Civil Engineering Reference
In-Depth Information
response we need a controller sensitive to error derivative. Such a control
can, however, not be used alone since it is not sensitive to steady-state errors
of any size, as at
t
3
, thus a combination of proportional plus derivative, for
example, makes sense.
The derivative control action can be represented by a function of the error
slope as the time domain equation:
D
(
t
) =
K
D
*
de
(
t
)/
dt
(7-6)
Since derivative control is usually used together with proportional control,
the actual derivative action appears in the format as below:
u
(
t
) =
K
p
[
e
(
t
)+
T
d
*
de
(
t
)/
dt
]
(7-7)
The derivative action then becomes:
D
(
t
) = (
K
p
*
T
d
)*
de
(
t
)/
dt
(7-8)
where
T
d
is called
derivative time
of derivative control. Derivative time is
actually a coefficient which has the unit of time. It determines how strong
the derivative control action is. A larger value of derivative time gives a
stronger degree of derivative control. In practice, derivative control is often
used together with proportional control or proportional control plus integral
control.
In addition to the stability argument already discussed, derivative functions
may also offer improvement in speed of response. P+I control can provide
satisfactory control stability for most process controls in buildings. A D
controller should be used very carefully since an incorrect parameter may
have a negative effect on the control loop stability. Different manufacturers
implement very different D control algorithms in their controller, which also
makes it difficult for operators to tune the D control parameters.
7.5 Proportional, integral and derivative functions
It appears that, when any given value of set-point is set on a proportional
controller, the controlled variable can be controlled at that set-point value
only at one particular load. In all other cases there is a non-zero offset and a
difference exists between the set-point and the controlled variable. In many
cases the proportional band can be set relatively narrow and the offset is
acceptably small. In cases where the load is steady for long periods it may
be possible to adjust the set-point so that the controlled value becomes equal
to the desired value, but this is not often convenient.
In a closed control loop, the proportional band can be reduced to reduce
the offset. But this is equivalent to increasing the gain as shown in the pre-
vious sections. This can produce oscillation and instability. Such effects set
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