... control1.1
To be precise, this form of on/off control is known as differential gap because there are two setpoints with a gap in between. While on/off control is possible with a single setpoint (FCE on when below setpoint and off when above), it is usually not practical due to the frequent cycling of the final control element. 
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... value1.2
In electronics, the unit of decibels is commonly used to express gains. Thankfully, the world of process control was spared the introduction of decibels as a unit of measurement for controller gain. The last thing we need is a third way to express the degree of proportional action in a controller! 
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... burden1.3
One could argue that the presence of loads actually justifies a control system, for if there were no loads, there would be nothing to compensate for, and therefore no need for an automatic control system at all! In the total absence of loads, a manually-set final control element would be enough to hold most process variables at setpoint. 
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...integral1.4
An older term for this mode of control is floating, which I happen to think is particularly descriptive. With a “floating” controller, the final control element continually “floats” to whatever value it must in order to completely eliminate offset. 
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... speed1.5
At least the old-fashioned mechanical odometers would. Modern cars use a pulse detector on the driveshaft which cannot tell the difference between forward and reverse, and therefore their odometers always increment. Shades of the movie Ferris Bueller's Day Off. 
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... this1.6
The equation for a proportional + integral controller is often written without the bias term ($b$), because the presence of integral action makes it unnecessary. In fact, if we let the integral term completely replace the bias term, we may consider the integral term to be a self-resetting bias. This, in fact, is the meaning of the word “reset” in the context of PID controller action: the “reset” term of the controller acts to eliminate offset by continuously adjusting (resetting) the bias as necessary. 
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... product1.7
Since integration is fundamentally a process of multiplication followed by addition, the units of measurement are always the product (multiplication) of the function's variables. In the case of reset (integral) control, we are multiplying controller error (the difference between PV and SP, usually expressed in percent) by time (usually expressed in minutes or seconds). Therefore the result will be an “error-time” product. In order for an integral controller to self-recover following windup, the error must switch signs and the error-time product accumulate to a sufficient value to cancel out the error-time product accumulated during the windup period. 
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... wind-up1.8
An example of such an application is where the output of a loop controller may be “de-selected” or otherwise “over-ridden” by some other control function. This sort of control strategy is often used in energy-conserving controls, where multiple controllers monitoring different process variables selectively command a single FCE. 
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... setpoint1.9
It should not be assumed that such spikes are always undesirable. In processes characterized by long lag times, such a response may be quite helpful in overcoming that lag for the purpose of rapidly achieving new setpoint values. Slave (secondary) controllers in cascaded systems – where the controller receives its setpoint signal from the output of another (primary, or master) controller – may similarly benefit from derivative action calculated on error instead of just PV. As usual, the specific needs of the application dictate the ideal controller configuration. 
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... “spike1.10
This is the meaning of the vertical-pointing arrowheads shown on the trend graph: momentary saturation of the output all the way up to 100%. 
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... value1.11
This is a good example of how integral controller action represents the history of the PV $-$ SP error. The continued offset of integral action from its starting point “remembers” the area accumulated under the rectangular “step” between PV and SP. This offset will go away only if a negative error appears having the same percent-minute product (area) as the positive error step. 
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... “spikes1.12
This is the meaning of the vertical-pointing arrowheads shown on the trend graph: momentary saturation of the output all the way up to 100% (or down to 0%). 
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... function1.13
In this example, I have omitted the constant of integration ($C$) to keep things simple. The actual integral is as such: $\int \sin x \> dx = - \cos x + C = \sin (x - 90^o) + C$. This constant value is essential to explaining why the integral response does not immediately “step” like the derivative response does at the beginning of the PV sine wavelet. 
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... D)1.14
An example of a case where it is better for gain ($K_p$) to influence all three control modes is when a technician re-ranges a transmitter to have a larger or smaller span than before, and must re-tune the controller to maintain the same loop gain as before. If the controller's PID equation takes the parallel form, the technician must adjust the P, I, and D tuning parameters proportionately. If the controller's PID equation uses $K_p$ as a factor in all three modes, the technician need only adjust $K_p$ to re-stabilize the loop. 
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... action1.15
This becomes especially apparent when using derivative action with low values of $\tau_i$ (aggressive integral action). The error-multiplying term ${\tau_d \over \tau_i} + 1$ may become quite large if $\tau_i$ is small, even with modest $\tau_d$ values. 
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... collapse1.16
Being a motion-balance mechanism, these bellows must act as spring elements in order to produce consistent pressure/motion behavior. Some pneumatic controllers employ coil springs inside the brass bellows assembly to provide the necessary “stiffness” and repeatability. 
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... mechanism1.17
Practical integral action also requires the elimination of the bias spring and adjustment, which formerly provided a constant downward force on the left-hand side of the beam to give the output signal the positive offset necessary to avoid saturation at 0 PSI. Not only is a bias adjustment completely unnecessary with the addition of integral action, but it would actually cause problems by making the integral action “think” an error existed between PV and SP when there was none. 
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... rate1.18
These restrictor valves are designed to encourage laminar air flow, making the relationship between volumetric flow rate and differential pressure drop linear rather than quadratic as it is for large control valves. Thus, a doubling of pressure drop across the restrictor valve results in a doubling of flow rate into (or out of) the reset bellows, and a consequent doubling of integration rate. This is precisely what we desire and expect from a controller with integral action. 
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... illustration1.19
In case you are wondering, this controller happens to be reverse-acting instead of direct. This is of no consequence to the feature of external reset. 
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... reliability1.20
The reason for this is the low component count compared to a comparable digital control circuit. For any given technology, a simpler device will tend to be more reliable than a complex device if only due to there being fewer components to fail. This also suggests a third advantage of analog controllers over digital controllers, and that is the possibility of easily designing and constructing your own for some custom application such as a hobby project. A digital controller is not outside the reach of a serious hobbyist to design and build, but it is definitely more challenging due to the requirement of programming expertise in addition to electronic hardware expertise. 
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... academic1.21
It is noteworthy that analog control systems are completely immune from “cyber-attacks” (malicious attempts to foil the integrity of a control system by remote access), due to the simple fact that their algorithms are fixed by physical laws and properties of electronic components rather than by code which may be edited. This new threat constitutes an inherent weakness of digital technology, and has spurred some thinkers in the field to reconsider analog controls for the most critical applications. 
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... enough1.22
The real problem with digital controller speed is that the time delay between successive “scans” translates into dead time for the control loop. Dead time is the single greatest impediment to feedback control. 
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...inverting1.23
This circuit configuration is called “inverting” because the mathematical sign of the output is always opposite that of the input. This sign inversion is not an intentional circuit feature, but rather a consequence of the input signal facing the opamp's inverting input. Non-inverting multiplier circuits also exist, but are more complicated when built to achieve multiplication factors less than one. 
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... swap1.24
This inversion of function caused by the swapping of input and feedback components in an operational amplifier circuit points to a fundamental principle of negative feedback networks: namely, that placing a mathematical element within the feedback loop causes the amplifier to exhibit the inverse of that element's intrinsic function. This is why voltage dividers placed within the feedback loop cause an opamp to have a multiplicative gain (division $\rightarrow$ multiplication). A circuit element exhibiting a logarithmic response, when placed within a negative feedback loop, will cause the amplifier to exhibit an exponential response (logarithm $\rightarrow$ exponent). Here, an element having a time-differentiating response, when placed inside the feedback loop, causes the amplifier to time-integrate (differentiation $\rightarrow$ integration). Since the opamp's output voltage must assume any value possible to maintain (nearly) zero differential voltage at the input terminals, placing a mathematical function in the feedback loop forces the output to assume the inverse of that function in order to “cancel out” its effects and achieve balance at the input terminals. 
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... second1.25
If this is not apparent, imagine a scenario where the +1.7 volt input existed for precisely one second's worth of time. However much the output voltage ramps in that amount of time must therefore be its rate of change in volts per second (assuming a linear ramp). Since we know the area accumulated under a constant value of 1.7 (high) over a time of 1 second (wide) must be 1.7 volt-seconds, and $\tau_i$ is equal to 3.807 seconds, the integrator circuit's output voltage must ramp 0.447 volts during that interval of time. If the input voltage is positive and we know this is an inverting opamp circuit, the direction of the output voltage's ramping must be negative, thus a ramping rate of $-$0.447 volts per second. 
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... Output1.26
The two input terminals shown, Input$_{(+)}$ and Input$_{(-)}$ are used as PV and SP signal inputs, the correlation of each depending on whether one desires direct or reverse controller action. 
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... capacitors1.27
This particular design has integral and derivative time value limits of 10 seconds, maximum. These relatively “quick” tuning values are the result of having to use non-polarized capacitors in the integrator and differentiator stages. The practical limits of cost and size restrict the maximum value of on-board capacitance to around 10 $\mu$F each. 
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... equation1.28
An interesting example of engineering tradition is found in electronic PID controller designs. While it is not too terribly difficult to build an analog electronic controller implementing either the parallel or ideal PID equation (just a few more parts are needed), it is quite challenging to do the same in a pneumatic mechanism. When analog electronic controllers were first introduced to industry, they were often destined to replace old pneumatic controllers. In order to ease the transition from pneumatic to electronic control, manufacturers built their new electronic controllers to behave exactly the same as the old pneumatic controllers they would be replacing. The same legacy followed the advent of digital electronic controllers: many digital controllers were programmed to behave in the same manner as the old pneumatic controllers, for the sake of operational familiarity, not because it was easier to design a digital controller that way. 
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... system1.29
Although the SPEC 200 system – like most analog electronic control systems – is considered “mature” (Foxboro officially declared the SPEC 200 and SPEC 200 Micro systems as such in March 2007), working installations may still be found at the time of this writing (2010). A report published by the Electric Power Research Institute (see References at the end of this chapter) in 2001 documents a SPEC 200 analog control system installed in a nuclear power plant in the United States as recently as 1992, and another as recently as 2001 in a Korean nuclear power plant. 
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...nest1.30
Foxboro provided the option of a self-contained, panel-mounted SPEC 200 controller unit with all electronics contained in a single module, but the split architecture of the display/nest areas was preferred for large installations where many dozens of loops (especially cascade, feedforward, ratio, and other multi-component control strategies) would be serviced by the same system. 
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... legend1.31
I once encountered an engineer who joked that the number “200” in “SPEC 200” represented the number of years the system was designed to continuously operate. At another facility, I encountered instrument technicians who were a bit afraid of a SPEC 200 system running a section of their plant: the system had never suffered a failure of any kind since it was installed decades ago, and as a result no one in the shop had any experience troubleshooting it. As it turns out, the entire facility was eventually shut down and sold, with the SPEC 200 nest running faithfully until the day its power was turned off! The functioning SPEC 200 controllers shown in the photograph were in continuous use at British Columbia Institute of Technology at the time of the photograph, taken in December of 2014. 
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... preferred1.32
Thanks to the explosion of network growth accompanying personal computers in the workplace, Ethernet is ubiquitous. The relatively high speed and low cost of Ethernet communications equipment makes it an attractive network standard over which a great many high-level industrial protocols communicate. 
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... mediocre1.33
An aspect common to many PLC implementations of PID control is the use of the “parallel” PID algorithm instead of the superior “ISA” or “non-interacting” algorithm. The choice of algorithm may have a profound effect on tuning, and on tuning procedures, especially when tuning parameters must be re-adjusted to accommodate changes in transmitter range. 
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... era1.34
Modern DDC systems of the type used for building automation (heating, cooling, security, etc.) almost always consist of networked control nodes, each node tasked with monitoring and control of a limited area. The same may be said for modern PLC technology, which not only exhibits advanced networking capability (fieldbus I/O networks, Ethernet, Modbus, wireless communications), but is often also capable of redundancy in both processing and I/O. As technology becomes more sophisticated, the distinction between a DDC (or a networked PLC system) and a DCS becomes more ambiguous. 
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... self-checks1.35
An example of such a self-check is scheduled switching of the networks: if the system has been operating on network cable “A” for the past four hours, it might switch to cable “B” for the next four hours, then back again after another four hours to continually ensure both cables are functioning properly. 
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... system1.36
To be fair, the Yokogawa Electric Corporation of Japan introduced their CENTUM distributed control system the same year as Honeywell. Unfortunately, while I have personal experience maintaining and using the Honeywell TDC2000 system, I have zero personal experience with the Yokogawa CENTUM system, and neither have I been able to obtain technical documentation for the original incarnation of this DCS (Yokogawa's latest DCS offering goes by the same name). Consequently, I can do little in this chapter but mention its existence, despite the fact that it deserves just as much recognition as the Honeywell TDC2000 system. 
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... crude1.37
Just to give some perspective, the original TDC2000 system used whole-board processors rather than microprocessor chips, and magnetic core memory rather than static or dynamic RAM circuits! Communication between controller nodes and operator stations occurred over thick coaxial cables, implementing master/slave arbitration with a separate device (a “Hiway Traffic Director” or HTD) coordinating all communications between nodes. Like Bob Metcalfe's original version of Ethernet, these coaxial cables were terminated at their end-points by termination resistors, with coaxial “tee” connectors providing branch points for multiple nodes to connect along the network. 
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... DCS1.38
I know of a major industrial manufacturing facility (which shall remain nameless) where a PLC vendor promised the same technical capability as a full DCS at approximately one-tenth the installed cost. Several years and several tens of thousands of man-hours later, the sad realization was this “bargain” did not live up to its promise, and the decision was made to remove the PLCs and go with a complete DCS from another manufacturer. Caveat emptor! 
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... system1.39
Although it is customary for the host system to be configured as the Link Active Scheduler (LAS) device to schedule and coordinate all fieldbus device communications, this is not absolutely necessary. Any suitable field instrument may also serve as the LAS, which means a host system is not even necessary except to provide DC power to the instruments, and serve as a point of interface for human operators, engineers, and technicians. 
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... options1.40
With the PID function block programmed in the flow transmitter, there will be twice as many scheduled communication events per macrocycle than if the function block is programmed into the valve positioner. This is evident by the number of signal lines connecting circled block(s) to circled block(s) in the above illustration. 
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... may1.41
The only reason I say “may” instead of “will” is because some modern digital controllers are designed to automatically switch to manual-mode operation in the event of a sensor or transmitter signal loss. Any controller not “smart” enough to shed its operating mode to manual in the event of PV signal loss will react dramatically when that PV signal dies, and this is not a good thing for an operating loop! 
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... level1.42
I once had the misfortune of working on an analog PID controller for a chlorine-based wastewater disinfection system that lacked output tracking. The chlorine sensor on this system would occasionally fail due to sample system plugging by algae in the wastewater. When this happened, the PV signal would fail low (indicating abnormally low levels of chlorine gas dissolved in the wastewater) even though the actual dissolved chlorine gas concentration was adequate. The controller, thinking the PV was well below SP, would ramp the chlorine gas control valve further and further open over time, as integral action attempted to reduce the error between PV and SP. The error never went away, of course, because the chlorine sensor was plugged with algae and simply could not detect the actual chlorine gas concentration in the wastewater. By the time I arrived to address the “low chlorine” alarm, the controller output was already wound up to 100%. After cleaning the sensor, and seeing the PV value jump up to some outrageously high level, the controller would take a long time to “wind down” its output because its integral action was very slow. I could not use manual mode to “unwind” the output signal, because this controller lacked the feature of output tracking. My “work-around” solution to this problem was to re-tune the integral term of the controller to some really fast time constant, watch the output “wind down” in fast-motion until it reached a reasonable value, then adjust the integral time constant back to its previous value for continued automatic operation. 
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... processes1.43
Boiler steam drum water level control, for example, is a process where the setpoint really should be left at a 50% value at all times, even if there maybe legitimate reasons for occasionally switching the controller into manual mode. 
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... loop1.44
It is very important to note that soft alarms are not a replacement for hard alarms. There is much wisdom in maintaining both hard and soft alarms for a process, so there will be redundant, non-interactive levels of alarming. Hard and soft alarms should complement each other in any critical process. 
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... mode1.45
Some PID controllers limit manual-mode output values as well, so be sure to check the manufacturer's documentation for output limiting on your particular PID controller! 
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... listing1.46
I have used a typesetting convention to help make my pseudocode easier for human beings to read: all formal commands appear in bold-faced blue type, while all comments appear in italicized red type. All other text appears as normal-faced black type. One should remember that the computer running any program cares not for how the text is typeset: all it cares is that the commands are properly used (i.e. no “grammatical” or “syntactical” errors). 
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... changes1.47
It should be noted that this is precisely what happens when you change the gain in a pneumatic or an analog electronic controller, since all analog PID controllers implement the “position” equation. Although the choice between “position” and “velocity” algorithms in a digital controller is arbitrary, it is much easier to build an analog mechanism or circuit implementing the position algorithm than it is to build an analog “velocity” controller. 
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... variable1.48
We call this an adaptive gain control system. 
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... controller1.49
Many instrument manufacturers sell simple, single-loop controllers for reasonable prices, comparable to the price of a college textbook. You need to get one that accepts 1-5 VDC input signals and generates 4-20 mA output signals, and has a “manual” mode of operation in addition to automatic – these features are very important! Avoid controllers that can only accept thermocouple inputs, and/or only have time-proportioning (PWM) outputs. 
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