3. Controllers and controller types
3.6 Controller setting, optimisation, quality
3.6.1 Setting rules from Chien, Hrones and Reswick
For control loops with delay but with no overshoot, the controller parameters can be determined from the
dwell time Tu*,
compensating time Tb and proportional gain K parameters of the step response. The setting rules are applicable for relationships of
Controller parameters from Chien, Hrones and Reswick
We can see that it is only possible to use these rules if a dwell time Tu* exists. If the dwell time is zero (for example 1st order control loop with no lag time), the rules would give an infinite value for the control gain Kp.
Step response of a controlled system
3.6.2 Setting rules from Ziegler-Nichols
The Ziegler-Nichols setting rules are widely used in practice and are a proven method of matching a controller to the controlled system.
The advantage of this method is that the control loop parameters do not need to be known explicitly. The necessary information about the control loop is obtained from the response of the closed control loop at the stability limit.
This is done by configuring the controller as a pure P controller and then increasing the control gain Kp or reducing the proportional range xp until the control loop begins to oscillate.
The necessary critical control gain Kp crit or the proportional band xp crit and the period Tcrit for the onset of sustained oscillation are used to determine the controller parameters.
The controller parameters are then calculated as follows:
3.6.3 Empirical settings
Particularly in simple and fast systems, with a little experience empirical settings quickly achieve the desired results.
The quality of the setting can be checked by applying reference value steps on the controller and interpreting the transient response of the controlled variable.
Empirical settings for PID controller:
Setting the P component
Setting the I component
Setting the D component
We begin with a pure P controller. The control gain Kp is increased until no more overshoot occurs. However, a more or less constant control deviation ep will occur.
The reset time Ti for the I component is now activated to reduce the remaining control deviation ep to zero. First of all, a long reset time Ti is selected, so that the integrator is slow and the system remains stable. The reset time Ti is then gradually reduced until the remaining control deviation ep is quickly compensated but the system still remains stable. It may be possible to slightly reduce the control gain Kp .
Finally, we can attempt to use a D component to further dampen the system and simultaneously increase the control gain Kp to make the system faster. To do this, we gradually increase the rate time Td and observe the response.
In simple systems with no lag time Tt an additional D-component often brings no further improvement. In this case, a pure PI controller produces the best response.
3.6.4 Assessment of control quality
The control quality is assessed using the step response of the closed control loop. Here, we differentiate between control behaviour and disturbance response.
the control behaviour describes the response of the control loop to a change in the reference value
the disturbance response reflects the influence of faults on the controlled variable
In order to obtain a comparative interpretation of the step responses, we introduce some characteristic variables.
The overshoot xOV is a temporary deviation of the controlled variable from the reference value. It is a measure of the control loop’s tendency to oscillation or of damping.
Remaining control deviation ep = w - x
Remaining control deviation ep = w - x
The remaining control deviation ep is a static value. It is a measure of the accuracy of the control. It is particularly important for P controllers and PD controllers. Overshoot xOV and remaining control deviation ep are often related to the reference value and specified in percent.
Peak time and compensation time
Peak time Tcr
The peak time is a measure of the speed of the control process. It is the time between the reference value step and when the tolerance band is first reached.
For the disturbance response, the peak time is time between the first movement outside the tolerance band and the first re-entry into the tolerance band. If the controlled variable has an excessive remaining control deviation ep , it is the time until the subsequent stationary final value is first reached.
Compensation time Tcs
The compensation time specifies the time from the reference value step until the controlled variable finally remains within the tolerance band.
For disturbance response, this is the time between when it first moves outside the tolerance band and finally remains within the tolerance band. The relationship between the peak time and the compensation time is a measure of the damping of the control loop. A short peak time and a long compensation time means low damping and a significant tendency to oscillation.