Chapter 9.6.3 - IBM Lotus Domino Server with a Sensor Delay

9.6.3 IBM Lotus Domino Server with a Sensor Delay

This example studies integral control of the IBM Lotus Domino Server. The
objective is to regulate RIS, the number of RPCs waiting for or receiving service
(which is approximately the same as the number of active users). This is done
by adjusting the tuning parameter MaxUsers. Presented below is a summary
and refinement of results reported in [53] in which integral control is used for a
product-level server.

Reference [53] models the IBM Lotus Domino Server in terms of the server
itself and a measurement sensor. In particular, this analysis concludes that it
is important to consider the manner in which measurements are collected (the
sensor) since this affects their accuracy and can introduce delays. The transfer
functions of the controller, the IBM Lotus Domino Server, and the sensor are
shown in the block diagram in Figure 9.29. The operating point is =
375, RIS = 325, and u(k) = MaxUsers(k) −, y(k) = RIS(k)−.
Note that the closed-loop transfer function from the reference to the output is

Figure 9.30 studies the effect of the integral control parameter K_I. Each subfigure
contains two plots, one for RIS(k) (which also displays the reference value)
and a second plot that shows the associated value of MaxUsers(k). Consider
K_I = 0.1. We see that there is a slow convergence to the reference value. If
K_I = 1, the convergence is faster. If K_I = 5, there are substantial oscillations.
First consider steady-state error. Observe that for all three values of K_I considered
in Figure 9.30, the controller is accurate in that RIS(k) is centered around
the reference value. This suggests that e_ss = 0. Such a conclusion is consistent
with Equation (9.22) in that F_R(1) = 1.

Figure 9.31 provides insights into the transient behavior displayed in Figure
9.30. The figure plots the magnitude and angle of the poles of Equation (9.22)
as K_I is varied. Note that there are three poles because the power of z in the
denominator of F_R(z) is 3. We see that when K_I ≈ 0, the dominant closed-
loop pole is close to 1, which explains the long settling time for K_I = 0.1 in
Figure 9.30(a). As K_I increases, the magnitude of the dominant pole is reduced.
For example, at K_I = 1, this magnitude is approximately 0.75. This is why
Figure 9.30(b) has a much shorter settling time than Figure 9.30(a). However,
for K_I > 1.5, we have a pair of complex poles. These poles result in controller-
induced oscillations, as is evident in Figure 9.30(c).

Fig. 9.29 Block diagram for integral control of the IBM Lotus Domino Server. Themeasurement

Fig. 9.30 Transient response of a control system incorporating a product-level Lotus Notes

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Chapter 9.6.3 - IBM Lotus Domino Server with a Sensor Delay

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