where β is the proportional mode selection factor, as earlier, and TI is the integral time. One manufacturer refers to this as “set point filtering.”
For the same reason that the proportional-on-measurement configuration option should not be used as the secondary controller in cascade loops, this configuration option should also be avoided for that application.
Set Point Ramping
Some controllers permit a step set point change to be made into a new target value. The actual set point used by the controller, however, is changed gradually (“ramped”) from its present value to the target value at a specified rate of change. This will result in a more gradual change in the process variable, considerably reducing overshoot.
INTEGRAL-ONLY MODE
Occasionally, it is desirable to eliminate the proportional and derivative modes entirely, utiliz-ing only the integral mode. Even when used alone, the integral mode, sensutiliz-ing the error between set point and measurement, will manipulate the controller output until that error is reduced to zero. For most control loops, however, the proportional mode will reduce the phase lag through the controller caused by the integral mode. Hence, proportional-plus-integral will produce superior performance to integral-only control.
With the PID control algorithm formulated as shown by Figure 4-13 and Equation 5-1, one cannot achieve a true integral-only controller by setting the gain and derivative time to zero since the gain is a common multiplier for all three modes. In a manufacturer’s library of soft-ware algorithms, a separate algorithm (integral-only) is normally provided. This will have the following form:
(5-5) The gain term may be expressed in several different ways, such as K, KI, or 1/TI. Also, some manufacturers may provide an integral-plus-derivative algorithm, in which case it may be con-verted into an integral-only algorithm simply by setting the derivative tuning parameter to zero.
I I
T s 1 T s 1
β
++
m = K e dt
∫
Which came first, the chicken or the egg? Commercially available analog controllers, using pneumatic mechanisms that achieved the general objectives of proportional, integral, and derivative control, were developed before a mathematical relationship for the “ideal” PID con-troller (Equations 4-5 and 5-1) had been formulated. When the working mechanisms were sub-sequently analyzed mathematically, they did not meet the “ideal” form. Instead, they could be described by the block diagram of Figure 5-5, and by the following equation, written in Laplace notation1:
(5-6)
(The “^” over the symbols indicates the entered value for the tuning parameters.)
We will show that, although the mathematical descriptions between the ideal PID and the tra-ditional analog PID controllers differ, by setting the tuning parameters properly, they can be made to behave identically. By some simple manipulations, Equation 5-6 can be reformulated to take the same form as Equation 4-6:
(5-7)
When this is done, the parameters that represent controller gain, integral time, and derivative time no longer have the same meaning as they do with the “ideal” controller. With the control-ler that is represented by Equations 4-5 and 4-6, the effective controlcontrol-ler gain, integral time, and derivative time are not directly set by the entered parameters , and , but by a combi-nation of these parameters. For example, if the parameter is adjusted, it affects the effec-tive value of controller gain, integral time, and time constant. Similarly for the other Figure 5-5. Block Diagram of Interactive Controller with All Modes on Error
(
I)(
D)
parameters. For this reason, the controller form that represents the original working mecha-nisms is often called the interactive form, whereas the “ideal” form is often called the nonin-teractive form.2
Thus, if one has an interacting controller, the equivalent parameters for a noninteracting con-troller are given by:
(5-8)
(5-9)
(5-10)
Conversely, if one has a noninteracting controller, the equivalent parameters for an interacting controller are given by:
(5-11)
(5-12)
(5-13)
where: . (5-14)
Example: Suppose we have two controllers, one formulated as a noninteractive controller, the other formulated as an interactive controller. Suppose, further, that the following controller tuning values are entered for each controller:
KC 2.0,
TI 8 minutes per repeat, TD 2 minutes.
2. Manufacturers do not use the terms interactive and noninteractive consistently. Later in this chapter, we will present another meaning some manufacturers apply to the term interactive when applied to PID. The terms series and parallel are also sometimes used to describe what we have called interactive and noninteractive controllers.
Finally, as we noted in chapter 4, some manufacturers refer to the noninteractive (standard) form as the “ISA”
form, although ISA has never endorsed a particular form of the PID control algorithm. Caution is advised when using manufacturer’s terminology.
values. For the interactive controller, however, the effective values would be the following:
Effective KC 2.5,
Effective TI 10 minutes/repeat, Effective TD 1.6 minutes.
On the other hand, suppose that we maintained the same dial settings for the noninteractive con-troller, but adjusted the dial settings for the interactive controller using Equations 5-11 – 5-14.
The effective controller tuning parameters for both controllers are now the same, even though the entered values are different. In other words, if the controllers were controlling identical pro-cesses, we could not discern a difference in their behavior.
To conclude this discussion, note the following points:
(1) If TD is set to zero, then there is no difference between the interactive and nonin-teractive forms.
(2) We can enter the effective controller tuning parameters directly if we have used a formal method (such as one of the Ziegler-Nichols methods described in chapter 6) to determine what these tuning parameters should be and if we have a noninter-active controller. If, however, we have an internoninter-active controller, we should calcu-late the required entry values from the effective values, according to Equations 5-11 – 5-14. (See discussion in the sidebar on page 132 relative to applicability of Ziegler-Nichols tuning relations to noninteractive or interactive controller.) (3) If we were unaware that we had an interactive controller and entered the required
effective values for the dial settings, then the actual effective values produced would be given by Equations 5-8 – 5-10. The error would not be too serious since the actual effective values are within 25 percent of the desired effective values.
(4) As a practical matter, if the controller we are tuning is an analog controller, then the error in calibration of the dial settings is probably greater than the error intro-duced by our failure to take into account the difference in the controller forms.
(5) Shinskey (see Ref. 5-1) claims that the interactive form is safer since it is impossi-ble to set a combination of dial settings that will produce an effective value of derivative time that is greater than the effective value of integral time. With a non-interactive form, nothing prevents the controller from being tuned, with the deriv-ative time in excess of the integral time.
(6) There is no functional, technical advantage to either the interactive or noninterac-tive form. The noninteracnoninterac-tive (standard) form has a wider choice of effecnoninterac-tive coef-ficients (i.e., TD can exceed TI for overshoot reduction on set point changes);
therefore, it is more flexible than the interactive form. The word “interactive”
often connotes benefits, as in interactive graphics. It has no such meaning here, however.
(7) With many microprocessor-based control systems, the control algorithm is formu-lated to mimic the analog controller (interactive form), not the ideal (noninterac-tive) form. Here, the conversion from required effective values into parameter entry values might be somewhat more important. Some manufacturers give the user the choice of the interactive or noninteractive form.
(See footnote on page 87 regarding inconsistency in nomenclature among various manufacturers.)
(8) Most computer-resident process control software systems use the noninteractive form.