Probability Applications

W. Jerry Parkinson and Ronald E. Smith 187
coeffi-
Figure 8.41. Fuzzy disturbance rejection for a leak in tank 1 with a friction
cient of 0.65 (test 1).
Figure 8.42. Probabilistic disturbance rejection for a leak in tank 1 with a friction
coefficient of 0.65 (test 1).
The integral error was computed in each test for each tank for each controller. These
values are listed in Table 8.8.
Figures 8.41 -8.46 and Table 8.8 demonstrate that the fuzzy and probabilistic controllers
are very much alike in their responses. The fuzzy controller does a little bit better on test 1
and the probabilistic controller does a little bit better on test 2. Both controllers beat the PI
controller quite handily. On reason is because the PI controller was "tuned" for the setpoint
tracking problem and is highly damped to reduce overshoot. This made it less responsive to
the disturbance rejection problem. However, with the standard PI controller, we have only
one set of control constants for all situations. Control constants that improve the disturbance
rejection response will hurt the setpoint tracking response. Note that none of the controllers
can do much with the level in tank 3 when there is a plug between tanks 1 and 3 since there
is no pump to supply input to tank 3.