26-03-2012, 12:31 PM
The Good Gain method for PI
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Introduction
The Good Gain method1 is a simple, experimental method which can be
used on a real process (without any knowledge about the process to be
controlled), or simulated system (in this case you need a mathematical
model of the process, of course)
Tuning procedure
The procedure described below assumes a PI controller, which is the most
commonly used controller function. However, a comment about how to
include the D-term, so that the controller becomes a PID controller, is also
given.
1. Bring the process to or close to the normal or specified operation
point by adjusting the nominal control signal u0 (with the controller
in manual mode).
2. Ensure that the controller is a P controller with Kp = 0 (set Ti = ∞
and Td = 0). Increase Kp until the control loop gets good
(satisfactory) stability as seen in the response in the measurement
signal after e.g. a step in the setpoint or in the disturbance (exciting
with a step in the disturbance may be impossible on a real system,
but it is possible in a simulator). If you do not want to start with
Kp = 0, you can try Kp = 1 (which is a good initial guess in many
cases) and then increase or decrease the Kp value until you observe
some overshoot and a barely observable undershoot (or vice versa if
you apply a setpoint step change the opposite way, i.e. a negative
step change), see Figure 2. This kind of response is assumed to
represent good stability of the control system. This gain value is
denoted KpGG.
Theoretical background
In the Good Gain method the process is controlled with a P-controller,
and the step response in the process output due to a step in the setpoint is
4This example is based on an existing system in the paper pulp factory Södra Cell Tofte
in Norway. The tank with conveyor belt is in the beginning of the paper pulp production
line.