denotes di/dt and int(p u) denotes òu dt. In case of an R-element there is no preference
for one of the two forms. For the I-element the integral form is preferred in the simulations. 20-sim
determines the preferred causal form and derives the equations automatically.
The energy flow or power P is the product of two conjugated signals, called effort (e) and flow ( f ):
P = ef (21.4)
Examples of this expression in the mechanical and electrical domain are
P = Fv or P = Tω (21.5)
P = ui (21.6)
where F is force, v is velocity, T is torque, ω is angular velocity, u is voltage, and i is current.

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