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Many PID loops control a mechanical device (for example, a valve). Mechanical maintenance can be a major cost and wear leads to control degradation in the form of either stiction or backlash in the mechanical response to an input signal. The rate of mechanical wear is mainly a function of how often a device is activated to make a change.
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 e(t) = r(t) − y(t) is the tracking error, a PID controller has the general form
(or with any other fixed real number > 1 in place of 2). Intuitively: an element z is "small" and "close to 0" iff its valuation ν(z) is large. The function |x-y|, supplemented by |0|=0, is the restriction of an absolute value defined on the field of fractions of the discrete valuation ring.
A Piping and Instrumentation Diagram (P&ID or PID) is a detailed diagram in the process industry which shows process equipment together with the instrumentation and control devices. It is also called as mechanical flow diagram (MFD).
Physical Interface Device, a class of a USB device; PID controller (proportional-integral-derivative controller), a control concept used in automation; Piping and instrumentation diagram (P&ID), a diagram in the process industry which shows the piping of the process flow etc. Principal ideal domain, an algebraic structure
In the context of PID controller, the setpoint represents the reference or goal for the controlled process variable. It serves as the benchmark against which the actual process variable (PV) is continuously compared.
Principal ideal domains are mathematical objects that behave like the integers, with respect to divisibility: any element of a PID has a unique factorization into prime elements (so an analogue of the fundamental theorem of arithmetic holds); any two elements of a PID have a greatest common divisor (although it may not be possible to find it ...
A photoionization detector or PID is a type of gas detector. Typical photoionization detectors measure volatile organic compounds and other gases in concentrations from sub parts per billion to 10 000 parts per million (ppm). The photoionization detector is an efficient and inexpensive detector for many gas and vapor analytes.