3.4

Relays for Computing and Programmers C. L. MAMZIC

(1970, 1985)

R. GILBERT

(1995)

B. G. LIPTÁK

(2005)

Large-Case, Cam-Actuated Time Function Generators (Programmers) Cost:

$1200 to $2500

Partial List of Suppliers:

ABB Automation Inc. (www.abb.com/processautomation) Bristol Babcock Inc. (www.controlwave.com) Emerson Process Management (www.easyddeltav.com) Honeywell Sensing and Control (www.honeywell.com/sensing) Invensys Process Systems (www.invensysips.com) Siemens Energy & Automation (www.sea.siemens.com/ia)

Large-Case, Adjustable Range and Hold Programmers Cost:

$2200 to $3500

Partial List of Suppliers:

ABB Automation Inc. (www.abb.com/processautomation) Invensys Process Systems (www.invensysips.com) Texas Analytical Controls Inc. (www.tac-controls.com)

Miniature and Large-Case Pneumatic Profile Tracers (Programmers) Inaccuracy:

± 0.25% of full scale

Cost:

$1800 to $4000

Partial List of Suppliers:

Aro Corp. (http://www.hydraulic-supply.com/html/productline/mfgprod/aro-corp.htm) Gaston County Dyeing Machine Co. (http://www.gaston-county.com/) Partlow Corp. (http://partlow.ttistore.com/) Pneucon, Inc. (http://www.pneucon.net/ ) Siemens Energy & Automation Inc. (www.sea.siemens.com)

Electric Line and Edge Follower Programmers Inaccuracy:

± 0.25% of full scale

Cost:

$1800 to $4000

Partial List of Suppliers:

Emerson Process Management (www.easydeltav.com) Honeywell Sensing and Control (www.honeywell.com/sensing) Jumo Process Control Inc. (www.jumousa.com) Moeller Electric Corp. (http://www.moellerusa.net/) MK Juchheim GmbH. (http://www.jumo.de/)

493 © 2006 by Béla Lipták

494

Transmitters and Local Controllers

Timing and Programming Equipment Cost:

$500 to $5000

Partial List of Suppliers:

ABB Automation Inc. (www.abb.com/processautomation) Aromat Corp. (www.aromat.com) Automatic Timing & Controls Co. (www.automatictiming.com) Crouzet Corp. (www.crouzet.com) Danaher Controls (www.dancon.com) Honeywell Sensing and Control (www.honeywell.com/sensing) Invensys Process Systems (www.invensysips.com) Johnson Controls Inc. (www.johnsoncontrols.com) Jumo Process Control Inc. (www.jumousa.com) Kessler-Ellis Products Co. (www.kep.com) Love Controls Corp. (www.lovecontrols.com) Newport Electronics Inc. (www.newportus.com) Omron Electronics Inc. (www.omron.com/oei) Red Lion Controls (www.redlion-controls.com) Square D/Schneider Electric Co (www.squared.com)

Drum Programmers for On-Off Event Sequencing Cost:

$2500 to $8000

Partial List of Suppliers:

Barber-Coleman Co. (http://www.barber-colman.com/) Honeywell Sensing and Control (www.honeywell.com/sensing) Moore Controls SA Pty Ltd. (www.moore.co.za) Omron Electronics Inc. (www.omron.com/oei) Siemens Energy & Automation Inc. (www.sea.siemens.com) Texas Instruments Far East Inc. (www.ti.com)

Computing Relays

© 2006 by Béla Lipták

Inaccuracy:

±1/2% for all types except the differentiating and integrating relays, which are ±15 % if uncompensated and ±1% if compensated in specially built units

Cost:

Prices shown are for pneumatic (and electronic) devices: High and low selectors $80 to $180 ($125 to $300) Adding and subtracting relays $100 to $200 ($250 to $500) Square root extractors and function generators $400 to $800 ($250 to $500) Scaling and proportioning relays $500 to $1000 ($250 to $500) Multiplying and dividing relays $600 to $1200 ($400 to $600)

Partial List of Suppliers:

ABB Automation Inc. (www.abb.com/processautomation) Acromag Inc. (www.acromag.com) Devar Inc. (www.devarinc.com) Dymec Inc. (www.dymec.com) Emerson Process Management (www.easydeltav.com) Fairchild Industrial Products Co. (www.fairchildproducts.com) Invensys Process Systems (www.invensysips.com) Johnson Controls Inc. (www.johnsoncontrols.com) Moore Industries International Inc. (www.miinet.com) MTL Inc. (www.mtl-inst.com) Robertshaw (www.robertshawindustrial.com) Rochester Power Instruments (www.rochester.com) Ronan Engineering Co. (www.ronan.com) Transmation Products Group (www.transmation.com) United Electric Controls (www.ueonline.com) Wilkerson Instrument Co. Inc. (www.wici.com)

3.4 Relays for Computing and Programmers

495

INTRODUCTION In our digital age, most computing and timing functions are done in software. Volume 3 of this handbook is devoted to the description of such and many other software packages. The topics discussed in this section are from the analog age when mathematical and time function generators were still dedicated hardware components. Computing functions were performed by pneumatic and analog electronic relays, while timing and sequencing was controlled by programmers. Some of the common relay functions and their symbols are listed in Table 3.4a. From the controller’s viewpoint automation is, in effect, a set of computing and timing elements that carry out the mathematical operations required to implement a control scheme. Summation, subtraction, multiplication, division, raising to a power, extracting the root, integration, and differentiation are important examples of such computing operations. Popular timing functions include lag elements, time function generators, ramp and hold programmers, event sequencers, and profile programmers. Both timing and computing functions are still available as stand-alone products or in combinations that add up to a complete controller.

TABLE 3.4a Relay Functions and Their Symbols* Symbol 1-0 or ON-OFF

Automatically connect, disconnect, or transfer one or more circuits, provided that this is not the first such device in a loop. (See Note 13 in Table 1.4b)

∑ or ADD

Add or totalize (add and subtract), with two or more inputs.

∆ or DIFF

Subtract (with two or more inputs)

±

Bias (single input)

AVG.

Average

% or 1 : 3 or 2 : 1 (typical)

Gain or attenuate (input:output), with single input Multiple (two or more inputs)

÷

Divide (two or more inputs) or SQ. RT.

n

x or x

1/n

1:1

Boost

> or HIGHEST (Measured Variable)

High-select. Select highest (higher) measured variable (not signal, unless so noted).

< or LOWEST (Measured Variable)

Low-select. Select lowest (lower) measured variable (not signal, unless so noted).

REV.

Reverse Convert

a. E/P or P/I (typical)

For input/output sequences of the following: Designation Signal E Voltage H Hydraulic I Current (electrical) O Electromagnetic or sonic P Pneumatic R Resistance (electrical) For input/output sequences of the following: A Analog D Digital

b. A/D or D/A

Multiplying and Dividing Relays In the force bridge multiplier-divider shown in Figure 3.4b, input pressures act on bellows in chambers A, B, and D. The output is a feedback pressure in chamber C. The bridge consists of two weigh-beams that pivot on a common movable fulcrum, with each beam operating a separate feedback loop. Any unbalance in moments on the left-hand beam causes a movement of the fulcrum position until a moment-balance is restored. An unbalance in moments on the right-hand beam results in a change in output pressure until balance is restored.

© 2006 by Béla Lipták

Raise to power Characterize

PNEUMATIC RELAYS In some existing plants, pneumatic computing relays are still used because of their simplicity, reliability, and safety advantages when used in processes with high fire and explosion potentials.

Extract square root

f(x)

MATHEMATICAL FUNCTIONS Most control systems require that the controller perform some sort of mathematical calculation before a control action is initiated. These calculations involve algebra as well as integral and differential calculus. The popular computing elements perform summations, subtractions, multiplication, division, raising to a power, extracting roots, and specific types of differentiation and integration. In the discussion that follows, these analog computing relays are grouped into pneumatic and electronic categories.

Function

∫

Integrate (time integral)

D or d/dt

Derivative or rate

I/D

Inverse derivative

Note: The use of a box enclosing a symbol is optional. The box is intended to avoid confusion by setting off the symbol from other markings on a diagram. * Permission by ISA to abstract from its standard ANSI/ISA S5.1 is gratefully acknowledged.

496

Transmitters and Local Controllers

Output zero adjustment AM “A”

P1 Input pressure

Characterized cam

“R” S

Force Y PB B

b

a

PA

b

Input zero adjustment

“B” θ

C

Baffle lever

Force x Nozzle

a

PD D

A

Beam mounted cam follower

Air supply

Feedback diaphragm Amplifying booster Output P0

PC output

Cam positioning cylinder

Input P2

FIG. 3.4c Multiplying and dividing relay characterized by a pneumatic cam.

Supply

FIG. 3.4b Multiplying and dividing relay, utilizing a pneumatic force bridge.

The equations that characterize the force bridge operation with respect to each subunit diaphragm in the unit shown in Figure 3.4b can be conveniently reduced to: C=

B×D A

3.4(1)

Multiplication results when the two input variables are connected to chambers B and D. Division results when the dividend is connected to either chambers B or D, with the divisor connected to A. Simultaneous multiplication and division results when B, D, and A chambers are used. The significant advantage of a cam-actuated multiplying and dividing relay is that it can operate with practically any type of nonlinear function that can be cut on a cam. These can include logarithmic functions, as in pH measurement, and computation in narrow, suppressed ranges of measurement, which results in good resolution. The pure multiplier-divider in Figure 3.4c, when used for temperature and pressure compensation, for example, uses input signals proportional to the total absolute temperature and pressure range, starting with zero. Since the usable temperature and pressure range might be a small percentage of the total measurement range, the results might lack precision. In Figure 3.4c, input pressure P1 and output P0 act on double-diaphragm capsules, and the net resultant force in each is in the direction of the larger area diaphragm. Input P1 creates force Y, which pulls the baffle, pivoted at A, away from the nozzle. Output pressure P0 creates force X, which moves the baffle closer to the nozzle. The θ input/output relationship is a function of the angle of the nozzle beam.

© 2006 by Béla Lipták

When angle θ is 45 degrees, the relationship is 1 : 1. This can also be considered the multiplication factor or gain, K. At larger angles, K is greater than 1, and at smaller angles, smaller than 1. The multiplicand P2 acts on the cam-positioning cylinder and thereby changes the nozzle beam angle in accordance with the cam characteristic. The zero adjusting springs subtract the 3-PSI (0.2-bar) zero from P1 and set a 3-PSI (0.2-bar) zero on the output, respectively. Adding, Subtracting, and Inverting Relays In the force balance arithmetic computing relay, Figure 3.4d, a signal pressure in chamber A acts downward on a diaphragm with unit effective area. A signal in chamber B also acts downward on an annular diaphragm configuration, likewise having an effective area of unity. Signal pressures in chambers C and D similarly act upward on unit effective diaphragm areas. Any unbalance in forces moves the diaphragm assembly with its integral nozzle seat. The change in nozzle seat clearance changes the nozzle backpressure and hence, changes the output pressure, which is fed back into chamber D until force balance is restored. The following equation describes the operation of the relay: T = A+ B−C ± K

3.4(2)

K is the spring constant. It is adjustable to give an equivalent bias of ±15 PSI (1.24 bar). The relay in Figure 3.4e is a modification of Figure 3.4d in that it incorporates additional input chambers and output feedback chambers. It can be used to add and/or average up to nine inputs. Figure 3.4e is an averaging relay for five inputs. The averaging feature keeps all signals in the same

3.4 Relays for Computing and Programmers

497

A±K A

B

B C D

C

Bias spring (±K )

Bias (±K) S

T

PV

Input E

A

Input D B C

Input C

D Input B Input to chamber “A”

Input A

Supply “S”

Output “T ”

Vent

FIG. 3.4d Pneumatic, adding, subtracting, inverting, and biasing relay.

standard 3- to 15-PSIG (0.2- to 1.0-bar) range. Its characteristic equation is: T=

A+ B+C+D+E ±K 5

3.4(3)

The relay shown in Figure 3.4d provides inverting or reversing action by setting the loading of the bias spring to a maximum and by connecting the input to subtracting chamber C. If the bias is set at +18 PSIG (1.2 bar), then a 3- to 15-PSIG (0.2- to 1.0-bar) signal in chamber C results in a 15- to 3-PSIG (1.0- to 0.2-bar) output. The equation describing this operation is: T = K −C

3.4(4)

Differentiating Relay A differentiating relay produces an output proportional to the rate of change of the input. Figure 3.4f shows an ideal pneumatic differentiating relay. The relay is basically similar in construction to the relay shown in Figure 3.4d, except that the annular effective diaphragm area between chambers B and C is more than ten times the effective area of the small diaphragms between chambers A and B—giving a gain of greater than ten. The input signal is transmitted unrestricted to chamber B and passes to chamber C through an adjustable restriction. When

© 2006 by Béla Lipták

Supply

Output (T )

FIG. 3.4e Multi-input averaging relay.

the input is steady, the forces resulting from pressures in B and C chambers cancel each other, so that the output equals the zero-spring setting (usually mid-scale, 9 PSIG [0.6 bar] if both positive and negative rates are to be measured). If the input pressure changes, a differential develops across the restriction. The relay transmits an output proportional to this differential. For accurate results, this differential must be directly proportional to the rate of change of input. Using a needle valve that produces laminar flow provides a linearly proportional volumetric flow, but the differential developed across the needle valve is a function of the mass flow, which varies with static pressure because of compressibility. This compressibility error is approximately ±15 %. The effect can be fully compensated, however, by the addition of a variable volume to chamber C, the restricted chamber. As the static pressure increases, tending to make the differential smaller because of higher mass flow rate, the volume increases proportionately to maintain a constant differential. The needle valve setting determines the rate time constant. The compensated relay is not a standard piece of hardware. In most cases, a noncompensated differentiating relay is satisfactory.

498

Transmitters and Local Controllers

x

X&T

A

ut Inp Output

B

C Time T= S

P.V.

dx dt

Input

T Diaphragm ring Supply

Output

FIG. 3.4g Fixed-ratio amplifying relay.

A B

the input and the adjustable top spring allows exact zero setting. The operating equation is:

C

T = AP1 + K Input (X)

Supply (S )

Output (T )

FIG. 3.4f Differentiating relay.

Scaling and Proportioning Relays Scaling, or proportioning, involves multiplication by a constant. Several approaches are available: 1. 2. 3. 4.

Special fixed-ratio relays Pressure transmitters Proportional controllers Adjustable ratio relays

The fixed-ratio scaler is the simplest if the correct ratio is available and if adjustability and exact ratio are unnecessary. Figure 3.4g shows such a relay. The input pressure is connected to the top chamber and acts on the upper diaphragm. Output acts upward on the small bottom diaphragm. The gain is a function of the relative effective areas of the large and small diaphragms as determined by the dimensions of the diaphragm ring. The bottom spring applies a negative bias to

© 2006 by Béla Lipták

3.4(5)

where A is the gain constant and K is the spring setting. Where the scaling must be exact and does not have to be adjusted periodically, pressure transmitters are an economical, reliable, and accurate choice. Where the scaling factor must be modified occasionally, conventional ratio relays, which often consist of the proportioning section of a controller, are commonly used. Integrating Relay Integration, the reverse of differentiation, essentially involves measurement of accumulated pressure resulting from a flow that is proportional to the offset (from some chosen reference) of the input variable. Figure 3.4h shows an ideal integration relay. The input signal loads chamber B. The output, it should be noted, is the accumulated pressure in chamber A, not the booster pilot output. The input signal determines the pressure differential across the needle valve. As in the case of the differentiation relay, with laminar flow across the needle valve, the volumetric flow is directly related to the differential. The mass flow, however, which determines the accumulated pressure, still varies with the static pressure because of compressibility. This effect is also compensated by connecting a variable volume to chamber A. The needle valve sets the proportionality constant of the integrator. Neither the compensated differentiating relay nor the compensated integrator is available as standard hardware. Usually, the noncompensated relay (actually a proportionalspeed floating controller) is satisfactory.

3.4 Relays for Computing and Programmers

499

Variable volume T

Input

A X

T&X B

t tpu Input

Output motion

Ou

Input motion

C T 3 PSIG (0.2 bar) output pressure

Time S

Input

P.V. q

L X cos q = 1 − L

X T 15 PSIG (1.0 bar) output pressure

FIG. 3.4i Square root extractor.

A B C

pilot nozzle. This increases the output pressure and moves the output feedback bellows upward until balance is restored. Since the length of the floating link is fixed, the angular displacement produced by movement of the output bellows follows the relationship:

Output (T ) Input (X )

cos θ = 1 −

Supply (S)

X L

3.4(7)

FIG. 3.4h Integrating relay.

A plot of the angle θ (output displacement) versus X (input displacement) in this equation shows the relationship to be virtually an exact square root for small angular motion.

Square Root Extractor Relay

High- and Low-Pressure Selector and Limiter

Square root extraction is commonly required to linearize signals from differential pressure-type flow transmitters. The force bridge, Figure 3.4b, provides square root extraction when the output is connected in common to the A and C chambers, giving the equation:

Selector relays are used in override systems. The high- pressure selector relay compares two pressures and transmits the higher of the two in its full value. In Figure 3.4j, the two input pressures act against a free-floating flapper disk. The differential pressure across the flapper always results in closure of the low-pressure port. In the low-pressure selector, Figure 3.4k, if input A is less than input B, the diaphragm assembly throttles the pilot

C2 = B × D

3.4(6)

Other solutions are based on: Input A

1. Use of a cam-characterized function generator 2. A geometric relationship, namely, change in cosine compared with the change in included angle, for smaller angular displacements (Figure 3.4i)

Input B

Output

Flapper

Starting with the input and output at 3 PSIG (0.2 bar), an increase in input causes the floating pilot link to restrict the

© 2006 by Béla Lipták

FIG. 3.4j High-pressure selector relay.

500

Transmitters and Local Controllers

Input A e0 e3

Bridge no.2 Amplifier

Output

Input B

e2 e1

FIG. 3.4k Low-pressure selector relay.

e0

Bridge no.1

FIG. 3.4m Multiplier-divider.

plunger to make the output equal to input A (the conventional action of a 1 : 1 booster relay). If input B is less than A, the supply seat of the pilot plunger is wide open so that pressure B is transmitted in its full value. By connecting a set reference pressure into one of the ports of the high-pressure selector, a low-limit relay results. Conversely, by connecting a set reference pressure into the low-pressure selector, a high-limit relay results. Limit relays are available with the reference-setting regulator built into the relay.

ELECTRONIC COMPUTING ELEMENTS Although electronic instrumentation is based on large-scale integrated circuits, computing functions based on discrete component operational amplifier, i.e., op amp, are still available. In addition, op amp concepts are at the heart of all the current and future electronic computing elements. Therefore, it is appropriate to review the electronic computing functions within their op amp context.

bridge is a trapezoid, the area of which can be calculated by the following equation: area = e1e2 tan θ

3.4(8)

The angle θ is established by the constant slope of the sawtooth, and thus area = Ke1e2

3.4(9)

The output voltage, e0, is amplified and filtered to a DC signal, and its voltage level will therefore be proportional to the area and, consequently, to the product of e1 and e2. Adding another diode bridge to the multiplier circuit produces a multiplier/divider (Figure 3.4m). The input to the amplifier is the output difference from the two bridge networks. e0 = A( Ke1e2 − Ke3e0 )

3.4(10)

where A = gain of the amplifier. Rearranging the equation yields:

Multiplying and Dividing In Figure 3.4l, inputs e1 and e2 are multiplied in the diode bridge. Conduction of the diodes in the bridge is dependent upon the relative magnitude of the inputs with respect to the constant slope of the sawtooth input. The output of the diode

e1e2 =

e0 + e3e0 AK

3.4(11)

The term e0 /AK is very small if the amplifier gain is high, and thus

Diode bridge

e2 e1

Amplifier

e0

e0 =

e1e2 e3

3.4(12)

Adding, Subtracting, and Inverting Sawtooth oscillator

FIG. 3.4l Multiplier.

© 2006 by Béla Lipták

Power supply

In Figure 3.4n, the two input potentials e1 and e2 are compared in the multiple comparator, which produces a proportional output to the amplifier. The current paths of the two inputs can be the same or opposite, resulting in either an adding or subtracting circuit, respectively.

3.4 Relays for Computing and Programmers

501

c e1 Multiple comparator e2

Amplifier

e0

e1

1

2

e0

Bias

FIG. 3.4p Integrator.

Power supply

Scaling and Proportioning FIG. 3.4n Adder, subtracter, and inverter.

Inverting is accomplished by biasing the comparator to produce maximum output with no input. Applying a reverse input (i.e., a reverse current input with respect to bias current) causes the output to decrease with increasing input. The feedback signal is such that the amplifier acts as a unity gain network.

Simple electronic scaling or proportioning involves combining a voltage divider circuit with an amplifier. The voltage divider circuit is connected to either the input or output side, depending upon whether the gain is to be greater or less than unity. In Figure 3.4q, the amplifier comes to balance when ∆ei equals zero. Since the voltage divider is on the output, only a portion of the amplifier output is fed back to counterbalance the input voltage. Therefore, the output will rise above e1, resulting in gains greater than one. The operation can be expressed as:

Differentiating The input amplifier in Figure 3.4o is a capacitor-coupled so that only the rate of change of the input signal is seen by the amplifier. Two diodes in the feedback of the amplifier allow its output to go positive or negative (depending on the direction of the rate of change) by an amount equal to the forward drop across the diodes (only a few tenths of a volt). The output amplifier inverts and amplifies this signal by its openloop gain. A small positive feedback is applied to the last amplifier to prevent output from “chattering” at the diodes’ switching point.

e0 = e1

( R1 + R2 ) R1

3.4(13)

An electronic scaler with a gain of less than one is constructed by a simple alteration of the circuit shown in Figure 3.4q. The voltage divider is moved from the amplifier output and placed across the e1 input. If the signal from the middle of the voltage divider is fed to the amplifier’s “+” terminal, then the resulting gain will be less than one. This can be expressed as: e0 = e1

R2 R1 + R2

3.4(14)

Integrating Square Root Extracting The first amplifier in Figure 3.4p, a simple inverting type, performs the integration function as the charge accumulates across the capacitor of the RC (resistor-capacitor) network. The second amplifier is an inverting, general-purpose type, which relates the output directly to the input.

e1

– +

– +

The square root converter combines a DC amplifier with a negative feedback diode network. As current into the amplifier increases, the amplifier gain decreases with decreased feedback resistance in the diode network. The gain typically varies according to seven straight line segments that approximate a square root function. This is accomplished by having seven diode-resistance

∆ei

e0 +

– + +

R1 e0

e1 R2 –

FIG. 3.4o Differentiator.

© 2006 by Béla Lipták

FIG. 3.4q Scaler with gain greater than one.

–

502

Transmitters and Local Controllers

technical support personnel needed to repair them are available in the plant, and they function well under various harsh plant operating conditions. All of the analog time functions discussed here are also available as digital or microprocessor-based units.

+e

Signal e1

CR1 Amplifier

Amplifier

e2

e0

CR2 Amplifier

FIG. 3.4r High-voltage selector.

paths in the feedback network automatically parallel each other with increasing input. The output stabilizes when the diode network modified feedback counterbalances the input. High- and Low-Voltage Selector and Limiter The higher of the two positive inputs in Figure 3.4r causes a higher negative potential at the cathode of one of the diodes (CR1 or CR2). The forward bias of this diode passes the higher input and reverse-biases the other diode to isolate the lower input. Thus if signal e1 drops below signal e2, CR2 is forward-biased to pass signal e2 and CR1 is reverse-biased to isolate signal e1. All the amplifiers are unity gain inverter types. Substituting a fixed input for one of the variables produces a lowlimit relay. To obtain a low-voltage selector, the diodes shown in Figure 3.4r are inverted and a negative supply is used. Thus, the least positive input forward-biases one of the diodes (by the least negative potential applied to the anodes of the diodes). This automatically reverse-biases the other diode and isolates the higher input from the output. TIMING ELEMENTS Common technologies for time management devices include discrete analog and digital circuits, microprocessor-based time functions, and pneumatic timing devices. Each of these choices may offer an advantage over the other, depending on the type of timing operation and process application of interest. These timing options are discussed below and also in Chapter 5, where the emphasis is on digital software-based systems. Here the timing elements are grouped for convenience into analog, digital, and microprocessor categories. In most process applications digital and microprocessor-based timing functions provide the same accuracy as their analog equivalents. Analog timing elements are still used in some cases because of historic, maintenance, and process environment reasons, that is, people have used them in the past and are comfortable with them,

© 2006 by Béla Lipták

Analog Timing Operations A simple but highly useful time function generator is the first-order lag function. In many industrial control schemes, motors and other loads must be energized in a time sequence provided by a lag function. First-order time functions are also used in controllers that provide reset and rate actions. Although a first-order time function is certainly available as a digital circuit or as a microprocessor-based unit, it can also be implemented in its analog or pneumatic versions. Electronic Time Delay Analog first-order lag circuits are common and are often used to generate delay times on applications involving the starting of motors. Such circuits are simple variable resistance and capacitance circuits that provide output voltages as a function of time as set by the values of the two variable circuit components. The integral equation that describes this type of circuit is as given in Equation 3.4(15): V (t ) = IR(1 − e −τ / RC )

3.4(15)

Voltages from circuits that follow Equation 3.4(15) vary exponentially with time. Thus, a motor starter that is monitoring V(t) will not respond until the voltage reaches a level it recognizes. The time delay that it takes for the voltage input signal to the motor to go from zero volts to the starter’s trigger voltage is controlled by the actual values of R and C, which are selected for the specific motor application. Pneumatic Time Delay The equivalent RC circuit in its pneumatic form is usually described by Equation 3.4(16):

τ dPi /dt + Pi = P0

3.4(16)

The solution of this differential equation with respect to Pi(t), which is the input pressure as a function of time, gives a pressure–time profile similar to the shape of the voltage–time profile obtained from the solution of Equation 3.4(15). The construction of a pneumatic system that follows Equation 3.4(16) is not difficult. The input air signal is fed to a laminar flow throttling device and a small-capacity single-port storage tank. The time delay in the output pressure signal is a function of the storage tank size and the restriction in the throttling device. As with its analog circuit counterpart, a pneumatic time lag device must be able to vary the time constant, τ, over a range from 5 seconds to about 20 minutes. On commercially available units, the resistance and capacity parameters are designed such that τ has an adjustable range from 5 to 300 seconds for each capacity. Therefore, a four-equal-capacity parallel system would allow an adjustable range from 20 seconds to 20 minutes.

3.4 Relays for Computing and Programmers

Digital Timing Operations This subject is discussed in more detail in Volume 3 and in Chapter 5 of this volume. The main distinction between the analog and digital worlds is the concept of a discrete event. For timing elements, the disadvantages of a discrete, i.e., digital- or microprocessorbased, timing function becomes significant in a control application only when the time between output signal updates is long; if the circuit does not quickly update the output signal to the process heater, then the ramp profile will have a lot of fluctuation in it. All of the timing functions are available as digital- or microprocessor-based products. Their selection depends on several constraints. First, the selected timing circuit must update its control signals at least twice as fast as the process can change the value of the process variable that is being controlled. Second, the selected timing element should be able to survive the chemical and mechanical environment it is to be subjected to. Finally, the product must function properly despite electrical noise. Microprocessor Timing Functions When compared to the older technologies, one major difference is the convenience with which additional control functions can be included with the microprocessor-based system. On the other hand it is desirable to make sure that the unit meets government and industry safety standards for the expected application. These include fire and explosion standards in hazardous environments. Second, will it meet the mechanical vibration and electrical requirements for the environment in which it will be installed? Third, do the input signal conditions required and the output signal characteristics delivered by the unit match the needs of the application?

PROGRAMMERS Step Programmers A step programmer is a process sequencer that does not have a practical analog circuit equivalent. Step programmers are used for on/off event sequencing, a subject that is discussed in more detail in Chapter 5 under the topics of PLCs and logic elements. These step programmers do not provide an analog output. A typical design consists of a perforated drum (Figure 3.4s). Each perforation represents a step in one channel. Drums are available with from 30 to 100 steps and from 16 to 93 channels. Inserting a nylon plug into a hole results in a switch actuation on the corresponding step and channel. The stepping can be initiated by a remote sensor switch, counter, timer, or pushbutton. These units are easily programmed and can replace complex logic and interlock circuits. They can not only replace such systems but can eliminate the need for their custom design and construction as well.

© 2006 by Béla Lipták

503

Nylon plugs

Geneva disc Typical output switch Motor

NC NO

Output terminals

FIG. 3.4s Drum programmer for on/off event sequencing.

Related to the step programmer is the multi-channel cam timer in which a number of individually adjustable cams are mounted on a single drive shaft and provide event-sequencing control. Profile Programmers There are three types of process profile programmers that use the same basic time function control mechanisms. Although the cam-type, the belt-type, and the electrostatic-line-type programmers have different mechanical operating principles, they fundamentally perform the same process control function. Each uses a tracing element that follows the movement of a rotating cam, belt, or electrostatic line. Each has a motion detection subsystem that converts the tracing element movements into a predetermined time-dependent control signal. The time dependence of the control signal depends on the shape, cut, or position of the programmer’s cam, belt, or electrostatic line. Cam Programmer Figure 3.4t shows the general layout for a cam-driven profile programmer. The cams of the cam-type programmers can be driven by pneumatic or electric motor drives that move the set-point index. This motion in the tracing element in turn generates a time-dependent standard, i.e., 3 to 15 PSIG, 4 to 20 mA DC, etc., output signal. The cams can be Motion transmitter

Set point index Motor driven cam

FIG. 3.4t Cam-type programmer.

504

Transmitters and Local Controllers

Front

To pressure switch

Quick-change endless belt program master

Motion transmitter

Tracer nozzle Analog tracer

Servo 20 PSIG (138 kPa)

Up to 25 digital tracks

Cable

Air supply Output

Plastic tubing Analog master cross section

Digital master cross section

Nozzle restriction

Pulley

FIG. 3.4u Pneumatic profile tracer programmer with synchronized on/off sequence control switches.

made of plastic or metallic materials. Traditionally, cam programmers have incorporated an integral controller, a sensor element, and a circular chart recorder in the same package. Cam programmers are used only on batch processes for the following reasons. • •

•

The making of the new cams and changing them is not a simple matter. The cam rise is limited for mechanical reasons to about a 50-degree cam rotation for full-scale movement of the tracing element. Although graphic lines are scribed onto the cam surface to facilitate cutting the cam to the desired shape, these coordinates are curvilinear. It is more difficult to lay out the cam design for cutting with such coordinates than it is to program a device that uses rectilinear coordinates, such as a belt programmer.

Belt Programmers Figure 3.4u illustrates an early belt-type profile programmer with pneumatic output. This specific unit was housed in a 6 in. by 6 in. recorder case. The time profile program was stored on a laminated, endless-belt plastic master. It combines an analog set-point program with up to 25 synchronizes digital tracks for operation of logic circuits, auxiliary equipment, solenoid valves, lights, etc. There is no limit to the slope the programmer can follow—even slopes of 90 degrees can be accommodated. Since the master program can be quickly changed, these programmers were often used where the program does require periodic change and where accurate reproduction of the program is essential, as in textile dyeing processes. The complete program is stored on the master, thus eliminating the need for having an operator make various program settings for each

© 2006 by Béla Lipták

change and therefore eliminating the chance for human error in setting the program. These programmers are accurate to within 1/4% of full scale, which makes them applicable when accuracy is one of the critical requirements of the operation. The endless belt master can be made up by plotting the desired analog program on the rectilinear chart and cutting the top portion away with scissors. The second layer serves as a backing and is also used to program the synchronized digital tracks. At any point of the program where a switch action is desired, a hole can be punched in with a conductor’s punch. The back of the analog program has a pressuresensitive adhesive that joins the two sections. A splice finishes the makeup of the master. In operation, a motor drives the master program. A cablemounted tracer nozzle senses the step on the analog program profile. The backpressure of the nozzle actuates a servo which, through the cable drive, keeps the tracer following the profile. Operating from the same servo drive is an accurate forcebalance-type motion detector. Sensing the back side of the digital master are a series of vertically aligned nozzles. Normally, their backpressure is high, since the master baffles the nozzles. However, if a punched hole presents itself, the backpressure of that particular nozzle drops to zero, actuating the connected pressure switch. Line Follower Programmers Electric line and edge follower programmers will perform with less than ±1/4% error. In the electrostatic line follower design, Figure 3.4v, the desired program curve is etched into a chart with a conductive surface, dividing it into two electrically isolated surfaces. These surfaces are energized by oppositely phased AC voltages, which establish a gradient across the gap. A noncontacting probe is used to sense the electrostatic fields developed by the surfaces. It energizes a

3.4 Relays for Computing and Programmers

Program line

505

Program chart E2

E1 Chart drive motor

Probe

E1 E3

115 VAC 60 Hz

Servo motor

Output pot

Servo amplifier

Output

E2 Chart-energizing transformer

FIG. 3.4v Electrostatic line follower programmer.

Adjustable Ramp-and-Hold Programmers For such batch processes in which the controlled variable must rise at a controlled rate, then hold at some preset value and, possibly, fall at a controlled rate, programmers such as that in Figure 3.4w are often preferable to cam types. This is particularly the case if the program must be changed periodically. These too are usually packaged as large-case circular chart recorders. In this type of programmer the set-point index is driven by a constant-speed motor. The rate of rise is set by adjustment of an interrupter timer, which makes contact for a set percentage of the basic timer cycle time. The movement of the index is therefore actually in steps, but the steps are so small that the operation is, for all practical purposes, continuous. The set-point rises until it coincides with the hold point index, at which point the hold timer is energized while the interrupter timer is deenergized. Controlled cooling rate requires driving the set-point index in reverse.

© 2006 by Béla Lipták

Hold period timer

Rate-of-rise control

Hold temperature index

Control index

Hold point Temperature

servo amplifier, which keeps the probe at zero potential as it tracks the line. Attached to the servo drive is the wiper of a potentiometer with its output proportional to line position. The photoelectric line follower type functions to keep the line centered between two slightly overlapping pickup heads. The detector must be manually set over the line at startup, and slope rate is limited by the speed of the follower mechanism. The photoelectric edge programmer is a common variation of the electrostatic line programmer. This type of programmer has a higher slope rate limit than does the line programmer. The edge detection system is basically a photocell detector attached to the tracing element. Line and edge programmers include digital control tracks as common additional features.

Hold time

Adjustable rate of rise Time

Rate of cool

FIG. 3.4w Adjustable ramp-and-hold programmer.

This type of programmer can come complete with a controller and a direct sensing element.

Bibliography ARC Report, “Batch Process Automation Strategies,” ARC Advisory Group, October 1999.

506

Transmitters and Local Controllers

Buckley, P. S., “Designing Long-Line Pneumatic Control Systems,” Instrumentation Technology, April 1969. Dyer, S. A., Wiley Survey of Instrumentation and Measurement, New York: Wiley, 2001. Eckman, D. P., Automatic Process Control, New York: John Wiley & Sons, 1958. Farmer, E., “Pneumatics in a Digital World,” Instruments and Control Systems, March 1979. Gassett, L. D., “Pneumatic or Electronic?” Chemical Engineering, June 2, 1969. Johnson, C. D., Process Control Instrumentation Technology, Prentice Hall, 7th ed., 2002.

© 2006 by Béla Lipták

Leonessa, A., et al., Nonlinear Switching Control Design, Heidelberg: Springer-Verlag, August 2000. Luyben, W. L., et al., Plantwide Process Control, New York: McGraw-Hill, 1998. Mamzic, C. L., “Pneumatic Controls Interface with Computers,” Instruments and Control Systems, October 1975. Nachtigal, C.N., Instrumentation and Control, New York: Wiley, 1990. Smith, C. A., and Corripio, A. B., Principles and Practice of Automatic Process Control, New York: John Wiley & Sons, 1985. “Timing and Programming Equipment,” Measurements and Control, September 1993.