That is, if R is a PID, and a and b are elements of R, and d is a greatest common divisor of a and b,

This is often accomplished using a PID controller system.

Of those who have an asymptomatic infection that is not detected by their doctor, approximately half will develop pelvic inflammatory disease ( PID ), a generic term for infection of the uterus, fallopian tubes, and / or ovaries.

A common closed-loop controller architecture is the PID controller.

The PID controller is probably the most-used feedback control design.

If u ( t ) is the control signal sent to the system, y ( t ) is the measured output and r ( t ) is the desired output, and tracking error, a PID controller has the general form

It should be noted that for practical PID controllers a pure differentiator is neither physically realisable or desirable due to amplification of noise and resonant modes in the system.

An arbitrary PID has much the same " structural properties " of a Euclidean domain ( or, indeed, even of the ring of integers ), but knowing an explicit algorithm for Euclidean division, and thus also for greatest common divisor computation, gives a concreteness which is useful for algorithmic applications.

So, given an integral domain R, it is often very useful to know that R has a Euclidean function: in particular, this implies that R is a PID.

However, if there is no " obvious " Euclidean function, then determining whether R is a PID is generally a much easier problem than determining whether it is a Euclidean domain.

In a ring all of whose ideals are principal ( a principal ideal domain or PID ), this ideal will be identical with the set of multiples of some ring element d ; then this d is a greatest common divisor of a and b. But the ideal ( a, b ) can be useful even when there is no greatest common divisor of a and b. ( Indeed, Ernst Kummer used this ideal as a replacement for a gcd in his treatment of Fermat's Last Theorem, although he envisioned it as the set of multiples of some hypothetical, or ideal, ring element d, whence the ring-theoretic term.

Pelvic inflammatory disease ( or disorder ) ( PID ) is a term for inflammation of the uterus, fallopian tubes, and / or ovaries as it progresses to scar formation with adhesions to nearby tissues and organs.

PID is a vague term and can refer to viral, fungal, parasitic, though most often bacterial infections.

In the United States, more than 750, 000 women are affected by PID each year, and the rate is highest with teenagers and first time mothers.

C. trachomatis is estimated to be the cause in about 60 % of cases of salpingitis, which may lead to PID.

* Getting regular gynecological ( pelvic ) exams with STI testing to screen for symptomless PID.

* Dalkon Shield — withdrawn from the market in 1975 for PID risk

PLCs may include logic for single-variable feedback analog control loop, a " proportional, integral, derivative " or " PID controller ".

A PID loop could be used to control the temperature of a manufacturing process, for example.

The converse does not hold since for any field K, K is a UFD but is not a PID ( to prove this look at the ideal generated by It is not the whole ring since it contains no polynomials of degree 0, but it cannot be generated by any one single element ).

In some situations this may be desirable, for example if the parent creates another child process it ensures that it will not be allocated the same PID.

By tuning the three parameters in the PID controller algorithm, the controller can provide control action designed for specific process requirements.

Note that the use of the PID algorithm for control does not guarantee optimal control of the system or system stability.

* Proven Methods and Best Practices for PID Control

By this time a procedure for determining whether the ring of all algebraic integers of a given quadratic field is a PID was well known to the quadratic form theorists.

Especially, Gauss had looked at the case of imaginary quadratic fields: he found exactly nine values of < math > D < 0 </ math > for which the ring of integers is a PID and conjectured that there are no further values.

But a local domain is a Dedekind ring iff it is a PID iff it is a discrete valuation ring ( DVR ), so the same local characterization cannot hold for PIDs: rather, one may say that the concept of a Dedekind ring is the globalization of that of a DVR.

Thus these are precisely the class of domains for which Frac ( R )/ Prin ( R ) forms a group, the ideal class group Cl ( R ) of R. This group is trivial if and only if R is a PID, so can be viewed as quantifying the obstruction to a general Dedekind domain being a PID.

In view of the well known and exceedingly useful structure theorem for finitely generated modules over a principal ideal domain ( PID ), it is natural to ask for a corresponding theory for finitely generated modules over a Dedekind domain.

The PID controller calculation ( algorithm ) involves three separate constant parameters, and is accordingly sometimes called three-term control: the proportional, the integral and derivative values, denoted P, I, and D. Heuristically, these values can be interpreted in terms of time: P depends on the present error, I on the accumulation of past errors, and D is a prediction of future errors, based on current rate of change.

To include the output filter, a PID controller is used, sometimes with additional integrating terms.

In computing, the process identifier ( normally referred to as the process ID or just PID ) is a number used by most operating system kernels, — such as that of UNIX, Mac OS X or Microsoft Windows — to temporarily uniquely identify a process.

On control systems like the tuning of the temperature of a furnace, or perhaps the motion-control of a heavy item like a gun or camera on a moving vehicle, the derivative action of a well-tuned PID controller can allow it to reach and maintain a setpoint better than most skilled human operators could.

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Since this is a cluster filesystem, that PID might refer to a process on any of the nodes which have the filesystem mounted.

Some fieldbus devices now support control schemes such as PID control on the device side instead of forcing the controller to do the processing.

launchd also has replaced init as PID 1 on Mac OS X and as a result it is responsible for starting the system at boot time.

A person moving on the other side of the glass would not be " seen " by the PID.

This can be mapped to command a specific duty cycle on the valve, or can use a PID based closed-loop control algorithm.

A PID controller calculates an " error " value as the difference between a measured process variable and a desired setpoint.

* Integral windup, an error condition that occurs in a PID controller