Pid Control; Proportional (P); Integral (I) - Lakeshore 336 User Manual

24 c 2: Cooling System Design and Temperature Control
HAPTER

2.7 PID Control

2.7.1 Proportional (P)

2.7.2 Integral (I)

Model 336 Temperature Controller
The cooling power of most cooling sources also changes with load temperature. This
is very important when operating at temperatures near the highest or lowest tem-
perature that a system can reach. Nonlinearities within a few degrees of these high
and low temperatures make it very difficult to configure them for stable control. If dif-
ficulty is encountered, it is recommended to gain experience with the system at tem-
peratures several degrees away from the limit and gradually approach it in small
steps.
Keep an eye on temperature sensitivity. Sensitivity not only affects control stability,
but it also contributes to the overall control system gain. The large changes in sensi-
tivity that make some sensors so useful may make it necessary to retune the control
loop more often.
For closed-loop operation, the Model 336 temperature controller uses an algorithm
called PID control. The control equation for the PID algorithm has three variable
terms: proportional (P), integral (I), and derivative (D). See FIGURE 2-2. Changing
these variables for best control of a system is called tuning. The PID equation in the
Model 336 is:
I e  
P e +
Heater Output =
where the error (e) is defined as: e = Setpoint – Feedback Reading.
Proportional is discussed in section 2.7.1. Integral is discussed in section 2.7.2. Deriv-
ative is discussed in section 2.7.3. Finally, the manual heater output is discussed in
section 2.7.4.
The Proportional term, also called gain, must have a value greater than 0 for the con-
trol loop to operate. The value of the proportional term is multiplied by the error (e)
which is defined as the difference between the setpoint and feedback temperatures,
to generate the proportional contribution to the output: Output (P) = Pe. If propor-
tional is acting alone, with no integral, there must always be an error or the output
will go to 0. A great deal must be known about the load, sensor, and controller to com-
pute a proportional setting (P). Most often, the proportional setting is determined by
trial and error. The proportional setting is part of the overall control loop gain, and so
are the heater range and cooling power. The proportional setting will need to change
if either of these change.
In the control loop, the integral term, also called reset, looks at error over time to build
the integral contribution to the output:

PI e   t d
Output (I) =
By adding the integral to proportional contributions, the error that is necessary in a
proportional only system can be eliminated. When the error is at 0, controlling at the
setpoint, the output is held constant by the integral contribution. The integral setting
(I) is more predictable than the gain setting. It is related to the dominant time con-
stant of the load. As discussed in section 2.8.3, measuring this time constant allows a
reasonable calculation of the integral setting. In the Model 336, the integral term is
not set in seconds like some other systems. The integral setting can be derived by
dividing 1000 by the integral seconds: I
de

----- -
+
dt D
dt
= 1000 / I
setting
.
seconds