ETTC'2003 - SEE

Phase (deg); Magnitude (dB)
To: Y(1)
50
0
-50
-100
-50
-100
-150
-200
-250
10 0
-300
10 1
Bode Diagrams
Frequency (rad/sec)
ETTC2003 European Test and Telemetry Conference
From: U(1)
Figure 2 – Bode diagrams of the test-bench
From this set of models, one is known as "nominal" and uncertainty
domains supplement the representation in the Nichols chart system (Figure 3).
0
Magnitude
( dB)
40
20
-20
-40
-60
Uncertainty domains
Nominal plant
-80
-400 -350 -300 -250 -200 -150 -100 -50
Phase (deg)
Figure 3 – Nichols diagram of the nominal plant with uncertainty domains.
The control law is then computed for the nominal model, but while taking
into account of uncertainties in order to guarantee the stability and the
performances of the linked system. Figure 4 shows an open-loop Nichols locus that
tangents a magnitude contour and the uncertainty domains that are positioned
compared to this contour in three different cases. For the cases (a) and (b), the
uncertainty domains cross the magnitude contour, so performances guaranteed by
the tangency of the contour (for example the overshoot of the response) are not
achieved. On the other hand, for the case (c), the uncertainty domains are wellpositioned
and performance may be guaranteed in spite of the uncertainties.
10 2
10 3