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Diagnosing the Beam Propeller Movement
of the Frontal Stand 5.4 MBD Implementation 1
correctly, is at its setpoint and the system’s (C1, S1, S2) behavior is conform the prediction. The
Lydia code is now:
( h_c2 and h_c1 and h_s1 and h_s2 ) => (Q = P);
In the same way Figure 5.4(c) shows how a third control loop can be nested over the other two.
The reader is encouraged to see how the three control loops concept has been embedded in Figure
5.3. Again, a correct functioning controller (C3) and system (C2, C1, S1, S2 and S3) implicate that
the actual value Y equals the setpoint value X. This can be described by the following Lydia code:
( h_c3 and h_c2 and h_c1 and h_s1 and h_s2 and h_s3 ) => (Y = X);
Modeling the Error Signal
As said before there is an error detection mechanism in place inside the beam propeller movement.
Three errors are related to the control loops. If the setpoint and actual value differ too much the
error signal becomes true. Figure 5.5 shows the concept.
ERROR = (A != B)
The square indicates the operation that determines whether or not input values of the controller are
valid.
(a) One control loop
Figure 5.5: Modeling the error signal
5.4.4 Discretization
The observables are CURRENT_ERROR, SPEED_ERROR, POSITION_ERROR, POSVAL_ERROR, and e_pos.
The first four are already in the boolean domain. e_pos should be derived from the values of Pact
and Pset. These two variables are integers with many possible values, and its derivative should be
discretized. As said before, the only thing that is of interest about the position of the frontal stand
is whether Pact and Pset do, or do not exceed their threshold. The discretization is defined as
follows:
{ 0, if (Pset − Pact) ∈ [−POS T HRESHOLD,POS T HRESHOLD] ;
e pos(B) =
1, all other cases
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