Measurement and Control Basics 3rd Edition (complete book)

Chapter 1 – Introduction to Process Control

25

ment begins to change. The derivative action shortens the response of the slow process to an upset.

In the next chapter we discuss such important characteristics of processes as time constants and dead time. By understanding these concepts you will be better able to select the proper control action type for effective control.

EXERCISES

1.1What are the three main factors or terms found in all process control systems? List examples of each type.

1.2List the four essential elements of a process control system.

1.3What function is performed by a process controller in a control loop?

1.4What type of instrument is identified by each of the following instrument tag numbers?: (a) PIC-200, (b) FV-250, (c) LC-500, and

(d) HS-100.

1.5What is the primary requirement of any process control system?

1.6Define the term system error with respect to a control system.

1.7For a proportional controller, (a) what gain corresponds to a proportional band of 150 percent and (b) what proportional band corresponds to a gain of 0.2?

1.8What is the main reason to use integral action with proportional control?

1.9Explain the concept of “reset windup” encountered in proportional-plus-integral controllers.

1.10What type of controller is used on the heat exchanger shown in Figure 1-17? Where is the controller located?

1.11Discuss the type of process that can most benefit from the use of PID control.

BIBLIOGRAPHY

1.Chemical Engineering magazine staff. Practical Process Instrumentation and Control, New York: McGraw-Hill, 1980.

2.Considine, D. M. (ed.). Process Industrial Instruments and Controls Handbook, 4th ed., New York: McGraw-Hill, 1983.

3.Honeywell International, Process Management Systems Division. An Evolutionary Look at Process Control, Honeywell International, 1981.

26Measurement and Control Basics

4.John, C. D. Process Control Instrumentation Technology, 2d ed., New York: John Wiley & Sons, 1982.

5.Kirk, F. W., and N. R. Rimboi. Instrumentation, 3d ed., Homewood, IL: American Technical Publishers, 1975.

6.Liptak, B. G. (ed.). Process Control Instrument Engineers' Handbook, rev. ed., Radnor, PA: Chilton Book, 1985.

7.Murrill, P. W. Fundamentals of Process Control Theory, 3d ed., Research Triangle Park, NC: ISA, 2000.

8.Ogata, K., Modern Control Engineering, Englewood Cliffs, NJ: Prentice-Hall, 1970.

9.Weyrick, R. C., Fundamentals of Automatic Control, New York: McGraw-Hill, 1975.

2

Process Control Loops

Introduction

We discussed the general concepts of process control in Chapter 1. In this chapter, we will cover the basic principles of process control loops. Singleloop feedback control is the most common type of control used in industrial processes, so it will be discussed in the greatest detail. We will then discuss other types of control loops, such as cascade, ratio, and feedforward. Finally, we will examine several common methods used to tune control loops.

Single-loop Feedback Control

In a feedback control loop, the variable to be manipulated is measured. This measured process value (PV) is then compared with a set point (SP) to generate an error signal (e = PV - SP). If a difference or error exists between the actual value and the desired value of the process, a process controller will take the necessary corrective action to return the process to the desired value. A block diagram of a single-feedback control loop is shown in Figure 2-1.

The measured process variable is sensed or measured by the appropriate instrumentation, such as temperature, flow, level, or analytical sensors. This measured value is then compared with the set point. The controller uses this comparison to adjust the manipulated variable appropriately by generating an output signal. The output signal is based in turn on whichever control strategy or algorithm has been selected. Because in the process industries the manipulated variable is most often a flow, the output of

27

28 Measurement and Control Basics

Manipulated		Controlled
Variable	Process	Variable
Control		Sensor
Valve
	Set Point
	Controller	Transmitter

Figure 2-1. Feedback control loop

the controller is usually a signal to a flow control valve, as shown in Figure 2-1.

During the operation of the process, disturbances can enter the process and drive the process variable in one direction or another. The single manipulated variable is used to compensate for all such process changes produced by the disturbances. Furthermore, if changes occur in the set point, the manipulated variable is altered to produce the needed change in the process output.

Process Controllers

The most dynamic device in a feedback control loop is the process controller. There are three types of controllers—mechanical, pneumatic, and elec- tronic—and they all serve the same function. They compare the process variable with the set point and generate an output signal that manipulates the process to make the process variable equal to its set point. Figure 2-2 shows a block diagram of a feedback control loop with an expanded view of its common functions. In this diagram the measurement transducer has been expanded into its two components: the sensor and the transmitter. The sensor measures the process variable, and then the transmitter converts the measurement into a standard signal such as 4 to 20 mA DC or 3 to 15 psig.

The controller consists of a feedback transmission system, a comparator with a set point input, controller functions, and an output transmission system. The comparator block measures the difference between the set point and the process variable. For this comparison to be useful, the set point and the process variable must have the same units of measure. For example, if the set point has the units of 0 to 10 mv, then the signal from

Chapter 2 – Process Control Loops

29

Manipulated		Controlled
Variable	Process	Variable
Control		Sensor
Valve
Output	Input
Transmission	Transmission	Transmitter
System	System
Controller	Comparator	Set Point
Function
Controller Case

Figure 2-2. Functional block diagram of feedback loop

the sensor must be converted into the same units. The purpose of the feedback transmission system is to convert the sensor signal into the correct units. For example, if the input signal is 4 to 20 mA DC the feedback circuit in the controller will convert the signal to 0 to 10 mv. The function of the output transmission system is to convert the signal from the feedback circuit into the form required by the final control device. The four common controller functions are proportional, proportional plus integral (PI), proportional plus derivative (PD), and proportional plus integral plus derivative (PID).

A front-panel view of a typical electronic process controller is shown in Figure 2-3. The controller has two vertical bar displays to give the operator a pictorial view of the process variable and the set point. It also has two short horizontal digital displays just above the vertical bars to give the operator a direct digital readout of the process variable and the set point. The operator uses dual push buttons with indicating arrows to adjust the set point and the manual output functions. The operator must depress the manual (“M”) push button to activate the manual output function.

During normal operation, the operator will select automatic (“A”) mode. Manual is generally used only during system startup or during a major upset condition when the operator must take control to stabilize the process. The controller shown in Figure 2-3 has both a horizontal bar display and a digital indicator to provide the operator with the value of the output

30 Measurement and Control Basics

	FIC100
REACTOR FLOW
PV	SP
	RSP
	A
	M
	OUT
	45.1

Figure 2-3. Typical electronic controller

signal from the controller. The square indicator marked “RSP” is used to indicate that the controller is using a remote set point.

Time Elements of a Feedback Loop

The various components of the feedback control loop shown in Figure 2-2 need time to sense an input change and transform this new condition into an output change. The time of response of the control loop is the combination of the responses of the sensor, the transmitter, the controller, the final control element, and the process.

An important objective in control system design is to correctly match the time response of the control system to that of the process. To reach this objective, it is necessary to understand the concept of time delays or “lags” in process control systems.

Time Lags

In process control, the term lag means any relationship in which some result happens after some cause. In a feedback control loop, lags act in series, the output of one being the input to another. For example, the lags

Chapter 2 – Process Control Loops

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around a simple temperature control loop would be the output of the electric controller to the input to a valve lag. The output of the valve lag is the input to a process heat lag. The output of process heat lag is the input to the measurement sensor lag. We will start our discussion of time response and time lag with sensor time response.

Sensor Time Response

In process sensors, the output lags behind the input process value that is being measured. Sensor output changes smoothly from the moment a change in measurement value occurs, even if the disturbance is sudden and discontinuous. It is interesting to note that the nature of the sensor time-response curve is the same for virtually all sensors, even though the sensors measure different physical variables.

A typical response curve for a process sensor is shown in Figure 2-4, where the input has been changed suddenly at time equal to zero.

Sensor Output (m)

mf

mi

Time (t)

t = 0

Change

Figure 2-4. Exponential time response of a sensor

This curve is described by the following equation for the output measurement m(t) as a function of time:

		m(t) = m	+ (m	f	– m )(1 – e–t/τ	)	(2-1)
		i			i
where
mi	=	the initial sensor output measurement
mf	=	the final sensor output value

τ= the sensor time constant

Note that the sensor output is in error during the transition time of the output value from mi to mf. The actual process variable was changed instantaneously to a new value at t = 0. Equation 2-1 relates initial sensor

32 Measurement and Control Basics

output, final sensor output, and the time constant that is a characteristic of the sensor. The significance of the time constant τ can be found by looking at the equation for the case where the initial sensor output is zero. In this special case, the sensor output value is as follows:

m(t) = mf(1 – e–t/τ )

If we wish to find the value of the output exactly τ change occurs, then

m(τ ) = mf(1 – e–1) m(τ ) = 0.632mf

(2-2)

seconds after a sudden

(2-3)

(2-4)

Thus, we see that one time constant (1τ ) represents the time at which the output value has changed by 63.2 percent of the total change. If we solve Equation 2-2 for time equal to 5τ, or five time constants, we find that

m(5τ ) = 0.993mf

(2-5)

This means that the sensor reaches 99.3 percent of its final value after five time constants.

The following example illustrates a typical sensor response application.

First-order Lag

The first-order lag is the most common type of time element encountered in process control. To study it, it is useful to look at the response curves when the system is subjected to a step input, as shown in Figure 2-5. The advantage of using a step input as a forcing function is that the input is at steady state before the change and then is instantaneously switched to a new value. When the output curve (y) is studied, the transition of the system can be observed as it passes from one steady state to a new one. The output or response to the step input applied at time zero (to) is not a step output but an output that lags behind the input and gradually tries to reach some final value.

The equation for the system shown in Figure 2-5 is as follows:

		τ	dy(t)	+ y(t) = Kx(t)	dvc		(2-6)
where			dt		dt
y(t)	=	the output y as a function of time
x(t)	=	the input x as a function of time

Chapter 2 – Process Control Loops

33

EXAMPLE 2-1

Problem: A sensor measures temperature linearly with a transfer function of 30 mv/°C and has a one-second time constant. Find the sensor output two seconds after the input changes rapidly from 25°C to 30°C. Also find the process temperature.

Solution: First, find the initial and final values of the sensor output:

mi = (30 mv/°C) (25°C)

mi = 750 mv

mf = (30 mv/°C)(30°C)

mf = 900 mv

Then, use Equation 2-1 to solve for the sensor output at t = 2 s. Note that e = 2.718.

m(t) = mi + (mf – mi)(1 – e–t/τ )

m(2) = 750 mv + (900 - 750) mv(1 – e–2)

m(2) = 879.7 mv

This corresponds to a process temperature at t = 2 s of

T(2) = (879.7 mv)/(30 mv/°C)

T(2) = 29.32°C

x

y

System

t

t

o

o

Step Input

Output

Figure 2-5. Response of a system to step

K

= a constant

τ= the system time constant

The system response is called a “first-order lag” because the output lags behind the input, and the differential equation for the system shown in Figure 2-5 is a linear first-order differential equation.

34 Measurement and Control Basics

Differential equations are difficult to understand in some cases. If the system as a whole contains several components with their own differential equations, it is very difficult to understand or solve the entire system.

The French mathematician Pierre-Simon Laplace developed a method to transform differential equations into algebraic equations so as to simplify the calculations for systems governed by differential equations. We will avoid most of the rigorous math of the Laplace transform method and simply give the steps required to transform a normal differential equation into an algebraic equation:

1.Replace any derivative symbol, d/dt, in the differential equation with the transform symbol s.

2.Replace any integral symbol, ∫ ...dt, with the symbol 1/s.

3.Replace the lowercase letters that represent variables with their corresponding uppercase letter in the transformed equation.

We can use the Laplace transform method to convert differential Equation 2-6 for our system into an algebraic equation. Since the system equation contains only a single derivative and no integral, it can be transformed using steps 1 and 3. When we transform the equation, it becomes

τ sY(s) + Y(s) = KX(s)

(2-7)

The transfer function for our system is defined as follows:

Output = Y (s)

(2-7a)

Input X (s)

Thus, solving Equation 2-7 results in the following equation:

	Y (s)		K		(2-7b)
	X (s) =		τs +1

This is the form of a first-order lag system. First-order lag systems in process applications are characterized by their capacity to store matter or energy. The dynamic shape of their response to a step input is a function of their time constant. This system time constant, designated by the Greek letter τ (tau), is meaningful both in a physical and a mathematical sense. Physically, it determines the shape of the response of a process or system to a step input. Mathematically, it predicts, at any instant, the future time period that is required to obtain 63.2 percent of the change remaining. The response curve in Figure 2-6 illustrates the concept of a time constant by showing the response of a simple first-order system to a step input. In this system, the output is always decreasing with time, that is, the rate of