Class 15 control action and controllers

ICE401: PROCESS INSTRUMENTATION
AND CONTROL
Class 15
Control Action and Controllers
Dr. S. Meenatchisundaram
Email: meenasundar@gmail.com
Process Instrumentation and Control (ICE 401)
Dr. S.Meenatchisundaram, MIT, Manipal, Aug – Nov 2015

Control System Parameters:
• Let us now examine the general properties of the controller
shown in Figure.
To review:
1. Inputs to the controller are a measured indication of both the
controlled variable and a setpoint representing the desired
value of the variable, expressed in the same fashion as the
measurement;

2. The controller output is a signal representing action to be
taken when the measured value of the controlled variable
deviates from the setpoint.
3. The measured indication of a variable is denoted by b, and
the actual variable is denoted by c. Thus, if a sensor measures
temperature by conversion to resistance, the actual variable is
temperature in degrees Celsius, but the measured indication
is resistance in ohms.
4. Further conversion may be performed by transducers or
transmitters to provide a current in mA, for example. In such
a case, the current becomes the measured indication of the
variable.

Error:
• The deviation or error of the controlled variable from the
setpoint is given by
e = r – b (15.1)
where
r = setpoint of variable (reference)
b = measured indication of variable
e = error
• Equation (15.1) expresses error in an absolute sense, or in
units of the measured analog of the control signal. Thus, if
the setpoint in a 4 to 20 mA range corresponds to 9.9 mA and
the measured value is 10.7 mA, we have an error of – 0.8mA.

• To describe controller operation in a general way, it is better
to express the error as percent of the measured variable range
(i.e., the span).
• The measured value of a variable can be expressed as percent
of span over a range of measurement by the equation
(15.2)
where cp = measured value as percent of measurement range
c = actual measured value
cmin = minimum of measured value
cmax = maximum of measured value
min
max min
100p
c c
c
c c
−
= ×
−

Cycling:
• One of the most important modes is an oscillation of the
error about zero. This means the variable is cycling above
and below the setpoint value.
• Such cycling may continue indefinitely, in which case we
have steady-state cycling. Here we are interested in both the
peak amplitude of the error and the period of the oscillation.
• If the cycling amplitude decays to zero, however, we have a
cyclic transient error. Here we are interested in the initial
error, the period of the cyclic oscillation, and decay time for
the error to reach zero.

Reverse and Direct Action:
• The error that results from measurement of the controlled
variable may be positive or negative, because the value may
be greater or less than the setpoint.
• How this polarity of the error changes the controller output
can be selected according to the nature of the process.
• A controller operates with direct action when an increasing
value of the controlled variable causes an increasing value of
the controller output. An example would be a level-control
system that outputs a signal to an output valve.
• Clearly, if the level rises (increases), the valve should be
opened (i.e., its drive signal should be increased).

Reverse and Direct Action:
• Reverse action is the opposite case, where an increase in a
controlled variable causes a decrease in controller output.
• An example of this would be a simple temperature control
from a heater. If the temperature increases, the drive to the
heater should be decreased.

Classification of Controller Modes:

Discontinuous Controller Modes:
Two-Position Mode:
• The most elementary controller mode is the ON/OFF, or two-
position, mode. This is an example of a discontinuous mode.
• It is the simplest and the cheapest. Although an analytic
equation cannot be written, we can, in general, write
• When the measured value is less than the setpoint, full
controller output results. When it is more than the setpoint,
the controller output is zero. A heater is a common example.
If the temperature drops below a setpoint, the heater is turned
ON. If the temperature rises above the setpoint, it turns OFF.
00%
0100%
p
p
e
p
e
<
= 
>

Neutral Zone:
• Any practical implementation of the two-position controller,
there is an overlap as increases through zero or decreases
through zero. In this span, no change in controller output
occurs.
• This is best shown in Figure 15.1, which plots p versus ep for
a two-position controller.
Figure 15.1 Two-position controller action with neutral zone

Neutral Zone:
• We see that until an increasing error changes by ∆ep above
zero, the controller output will not change state.
• In decreasing, it must fall ∆ep below zero before the controller
changes to the 0% rating.
• The range 2∆ep, which is referred to as the neutral zone or
differential gap, is often purposely designed above a certain
minimum quantity to prevent excessive cycling.
• The existence of such a neutral zone is an example of
desirable hysteresis in a system.

Figure 15.2 On–off controller response

Figure 15.3 On–off controller response with dead band

Example:
15.1 A liquid-level control system linearly converts a
displacement of 2 to 3 m into a 4 to 20-mA control signal. A
relay serves as the two-position controller to open or close an
inlet valve. The relay closes at 12 mA and opens at 10 mA. Find
(a) the relation between displacement level and current,
(b) the neutral zone or displacement gap in meters.
Solution: The relation between level and a current is a linear
equation such as H = K I + H0
Solving yields: K=0.0625 m/mA, H0=1.75m, HH=2.5m, and
HL=2.375m.
Neutral zone is 2.5 – 2.375 = 0.125m

Assignment 2.1:
The temperature of water in a tank is controlled by a two-
position controller. When the heater is off the temperature drops
at 2 K per minute. When the heater is on the temperature rises at
4 K per minute. The setpoint is 323 K and the neutral zone is
±4% of the setpoint. There is a 0.5-min lag at both the on and off
switch points. Find the period of oscillation and plot the water
temperature versus time.

Multi-Position Mode:
• A logical extension of the previous two-position control
mode is to provide several intermediate, rather than only two,
settings of the controller output.
• This discontinuous control mode is used in an attempt to
reduce the cycling behavior and overshoot and undershoot
inherent in the two-position mode.
• As an example, a three position controller can be
represented as
1
1 1
1
100%
50%
0%
p
p
p
e e
p e e e
e e
 >

= − < <
 < −

Multi-Position Mode:
• As long as the error is between and of the setpoint, the
controller stays at some nominal setting indicated by a
controller output of 50%.
• If the error exceeds the setpoint by or more, then the output
is increased by 100%. If it is less than the setpoint by or
more, the controller output is reduced to zero.
• Figure 15.4 illustrates this mode graphically. Some small
neutral zone usually exists about the change points, but not
by design; thus, it is not shown. This type of control mode
usually requires a more complicated final control element,
because it must have more than two settings.

Figure 15.4 Three-position controller action

Figure 15.5 Relationship between error and three-position controller action, including
the effects of lag

References:
• Process Control Instrumentation Technology, by Curtis D.
Johnson, Eighth Edition, Pearson Education Limited.

Class 15 control action and controllers

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