1. CONTROL SYSTEM INSTRUMENTATION

5. 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).

6. Standard Instrumentation Signal Levels
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.

7. 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.

8. Chapter 9

9. 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

10. Final Control Elements
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.

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

12. Air-to-Open vs. Air-to-Close 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.

13. Figure 9.7 A pneumatic control valve (air-to-open).

14. 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).
Steam pressure in a reactor heating coil.
Flow rate of reactants into a polymerization reactor.
Flow of effluent from a wastewater treatment holding tank into a river.
Flow of cooling water to a distillation condenser.

15. Specifying and Sizing Control Valves
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:

16. 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:

17. Figure 9.8 Control valve characteristics.

18. Figure 9.16 Schematic diagram of a thermowell/thermocouple.

19. 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

20. Figure 9.13 Analysis of types of error for a flow instrument whose range is 0 to 4 flow units.

21. Figure 9.14 Analysis of instrument error showing the increased error at low readings (from Lipták (1971)).

22. Figure 9.15 Nonideal instrument behavior: (a) hysteresis, (b) deadband.

23. Example: Flow Control Loop
Assume FT is direct-acting.
1. Air-to-open (fail close) valve ==> ?
2. Air-to-close (fail open) valve ==> ?

24. 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)

25. For proportional control, when Kc > 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 < 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.

26. Figure 8. 11 Reverse and direct-acting proportional controllers
Figure 8.11 Reverse and direct-acting proportional controllers. (a) reverse acting (Kc > 0. (b) direct acting (Kc < 0)

27. Example: Liquid Level Control
Control valves are air-to-open
Level transmitters are direct acting
Questions: Type of controller action?

28. PID Controller Transfer function (ideal) Transfer function (actual)
Ideal controller
Transfer function (ideal)
Transfer function (actual)
α = small number (0.05 to 0.20)
lead / lag units

29. 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

30. 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 Typical process responses with feedback control.

31. Figure 8.13. Proportional control: effect of controller gain.
Figure PID control: effect of derivative time.

32. Figure 8.14. PI control: (a) effect of reset time (b) effect of controller gain.

33. Chapter 8

37. 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, …

38. 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 have the same meaning as in Eq 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.

39. In the velocity form, the change in controller output is calculated
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:

40. (8-27)

41. The velocity form has three advantages over the position form:
It inherently contains anti-reset windup because the summation of errors is not explicitly calculated.
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.
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.

42. Transmitters

43. Typical Air-Operated Control Valve

44. Control Valve Characteristics
The valve equation for liquids is
Linear-trim valves:
Equal-percentage-trim valves:

45. Control Valve Characteristics

46. Equal-Percentage Valves
20 ≦ α ≦ 50

47. Installed Characteristics

48. Installed Characteristics