Page 89 - Mechatronic Systems Modelling and Simulation with HDLs

78 4 MODELLING IN HARDWARE DESCRIPTION LANGUAGES

voltage law is applied for potential quantities, which means that all ACROSS quan-
tities in a closed loop add up to zero. For the flow quantities, Kirchhoff’s current
law applies. Thus all THROUGH quantities at a node add up to zero. In addition to
the declared quantities others are implicitly defined such as, for example, q’DOT,
q’INTEG and q’DELAYED(t). These denote the derivative of the quantity q with
respect to time, the integral of the quantity q with respect to time and a quan-
tity q delayed by time t. In addition to the potentials and flows it is sometimes
worthwhile considering quantities that are not subject to Kirchhoff’s laws. For
example, in control technology signal flow diagrams or block diagrams are often
considered, in which the individual quantities do not occur in pairs and furthermore
have a direction. Kirchhoff’s laws in particular do not apply to these quantities. In
VHDL-AMS such quantities can also be used, as is demonstrated by the following
example of a combined adder/integrator, see Hardware description 4.11 and [16].

ENTITY adder_integrator IS
GENERIC (k1,k2: real);
PORT (QUANTITY in1, in2: IN real;
QUANTITY outp: OUT real);
END ENTITY adder_integrator;

ARCHITECTURE signal_flow OF adder_integrator IS
QUANTITY qint: real;
BEGIN -- defining equations ...
qint == k1*in1 + k2*in2;
outp == qint’INTEG; -- Integration
END ARCHITECTURE signal_flow;

Hardware description 4.11 Signal flow modelling of a combined adder/integrator

Discontinuities
In the case of mechanical models in particular, non-continuous relationships also
often have to be modelled. These are illustrated in what follows based upon the
example of a bouncing ball, see Hardware description 4.12 and Bakalar et al. [16].
Two discontinuities are considered in this model. The first of these is the start of
the simulation at which the initial state is set at the first BREAK command. The
second discontinuity consists of the fact that the bouncing ball reverses its velocity
when the it hits a surface, i.e. at s ≤ 0. This corresponds with an elastic impact.
Furthermore, the IF instruction ensures that the braking effect of air resistance acts
with gravity when rising and against gravity when falling.

LIBRARY disciplines; -- Reference to a package with
USE disciplines.mechanical.all; -- the mechanical declarations
ENTITY ball IS -- Autonomous model,
END ENTITY ball; -- no connections
ARCHITECTURE simple OF ball IS