Chapter 3 SystemEvaluation
MATRIXx Xmath Robust Control Module 3-8 ni.com
The four transfer matrices are labeled e/d, e/n, u/d, and u/n in the final plot.
The plots in the top row, consisting of e/d and e/n, show the regulation or
tracking achieved by the controller. If both these quantities are small, then
the disturbance d and the sensor noise n will not make the error signal e
large.
The bottom row of plots, consisting of u/d and u/n, show the actuator effort
used by the controller. If these are both small, then the actuator effort u,
which results from the disturbance d and the sensor noise n will be small.
A classic trade-off in controller design boils down to a choice between
making the top row of a perfplot( ) small (good regulation/tracking)
and making the bottom row small (low actuator effort). For example, by
varying the design parameter ρ in the lqgltr( ) regulator design process,
the magnitude of the top two transfer matrices can be traded off against the
magnitude of the bottom two. Increasing ρ makes the top two magnitudes
smaller but makes the bottom two larger.
The columns of a perfplot( ) have a dual interpretation. The plots in the
left column, e/d and u/d, show how sensitive the system is to the process
noise or disturbance d. The plots in the right column, e/n and u/n, show how
sensitive the system is to the sensor noise n. Again, there is a trade-off
between making the magnitudes of the transfer matrices on the left small
(good disturbance rejection) and making the magnitudes of the transfer
matrices on the right small (low sensitivity to sensor noise). In the
lqgltr( ) estimator design, the parameter ρ controls the relative
magnitude of the left and right plots. Increasing ρ makes the left two
magnitudes smaller but makes the right two larger. Refer to Example3-3.
Example 3-3 Example of perfplots()
Consider the simple closed-loop system shown in Figure 3-4.
Figure 3-4. Closed-Loop System
disturbance e
1
s
+
+
+
–
K
n
noise