Lake Shore Model 370 AC Resistance Bridge User’s Manual
2.10.2
Closed Loop PID Control
Closed loop PID control, often called feedback control, is the control mode most often associated with temperature
controllers. In this mode the controller attempts to keep the load at exactly the user entered setpoint that can be entered in
resistance or temperature. To do this, it uses feedback from the control sensor to calculate and actively adjust the control
(heater) output. The Model 370 uses a control algorithm called PID that refers to the three terms used to tune the
controller for each unique system.
The PID control equation has three variable terms: proportional (P), integral (I), and derivative (D). See Figure 2-4.
Changing these variables for best control of a system is called tuning. The PID equation in the Model 370 is:
⎥⎦
⎤
⎢⎣
⎡
+
+
=
∫
dt
de
D
dt
e
I
e
P
Output
Heater
)
(
where the error (e) is defined as: e = Setpoint – Feedback Reading.
2.10.2.1 Proportional
(P)
The Proportional term, also called gain, must have a value greater than zero for the control 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 proportional is acting alone,
with no integral, there must always be an error or the output will go to zero. A great deal must be known about the load,
sensor, and controller to compute 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.
2.10.2.2 Integral
(I)
In the control loop, the integral term, also called reset, looks at error over time to build the integral contribution to the
output:
dt
e
I
P
I
Output
∫
⋅
=
)
(
)
(
1
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 zero, controlling at the setpoint, the output is held constant by the integral contribution.
The integral setting (I) is more predictable than the proportional setting. It is related to the dominant time constant of the
load. As discussed in Paragraph 2.7.3, measuring this time constant allows a reasonable calculation of the integral
setting. In the Model 370, the integral term is set in seconds and a
smaller setting creates a
more
active integrator
.
2.10.2.3 Derivative
(D)
The derivative term, also called rate, acts on the change in error with time to make its contribution to the output:
dt
de
PD
D
Output
=
)
(
.
By reacting to a fast changing error signal the derivative can work to boost the output when the setpoint changes quickly,
reducing the time it takes for temperature to reach the setpoint. It can also see the error decreasing rapidly when the
temperature nears the setpoint and reduce the output for less overshoot. The derivative term can be useful in fast
changing systems but it is often turned off during steady state control because it reacts too strongly to small disturbances
or noise. The derivative setting (D) is related to the dominant time constant of the load similar to the integral (I) and is
also set in seconds but a
smaller setting creates a
less
active derivative
.
2.10.2.4 Manual
Output
The Model 370 has a control parameter that is not a normal part of a PID control loop. Manual output can be used for
open loop control, meaning feedback is ignored and the heater output stays at the users manual setting. This is a good
way to put constant heating power into a load when needed. The manual output term can also be added to the PID output.
Some users prefer to set an output value near that necessary to control at a setpoint and let the closed loop make up the
small difference.
NOTE:
Manual Output should be set to 0 when not in use.
Theory of Operation
2-19
