Chemtrac HydroAct HA4, User Manual

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64 Chapter 4. Controls
and control offsets are to be expected. Control offsets in a purely proportional system are referred
to as proportional droop. Offsets occur in systems where there is an opposing process affecting
the process variable. For example, chlorine will evaporate from a pool surface. When the rate of
loss is equal to the rate of chlorine addition then a steady state will be achieved. This equilibrium
point will be at a chlorine concentration below the set point. A dosing pump being controlled by a
P controller will be slightly off when the setpoint is reached.
PI Controller Integral action enables PI controllers to eliminate offset, which is a major weakness of a
P controller. PI controllers provide a balance of complexity and capability that makes them by far
the most widely used algorithm in process control applications. A dosing pump controlled by a PI
controller will still be pumping when the setpoint is reached.
PD Controller PD control is useful for fast response controllers that can tolerate, or are not affected
by, a control offset. Derivative action acts on the rate of change of the process variable error.
This provides a fast response but is susceptible to measurement noise. PD controllers can be
useful in applications where overshoot can not be tolerated, such as batch pH neutralization.
PID Controller Used in applications where control provided by other permutations of P, I and D actions
are inadequate. The PID controller calculates an error value between a measured process
variable and a desired setpoint. The calculated error is used in three separate calculations that
calculate an output proportional to the error (the proportional term), an output proportional to the
magnitude and duration of the error (the integral term) and an output proportional to the rate of
change of the error (derivative term). The PID controller output is the sum of the three constituent
terms as shown in figure 4.1. The result is in the form a decimal fraction
1
that is converted to a
percentage for control output.
4.1.1.1.1 Proportional Term
The proportional term produces an output value that is proportional to the current error value. The
proportional response can be adjusted by multiplying the error by the proportional gain, adjustable in
the PID configuration.
P
out
= K
p
. e
where P
out
is the proportional term output, K
p
is the proportional gain and e is the error.
A large proportional gain value gives a large change in the output for a given change in the error. If
the proportional gain is too high, the system can become unstable and overshoot will occur. Too small
a gain value results in a small output response to a large input error, and a less responsive controller.
If the proportional gain is too low, the control action may be too small when responding to system
disturbances and may not achieve a setpoint.
4.1.1.1.2 Integral term
The Integral term is proportional to both the magnitude of the error and the duration of the error. The
integral in a PID controller is the sum of all the measured error over time and gives the accumulated
offset that should have been corrected previously. The accumulated error is then multiplied by the
integral gain, adjustable in the PID configuration.
I
out ( t )
= I
out ( t − 1)
+ K
i
. e
where I
out
is the integral term output, K
i
is the integral gain and e is the error.
The integral term accelerates the movement of the process towards setpoint and eliminates the
residual steady state error that occurs with a pure proportional controller. However, since the integral
term responds to accumulated errors from the past, it can cause the present value to overshoot the
setpoint value.
1
Value is in the range 0..1, where 1 is equivalent to 100%