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  2. Proportional–integral–derivative controller - Wikipedia

    en.wikipedia.org/wiki/Proportional–integral...

    PID controllers often provide acceptable control using default tunings, but performance can generally be improved by careful tuning, and performance may be unacceptable with poor tuning. Usually, initial designs need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired.

  3. Principal ideal domain - Wikipedia

    en.wikipedia.org/wiki/Principal_ideal_domain

    The key result is the structure theorem: If R is a principal ideal domain, and M is a finitely generated R-module, then is a direct sum of cyclic modules, i.e., modules with one generator. The cyclic modules are isomorphic to R / x R {\displaystyle R/xR} for some x ∈ R {\displaystyle x\in R} [ 4 ] (notice that x {\displaystyle x} may be equal ...

  4. Ziegler–Nichols method - Wikipedia

    en.wikipedia.org/wiki/Ziegler–Nichols_method

    The Ziegler–Nichols tuning (represented by the 'Classic PID' equations in the table above) creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications. This tuning rule is meant to give PID loops best disturbance rejection. [2]

  5. OBD-II PIDs - Wikipedia

    en.wikipedia.org/wiki/OBD-II_PIDs

    OBD-II PIDs (On-board diagnostics Parameter IDs) are codes used to request data from a vehicle, used as a diagnostic tool.. SAE standard J1979 defines many OBD-II PIDs. All on-road vehicles and trucks sold in North America are required to support a subset of these codes, primarily for state mandated emissions inspections.

  6. Piping and instrumentation diagram - Wikipedia

    en.wikipedia.org/wiki/Piping_and_instrumentation...

    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).

  7. Principal ideal - Wikipedia

    en.wikipedia.org/wiki/Principal_ideal

    Any Euclidean domain is a PID; the algorithm used to calculate greatest common divisors may be used to find a generator of any ideal. More generally, any two principal ideals in a commutative ring have a greatest common divisor in the sense of ideal multiplication.

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  9. Structure theorem for finitely generated modules over a ...

    en.wikipedia.org/wiki/Structure_theorem_for...

    In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules over a principal ideal domain (PID) can be uniquely decomposed in much the same way that integers have a prime factorization.