One form of on-demand tuning is simply an automation of the open-loop testing method for controller tuning that was described in the previous chapter. In its simplest form, the controller uses existing tuning parameters until a command is given or a button labeled “tune” is pressed.
Then the following procedure is carried out automatically:
• The control loop is switched to manual;
• The controller output is changed by a specified amount. The amount of change is usu-ally established in advance by the user as a configuration parameter;
• The response to the step change in controller output is sampled and stored until the complete response is observed;
• Some type of numerical analysis is performed on the response data to determine an approximate mathematical model for the process; this may be as simple as first-order plus dead time;
• Once process model parameters have been determined, some type of correlating equa-tions are utilized to determine tentative values for controller tuning parameters. These equations could be one of the equations sets presented in Table 6-1, or they could be proprietary equations provided by the manufacturer;
• The tentative tuning values are displayed to the user for confirmation. If confirmed, they are inserted into the control algorithm.
Several elaborations on this on-demand tuning procedure may be incorporated. For example, one manufacturer’s self-tuning algorithm first makes a single step to determine the approxi-Figure 7-1. Scheduled Tuning
to settle, then a second step is applied for a length of time equal to 2.5 times the sum of the pre-liminary estimates of dead time and time constant. This step permits the process gain to be estimated. When this step is removed, the algorithm makes a final estimate of dead time and process time constant. The objective of this sequence is to obtain better process response data than a single step test would provide.
Another elaboration of this on-demand tuning procedure could be to fit a more precise process model to the data than a simple first-order plus dead time.
In all of these cases, the essence of the technique is the same—make an open-loop step test, observe the process, and calculate tuning parameters.
The problems with this on-demand technique are the same as those presented in chapter 6 for manually initiated open-loop testing. Furthermore, a load upset may occur midway through the response that masks the controller output’s response to the step change. Because of these problems, the requirement for confirmation permits plant personnel to apply discretion before the parameters are used on line by the control algorithm.
The advantages of this on-demand tuning technique are its simplicity and the fact that the user does not need expertise in controller tuning. For these reasons, this technique is widely used, especially by the so-called quarter-DIN controllers that are targeted for the lower end of the controller market.
The technique can also be combined with other techniques. For instance, it can be combined with scheduled tuning to determine tuning parameters for multiple operating regions. Within any operating region, the user can command a “tune” operation, which initiates the bump-test procedure described previously. If the resulting parameter set is confirmed, then the parame-ters are entered into the table for the appropriate operating region.
Another approach to on-demand tuning, based upon the work of Åström and Hägglund (Ref.
7-1), is called the “relay method.” It is related to the closed-loop tuning technique described in chapter 6. When the command to tune is given, the controller is left in automatic at its current operating point. This approach utilizes preconfigured high and low limits on the controller out-put. These limits should be a selected amount above and below the current controller outout-put.
An on/off control strategy (relay controller) is used. This causes the controller output to vary in a square-wave fashion between the minimum and maximum output limits. Consequently, the process variable will oscillate in an approximate sine wave as shown in Figure 7-2.
If the time in which the controller output dwells on one limit exceeds the dwell time at the other limit, then both the high and low limits are moved an equal amount in the direction of the longer dwell time. When the output response is symmetrical (dwell times at each limit are equal), the period of oscillation is the same as the ultimate period, PU, which is determined by the closed-loop test method described in chapter 6. (This is proven in Ref. 7-1.) Furthermore,
the ultimate gain, KCU, is a function of the ratio of amplitude of oscillation of the process vari-able and controller output. Specifically:
(7-1) where: ∆V = Amplitude of square-wave oscillation of controller output
∆PV = Amplitude of oscillation of process variable.
Once KCU and PU have been determined, then an appropriate tuning parameter correlation, such as Table 6-2, can be used to determine tuning parameters. This procedure, or some modi-fication of it, has been automated and is the basis of several vendors’ automated loop-tuning procedure.