CONTROL SYSTEM INSTRUMENTATION

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CONTROLSYSTEM INSTRUMENTATION
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Control System Instrumentation
Figure 9.3 A typical process transducer.
Transducers and Transmitters

• Figure 9.3 illustrates the general configuration
  of a measurement transducer it typically
  consists of a sensing element combined with a
  driving element (transmitter).

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• Transducers for process measurements convert the
  magnitude of a process variable (e.g., flow rate,
  pressure, temperature, level, or concentration)
  into a signal that can be sent directly to the
  controller.
• The sensing element is required to convert the
  measured quantity, that is, the process variable,
  into some quantity more appropriate for
  mechanical or electrical processing within the
  transducer.

Standard Instrumentation Signal Levels

• Before 1960, instrumentation in the process
  industries utilized pneumatic (air pressure)
  signals to transmit measurement and control
  information almost exclusively.
• These devices make use of mechanical
  force-balance elements to generate signals in the
  range of 3 to 15 psig, an industry standard.

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• Since about 1960, electronic instrumentation has
  come into widespread use.

Sensors The book briefly discusses commonly used
sensors for the most important process variables.
(See text.)
Transmitters

• A transmitter usually converts the sensor output
  to a signal level appropriate for input to a
  controller, such as 4 to 20 mA.
• Transmitters are generally designed to be direct
  acting.
• In addition, most commercial transmitters have an
  adjustable input range (or span).
• For example, a temperature transmitter might be
  adjusted so that the input range of a platinum
  resistance element (the sensor) is 50 to 150 C.

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Chapter 9
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• In this case, the following correspondence is
  obtained

Input Output
50 C 4 mA
150 C 20 mA

• This instrument (transducer) has a lower limit or
  zero of 50 C and a range or span of 100 C.
• For the temperature transmitter discussed above,
  the relation between transducer output and input
  is

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The gain of the measurement element Km is 0.16
mA/C. For any linear instrument
Final Control Elements

• Every process control loop contains a final
  control element (actuator), the device that
  enables a process variable to be manipulated.
• For most chemical and petroleum processes, the
  final control elements (usually control valves)
  adjust the flow rates of materials, and
  indirectly, the rates of energy transfer to and
  from the process.

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Figure 9.4 A linear instrument calibration
showing its zero and span.
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Control Valves

• There are many different ways to manipulate the
  flows of material and energy into and out of a
  process for example, the speed of a pump drive,
  screw conveyer, or blower can be adjusted.
• However, a simple and widely used method of
  accomplishing this result with fluids is to use a
  control valve, also called an automatic control
  valve.
• The control valve components include the valve
  body, trim, seat, and actuator.

Air-to-Open vs. Air-to-Close Control Valves

• Normally, the choice of A-O or A-C valve is based
  on safety considerations.

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Figure 9.7 A pneumatic control valve
(air-to-open).
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• We choose the way the valve should operate (full
  flow or no flow) in case of a transmitter
  failure.
• Hence, A-C and A-O valves often are referred to
  as fail-open and fail-closed, respectively.

Example 9.1 Pneumatic control valves are to be
specified for the applications listed below.
State whether an A-O or A-C valve should be used
for the following manipulated variables and give
reason(s).

1. Steam pressure in a reactor heating coil.
2. Flow rate of reactants into a polymerization
   reactor.
3. Flow of effluent from a wastewater treatment
   holding tank into a river.
4. Flow of cooling water to a distillation condenser.

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Valve Positioners
Pneumatic control valves can be equipped with a
valve positioner, a type of mechanical or digital
feedback controller that senses the actual stem
position, compares it to the desired position,
and adjusts the air pressure to the valve
accordingly.
Specifying and Sizing Control Valves
A design equation used for sizing control valves
relates valve lift to the actual flow rate q
by means of the valve coefficient Cv, the
proportionality factor that depends predominantly
on valve size or capacity
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• Here q is the flow rate, is the flow
  characteristic, is the pressure drop
  across the valve, and gs is the specific gravity
  of the fluid.
• This relation is valid for nonflashing fluids.
• Specification of the valve size is dependent on
  the so-called valve characteristic f.
• Three control valve characteristics are mainly
  used.
• For a fixed pressure drop across the valve, the
  flow characteristic is
  related to the lift , that is,
  the extent of valve opening, by one of the
  following relations

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Figure 9.8 Control valve characteristics.
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Figure 9.16 Schematic diagram of a
thermowell/thermocouple.
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Dynamic Measurement Errors An energy balance on
the thermowell gives
where U is the heat transfer coefficient and A is
the heat transfer area. Rearranging gives
Converting to deviation variables and taking the
Laplace transform gives
with
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Figure 9.13 Analysis of types of error for a flow
instrument whose range is 0 to 4 flow units.
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Figure 9.14 Analysis of instrument error showing
the increased error at low readings (from Lipták
(1971)).
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Figure 9.15 Nonideal instrument behavior (a)
hysteresis, (b) deadband.
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• Example Flow Control Loop

Assume FT is direct-acting. 1. Air-to-open (fail
close) valve gt ? 2. Air-to-close (fail open)
valve gt ?
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• Automatic and Manual Control Modes
• Automatic Mode
• Controller output, p(t), depends on e(t),
  controller
• constants, and type of controller used.
• ( PI vs. PID etc.)
• Manual Mode
• Controller output, p(t), is adjusted
  manually.
• Manual Mode is very useful when unusual
• conditions exist
• plant start-up
• plant shut-down
• emergencies
• Percentage of controllers "on manual ??
• (30 in 2001, Honeywell survey)

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• For proportional control, when Kc gt 0, the
  controller output p(t) increases as its input
  signal ym(t) decreases, as can be seen by
  combining Eqs. 8-2 and 8-1

• This controller is an example of a reverse-acting
  controller.
• When Kc lt 0, the controller is said to be direct
  acting because the controller output increases as
  the input increases.
• Equations 8-2 through 8-16 describe how
  controllers perform during the automatic mode of
  operation.
• However, in certain situations the plant operator
  may decide to override the automatic mode and
  adjust the controller output manually.

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Figure 8.11 Reverse and direct-acting
proportional controllers. (a) reverse acting (Kc
gt 0. (b) direct acting (Kc lt 0)
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• Example Liquid Level Control
• Control valves are air-to-open
• Level transmitters are direct acting

Questions Type of controller action?
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• PID Controller
• Ideal controller

• Transfer function (ideal)

• Transfer function (actual)
• a small number (0.05 to 0.20)

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Controller Comparison
P - Simplest controller to tune (Kc). -
Offset with sustained disturbance or setpoint
change.
PI - More complicated to tune (Kc, ?I) . -
Better performance than P - No offset -
Most popular FB controller
PID - Most complicated to tune (Kc, ?I, ?D)
. - Better performance than PI - No
offset - Derivative action may be affected by
noise
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Typical Response of Feedback Control
Systems Consider response of a controlled system
after a sustained disturbance occurs (e.g., step
change in the disturbance variable)
Figure 8.12. Typical process responses with
feedback control.
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Figure 8.13. Proportional control effect of
controller gain.
Figure 8.15. PID control effect of derivative
time.
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Figure 8.14. PI control (a) effect of reset time
(b) effect of controller gain.
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Chapter 8
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Position and Velocity Algorithms for Digital PID
Control
A straightforward way of deriving a digital
version of the parallel form of the PID
controller (Eq. 8-13) is to replace the integral
and derivative terms by finite difference
approximations,
where the sampling period (the time
between successive measurements of the
controlled variable) ek error at the kth
sampling instant for k 1, 2,
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There are two alternative forms of the digital
PID control equation, the position form and the
velocity form. Substituting (8-24) and (8-25)
into (8-13), gives the position form,
Where pk is the controller output at the kth
sampling instant. The other symbols in Eq. 8-26
have the same meaning as in Eq. 8-13. Equation
8-26 is referred to as the position form of the
PID control algorithm because the actual value of
the controller output is calculated.
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In the velocity form, the change in controller
output is calculated. The velocity form can be
derived by writing the position form of (8-26)
for the (k-1) sampling instant


(8-27) Note that the summation still begins at j
1 because it is assumed that the process is at
the desired steady state for
and thus ej 0 for . Subtracting (8-27)
from (8-26) gives the velocity form of the
digital PID algorithm
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(8-27)
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The velocity form has three advantages over the
position form

1. It inherently contains anti-reset windup because
   the summation of errors is not explicitly
   calculated.
2. This output is expressed in a form, , that
   can be utilized directly by some final control
   elements, such as a control valve driven by a
   pulsed stepping motor.
3. For the velocity algorithm, transferring the
   controller from manual to automatic mode does not
   require any initialization of the output ( in
   Eq. 8-26). However, the control valve (or other
   final control element) should be placed in the
   appropriate position prior to the transfer.

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Transmitters
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Typical Air-Operated Control Valve
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Control Valve Characteristics

• The valve equation for liquids is
• Linear-trim valves
• Equal-percentage-trim valves

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Control Valve Characteristics
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Equal-Percentage Valves

• 20 ? a ? 50

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Installed Characteristics
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Installed Characteristics