Page 70 - Chemical Process Equipment - Selection and Design

42 PROCESS CONTROL

EXAMPLE 3.1 Proportional-integral -derivative:
Constants of PID Controllers from Response Curves to a Step
Input % PB = 83RL/Am = 38.6%,
The method of Ziegler and Nichols [Trans ASME, (Dec. 1941)] will Ki = 2L = 4.8 min,
be used. The example is that of Tyner and May (Process
Engineering Control, Ronald, New York, 1967). The response to a Kd = 0.5L = 1.2 min.
change of 2 psi on the diaphragm of the control valve is shown. The
full range of control pressure is from 3 to 15psi, a difference of These are approximate instrument settings, and may need to be
12psi, and the range of temperature is from 100 to 200"F, a adjusted in process. PB is proportional band.
A recent improvement of the Ziegler-Nichols method due to
difference of 100°F. Evaluate the % displacement of pressure as
Yuwana and Seborg [AZChE J. 28, 434 (1982)] is calculator
programmed by Jutan and Rodriguez [Chem. Eng. 91(18), 69-73
Am = 100(2/12) = 16.7%.
(Sep. 3, 1984)l.
From the curve, the slope at the inflection point is
Am (t) = 2 psig
R = 17.5/100(7.8 - 2.4) = 3.24%/min,
and the apparent time delay is the intercept on the abscissa,

L = 2.40 min.
The values of the constants for the several kinds of controllers are
Proportional: lOO/K, = % PB = 100RL/Am = 100(3.24)(2.4)/
16.7 = 46.6%.
Proportional-integral: % PB = llORL/Am = 51.2%

Ki = L/0.3 = 8 min Time (min)

case, details of detectors and transmitters as well as all other of individual variables are shown in the rest of this chapter with the
elements of a control system are summarized on instrument various equipment (say pumps or compressors) and processes (say
specification forms. The simplified coding used in this chapter is distillation or refrigeration) and on the earlier flowsketches of this
summarized on Figure 3.4. and the preceding chapters, but some general statements also can
be made here. Most control actions ultimately depend on regulation
of a flow rate with a valve.
CASCADE (RESET) CONTROL
Some control situations require interacting controllers. On Figure TEMPERATURE
3.19(d), for instance, a composition controller regulates the setpoint Temperature is regulated by heat exchange with a heat transfer
of the temperature controller of a reactor and on Figure 3.15(g) the medium (HTM). The flow rate of the HTM may be adjusted, or the
set point of the reflux flow rate is regulated by composition or condensing pressure of steam or other vapor, or the amount of heat
temperature control. Composite systems made up of regions that transfer surface exposed to condensing vapor may be regulated by
respond with varying degrees of speed or sluggishness are flooding with condensate, which always has a much lower heat
advantageously equipped with cascade control. In the reactor of transfer coefficient than that of condensing vapor. In a reacting
Figure 3.19(b), the temperature TT-1 of the vessel contents system of appropriate vapor pressure, a boiling temperature at
responds only slowly to changes in flow rate of the heat transfer some desired value can be maintained by refluxing at the proper
medium, but the temperature TT-2 of the HTM leaving the cooling controlled pressure. Although examples of temperature control
coil is comparatively sensitive to the flow rate. Accordingly, appear throughout this chapter, the main emphasis is in the section
controller TC-2 is allowed to adjust the setpoint of the primary on heat exchangers.
controller TC-1 with an overall improvement in control of the
reactor temperature. The controller being reset is identified on PRESSURE
flowsheets.
Pressure is controlled by regulating the flow of effluent from the
3.2. INDIVIDUAL PROCESS VARIABLES vessel. The effluent may be the process stream itself or a non-
condensable gas that is generated by the system or supplied for
The variables that need to be controlled in chemical processing are blanketing purposes. The system also may be made to float on the
temperature, pressure, liquid level, flow rate, flow ratio, com- pressure of the blanketing gas supply. Control of the rate of
position, and certain physical properties whose magnitudes may be condensation of the effluent by allowing the heat transfer surface to
influenced by some of the other variables, for instance, viscosity, flood partially is a common method of regulating pressure in
vapor pressure, refractive index, etc. When the temperature and fractionation systems. Throttling a main effluent vapor line usually
pressure are ked, such properties are measures of composition is not done because of the expense of large control valves. Figure
which may be known exactly upon calibration. Examples of control 3.5 shows vacuum production and control with steam jet ejectors.