Rockwell Automation RSLogix 5000 Fuzzy Designer - Manual (Page 53)

Publication LOGIX-UM004A-EN-P - March 2007
FuzzyDesigner Component Library 53
The component can be used as a conventional PID controller with
supervised parameters defined by component input links. The
component output link provides a crisp value representing the control
variable.
The component functionality is defined through the equation format
with the option of using either independent gains or dependent gains.
When the independent gains option is used, the proportional, integral
and derivative gains affect only their specific proportional, integral or
derivative terms respectively. When the dependent gains option is
used, the proportional gain is replaced with a controller gain, which
affects all three parts. Both formats are shown in the following
equations.
Where parameter b can be defined by the user and has to be in
interval [0,1]. The default value is 1. This parameter dampens the
influence of the setpoint on the proportional action.
The component allows two formats of derivative term O(t). Derivative
input to the controller can be either the process variable PV(t) or the
error E(t). Use of the process variable eliminates output spikes
resulting from setpoint changes. Use of the error allows fast responses
to setpoint changes when the algorithm can tolerate overshoots.
The algorithm is implemented in the discrete form.
Numerical integration is implemented as follows:
where T
s
is the loop update time.
Numerical derivation is implemented as follows:
The calculation of the derivative term is enhanced by using a
smoothing first order low pass digital filter. This filter eliminates large
derivative term spikes caused by noise in the process variable.
( )
( )
Bias
dt
t dO
D dt t E I t PV t SP b P CV
Bias
dt
t dO
D dt t E I t PV t SP b P CV
t
t
+ + ⋅ + − ⋅ =
+
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+ ⋅ + − ⋅ =
∫
∫
0
0
) (
) ( ) ( ) (
) (
) ( ) ( ) (
1
:
−
+ = ⋅ ∫
k s k k
Iterm T IE Iterm Edt I
s
k k
k T
O O
O
dt
dO
1 : −
−
= Δ