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# Glossary (PID and Fuzzy Logic Toolkit)

LabVIEW 2012 PID and Fuzzy Logic Toolkit Help

Edition Date: June 2012

Part Number: 370401J-01

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LabVIEW Glossary

## A

algorithm A prescribed set of well-defined rules or processes for the solution of a problem in a finite number of steps.
antecedent The IF portion of a rule in a fuzzy system.
antecedent connective An operator that specifies how to calculate the truth value of an aggregated rule antecedent.
anti-reset windup A method that prevents the integral term of the PID algorithm from moving too far beyond saturation when an error persists.
autotuning Automatically testing a process under control to determine the controller gains that will provide the best controller performance.
Autotuning Wizard An automated graphical user interface provided in the PID Autotuning VI. The Autotuning Wizard gathers some information about the desired control from the user and then steps through the PID autotuning process.

## B

bias The offset added to a controller output (manipulate variable).
Boolean set theory Traditional set theory based on strict membership or non-membership of elements to a set. Examples are TRUE or FALSE, ON or OFF, 1 or 0, and so on.
bumpless transfer A process in which the next output always increments from the current output, regardless of the current controller output value; therefore, transfer from automatic to manual control is always bumpless.

## C

cascade control Control in which the output of one controller is the setpoint for another controller.
Center of Area (CoA) Method of defuzzification in which the crisp output is determined by the geometrical center of area of the composite output membership functions within the range of the output linguistic variable. Also known as Center of Gravity (CoG).
Center of Maximum (CoM) Method of defuzzification in which the crisp output is determined by a weighted average of the typical values of each output membership function. This method is equivalent to the Center of Area method using singleton sets.
Center of Sums (CoS) Method of defuzzification in which the crisp output is determined by a weighted average of the center of area of each output membership function.
closed loop A signal path which includes a forward path, a feedback path, and a summing point and which forms a closed circuit. Also called a feedback loop.
consequent The THEN portion of a rule in a fuzzy system.
controller Hardware and/or software used to maintain parameters of a physical process at desired values.
controller output See manipulated variable.
crisp value A finite single value such as a measured physical quantity, for example, x = 5.3 m.
cycle time The time between samples in a discrete digital control system.

## D

damping The progressive reduction or suppression of oscillation in a device or system.
deadtime (Td) The interval of time, expressed in minutes, between initiation of an input change or stimulus and the start of the resulting observable response.
defuzzification The process of converting the degrees of membership of output linguistic variables within their linguistic terms into crisp numerical values.
degree of membership A value that represents the degree of partial membership of a linguistic variable within a linguistic term. This value can range from 0 to 1.
degree of support A weighting value, ranging from 0 to 1, that is applied to each rule in the rule base of a fuzzy controller. This weighting value represents the relative significance of each rule and allows for fine-tuning of the rule base.
derivative (control) action Control response to the time rate of change of a variable. Also called rate action.
derivative kick A sudden change in PID controller output resulting from derivative action applied to the error signal after a change in setpoint value. Derivative kick is normally avoided in PID control by applying derivative action only to the process variable and not to the error signal.
deviation Any departure from a desired value or expected value or pattern.
downstream loop In a cascade, the controller whose setpoint is provided by another controller.

## E

EGU Engineering units. Also abbreviated EU.
expert A human operator of a system or process that has acquired knowledge related to controlling the process through experience.

## F

FC Flow controller.
feedback control Control in which a measured variable is compared to its desired value to produce an actuating error signal that is acted upon in such a way as to reduce the magnitude of the error.
feedback loop See closed loop.
fuzzification The process of associating crisp input values with the linguistic terms of corresponding input linguistic variables..
fuzzy controller A controller that uses defined rules to control a fuzzy system based on the current values of input linguistic variables.
fuzzy logic An extension of traditional Boolean set theory that allows for partial membership in a set.
fuzzy system A system of input and output variables associated using fuzzy logic.

## G

gain For a linear system or element, the ratio of the magnitude, or amplitude, of a steady-state sinusoidal output relative to the causal input; the length of a phasor from the origin to a point of the transfer locus in a complex plane. Also called the magnitude ratio.
gain scheduling The process of applying different controller gains for different regions of operation of a controller. Gain scheduling is most often used in controlling nonlinear physical processes.

## I

implication method A mathematical method for scaling the membership functions of an output linguistic variable based on the rule weight before performing defuzzification.
integral (control) action Control action in which the output is proportional to the time integral of the input. That is, the rate of change of output is proportional to the input.
ISA Instrument Society of America. The organization that sets standards for process control instrumentation in the United States.

## K

Kc Controller gain.

## L

lag A lowpass filter or integrating response with respect to time.
linearity factor A value ranging from 0 to 1, used to specify the linearity of a calculation. A value of 1 indicates a linear operation. A value of 1 indicates a squared nonlinear operation.
linguistic term A word or set of words that represents categories for the values of a linguistic variable. A linguistic term is defined quantitatively by the corresponding membership function.
linguistic variable A word or set of words that represents an input variable or output variable of a fuzzy system.
load disturbance The ability of a controller to compensate for changes in physical parameters of a controlled process while the setpoint value remains constant.
loop cycle time Time interval between calls to a control algorithm.

## M

magnitude ratio See gain.
manipulated variable A quantity or condition that is varied as a function of the actuating error signal so as to change the value of the directly controlled variable. Also called controller output.
Mean of Maximum (MoM) Method of defuzzification in which the crisp output is determined by selecting a value corresponding to the maximum degree of membership of the composite output membership function. If there are multiple maximums, the mean of the corresponding values is selected.
membership function A numerical function that quantitatively defines the degrees of membership of a linguistic variable within a linguistic term.
modified Center of Area (mCoA) Method of defuzzification in which the crisp output is determined by the geometrical center of area of the composite output membership functions. Unlike the Center of Area method, this method allows the crisp output to realize the full range of the output variable.

## N

noise In process instrumentation, an unwanted component of a signal or variable. Noise may be expressed in units of the output or in percent of output span.

## O

output limiting Preventing a controller output (manipulated variable) from traveling beyond a desired maximum range.
overshoot The maximum excursion beyond the final steady-state value of output as the result of an input change. Also called transient overshoot.

## P

P Proportional.
P controller A controller which produces proportional control action only; that is, a controller that has only a simple gain response.
partial membership In fuzzy logic, a condition in which the value of a member partially fulfills the requirements of the membership function of a set.
PC Pressure controller.
PD Proportional, derivative.
PD controller A controller that produces proportional plus derivative (rate) control action.
PI Proportional, integral.
PI controller A controller that produces proportional plus integral (reset) control action.
PID Proportional, integral, derivative.
PID control A common control strategy in which a process variable is measured and compared to a desired set point to determine an error signal. A proportional gain (P) is applied to the error signal, an integral gain (I) is applied to the integral of the error signal, and a derivative gain (D) is applied to the derivative of the error signal. The controller output is a linear combination of the three resulting values.
PID controller A controller that produces proportional plus integral (reset) plus derivative (rate) control action.
process gain (K) For a linear process, the ratio of the magnitudes of the measured process response to that of the manipulated variable.
process variable (PV) The measured variable (such as pressure or temperature) in a process to be controlled.
proportional action Control response in which the output is proportional to the input.
proportional band (PB) The change in input required to produce a full range change in output due to proportional control action. PB = 100 /Kc.

## Q

quarter-decay ratio A response in which the amplitude of each oscillation is one-quarter that of the previous oscillation.

## R

ramp The total (transient plus steady-state) time response resulting from a sudden increase in the rate of change from zero to some finite value of the input stimulus. Also called ramp response.
rate action Control response to the time rate of change of a variable. Also called derivative control action.
reset rate Of proportional plus integral or proportional plus integral plus derivative control action devices: for a step input, the ratio of the initial rate of change of output due to integral control action to the change in steady-state output due to proportional control action.

Of integral control action devices: for a step input, the ratio of the initial rate of change of output to the input change. Also called integral action rate.
rule A linguistic representation of the relationships between input and output linguistic variables based on their linguistic terms.
rule base The set of rules for a fuzzy system.

## S

selector control The use of multiple controllers and/or multiple process variables in which the connections may change dynamically depending on process conditions.
setpoint (SP) An input variable which sets the desired value of the controlled process variable.
singleton A normalized membership function with an infinitely small width. A singleton is used to model a crisp value with a fuzzy set.
SP See setpoint.
span The algebraic difference between the upper and lower range values.
stochastic uncertainty The degree of uncertainty of the occurrence of a given future nondeterministic event.

## T

time constant (T) In process instrumentation, the value T (in minutes) in an exponential response term, A exp (–t/T), or in one of the transform factors, such as 1 + sT.
transient overshoot See overshoot.
trapezoidal integration A numerical of integration in which the current value and the previous value are used to calculate the addition of the current value to the integral value.

## W

windup area The time during which the controller output is saturated at the maximum or minimum value. The integral action of a simple PID controller continues to increase (wind up) while the controller is in the windup area.