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PID

A proportional–integral–derivative (PID) controller is a that computes an value as the between a prescribed setpoint and a measured , then applies a corrective output to minimize this using proportional, , and terms. The proportional term provides an output proportional to the current , the term accounts for accumulated past errors to eliminate steady-state offsets, and the term predicts future errors by considering the rate of change, enabling responsive control in dynamic systems. Originating from early mechanical governors like James Watt's 1788 device for proportional speed control, PID principles evolved into explicit three-term formulations by the 1920s, notably with Nicolas Minorsky's 1922 application to ship steering gear, marking the first documented use of and actions alongside . Commercial pneumatic PID controllers emerged in the 1930s and 1940s, with tuning methods like Ziegler-Nichols formalized in 1942 to optimize performance across diverse processes. Today, PID controllers dominate industrial automation, regulating variables such as in furnaces, in pipelines, rates in chemical plants, and speed in motors, owing to their robustness, simplicity, and adaptability via parameter tuning despite challenges in achieving optimal gains for nonlinear or unstable systems.

Control Systems and Engineering

Proportional-integral-derivative controller

The proportional-integral-derivative (PID) controller is a feedback mechanism in control engineering that regulates dynamic systems by minimizing the error between a desired setpoint and measured process variable. It computes a control signal as a linear combination of the current error (proportional term), accumulated past errors (integral term), and rate of error change (derivative term), enabling precise adjustment of actuators like valves or motors. First analyzed theoretically by Nicolas Minorsky in 1922 for automatic ship steering, where he modeled helmsman behavior to stabilize vessels against disturbances, the PID approach addressed directional stability in nonlinear hydrodynamic systems. By the mid-20th century, pneumatic and electronic PID implementations had proliferated in industrial processes, supplanting manual control for applications requiring steady-state accuracy and transient response, with Ziegler and Nichols formalizing tuning rules in 1942 to standardize deployment. The mathematical formulation of a continuous-time PID controller is u(t) = K_p e(t) + K_i \int_0^t e(\tau) \, d\tau + K_d \frac{de(t)}{dt}, where e(t) = r(t) - y(t) is the (setpoint r(t) minus output y(t)), and K_p, K_i, K_d are tunable gains. The proportional K_p e(t) yields immediate corrective action scaled to error magnitude, reducing response time but risking if used alone; the K_i \int e(\tau) \, d\tau sums errors over time to drive steady-state to zero, countering persistent disturbances like load changes; the K_d \frac{de(t)}{dt} anticipates error trends by rapid variations, improving at the cost of sensitivity. In discrete implementations for systems, such as microcontrollers, the approximates as a and as a difference, with anti-windup mechanisms clamping accumulation during to prevent excessive buildup. Tuning PID gains empirically remains central to achieving stability and performance, with the Ziegler-Nichols method inducing sustained oscillations via proportional-only control to measure ultimate K_u and P_u, then setting K_p = 0.6 K_u, K_i = 2 K_p / P_u, K_d = K_p P_u / 8 for a quarter-amplitude decay response. This oscillation-based , derived from pneumatic controller tests, prioritizes speed over minimal overshoot, often yielding quarter-wave but risking in processes with long dead times or nonlinearity; modern alternatives include relay auto- or optimization via genetic algorithms for model-based refinement. Pros include conceptual simplicity and robustness to unmodeled dynamics in linear systems, while cons encompass trial-and-error dependency and potential for aggressive inducing wear or oscillations in stiff processes. PID controllers underpin diverse applications, from household thermostats maintaining via proportional integrated over deviations, to industrial motor speed compensating torque disturbances, and for tracking. In electric vehicles, they regulate by adjusting inverter currents for demands, with gains tuned to handle battery state-of-charge variations and nonlinear motor dynamics, as in brushless drives achieving sub-1% speed error under load. Fractional-order variants, extending to non-integer derivatives, enhance performance in EVs by better approximating viscoelastic behaviors in tire-road interactions as of 2025 implementations. Despite ubiquity, PID limitations include proportional-derivative induced overshoot amplifying setpoint transients, integral windup inflating control effort during saturation (e.g., valve closure limits), and inadequacy for highly nonlinear or time-varying systems where fixed gains fail causal prediction, necessitating gain scheduling or model predictive overrides. In saturated actuators, unchecked integration delays recovery, exacerbating instability; for nonlinearities like dead zones or friction, pure PID yields suboptimal tracking, prompting hybrid cascades. Recent advancements integrate adaptive mechanisms, such as (e.g., DDPG algorithms tuning gains online for hydraulic servos with 20-30% reduced ) or neural networks self-adjusting parameters from performance data, addressing windup via predictive clipping and enabling deployment in uncertain environments like autonomous drones post-2020./09:Proportional-Integral-Derivative(PID)_Control/9.06:_PID_Downsides_and_Solutions)

Medicine

Pelvic inflammatory disease

(PID) is an ascending polymicrobial of the upper genital tract, encompassing the , fallopian tubes, ovaries, and adjacent structures, typically originating from pathogens in the or . While and remain primary sexually transmitted causes, comprising up to 85% of cases alongside bacterial vaginosis-associated organisms, PID increasingly involves anaerobes such as species and other non-sexually transmitted factors like vaginal , insertion, or postpartum . Cultures from laparoscopic specimens indicate polymicrobial etiology in 30-40% of cases, underscoring that untreated lower tract s facilitate pathogen ascension, often without overt . Common symptoms include acute lower abdominal pain, cervical motion tenderness on bimanual exam, fever exceeding 38.3°C, and mucopurulent vaginal discharge, though up to 50% of cases may be subclinical, delaying detection and exacerbating tubal damage. Diagnosis relies on CDC minimal criteria—lower abdominal or pelvic pain plus adnexal or uterine tenderness—warranting empiric treatment to avert complications, as laparoscopy (gold standard) is rarely feasible. However, these criteria exhibit low specificity (e.g., 65-90% false positives in some cohorts), fostering overdiagnosis and unnecessary antibiotic exposure, while underdiagnosis risks silent progression; cohort studies highlight the trade-off, with empirical therapy justified by high complication rates in untreated cases despite diagnostic ambiguities. Treatment follows 2021 CDC guidelines emphasizing broad-spectrum coverage for , , and anaerobes: outpatient regimens include 500 mg intramuscularly once plus 100 mg orally twice daily for 14 days, with or without 500 mg orally twice daily for enhanced anaerobic efficacy. Severe cases (e.g., , high fever, tubo-ovarian ) require inpatient intravenous 1 g daily plus 100 mg every 12 hours, with added; clinical improvement is expected within 72 hours, prompting reassessment or switch to oral therapy. Intrauterine devices need not be removed routinely unless response fails within 48-72 hours. Resolution occurs in 80-90% with prompt antibiotics, though rising N. gonorrhoeae resistance to cephalosporins (e.g., MIC creep reported in 2023 surveillance) threatens efficacy, necessitating surveillance and potential regimen updates. Long-term complications arise from tubal scarring and adhesions: approximately 10-15% of women experience after a single episode, escalating to 20-25% after two and over 50% after three, per historical cohort data. risk increases 6-10-fold due to distal tubal occlusion, while chronic affects 15-20% of cases, often persisting despite resolution. These outcomes causally link to delayed and recurrent episodes, driven by persistent lower tract colonization rather than isolated events. Behavioral risk factors predominate, with women reporting four or more lifetime sexual partners facing over threefold higher hospitalization risk for PID via elevated exposure. Multiple or new partners, unprotected intercourse, and douching facilitate ascension, independent of systemic barriers; prevention hinges on routine STI screening (e.g., annual /gonorrhea tests for sexually active women under 25), consistent barrier contraception, and partner tracing, reducing incidence by limiting introduction. Empirical models confirm as the proximal driver in dynamics, contrasting narratives emphasizing over personal .

Primary immunodeficiency

Primary immunodeficiencies (PIDs), also termed inborn errors of immunity, comprise a heterogeneous group of over 485 genetically determined disorders that impair the development or function of components, resulting in heightened susceptibility to infections, , , and inflammatory conditions. These defects arise from monogenic disrupting innate or adaptive immunity, with classifications organized by the affected immunological pathway, such as combined immunodeficiencies (e.g., or SCID, involving T- and B-cell defects), predominantly antibody deficiencies (e.g., agammaglobulinemia), phagocytic disorders, and complement deficiencies, as delineated in the International Union of Immunological Societies (IUIS) 2022 update. Unlike secondary immunodeficiencies caused by extrinsic factors like or , PIDs stem from heritable or genetic alterations, underscoring a causal primacy of molecular defects over environmental influences in disease manifestation. Epidemiological data indicate an overall incidence of PIDs around 1 in 10,000 live births for severe forms, with estimates reaching 50.5 cases per 100,000 , though underdiagnosis affects 70-90% globally due to subtle presentations in milder . Clinical onset often manifests in infancy or early childhood with recurrent sinopulmonary bacterial infections, opportunistic pathogens (e.g., in T-cell defects), , and chronic , attributable mechanistically to deficient production, impaired T-cell mediated , or phagocytic dysfunction rather than nonspecific hygiene factors. , first described by Ogden in 1952, exemplifies a B-cell intrinsic defect due to BTK gene mutations, leading to absent mature B cells and profound . Diagnosis hinges on clinical suspicion prompted by family history, persistent infections despite treatment, and laboratory confirmation via quantitative immunoglobulins, lymphocyte subset analysis by (e.g., absent + B cells in agammaglobulinemia or low + T cells in SCID), and next-generation sequencing panels targeting PID-associated genes, which have expanded diagnostic yield since the . Differentiation from secondary causes requires excluding reversible factors like protein through longitudinal testing and genetic verification, as transient of infancy may mimic but resolves spontaneously. Management strategies are etiology-specific: immunoglobulin replacement therapy (IVIG or SCIG) for deficiencies reduces infection frequency by 50-70% in controlled studies by replenishing opsonizing antibodies and neutralizing pathogens. For severe forms like SCID, (HSCT) offers curative potential, with 5-year survival rates exceeding 87% when performed early, particularly post-newborn screening implementation since the 2010s, though outcomes decline with delayed diagnosis or mismatched donors due to graft failure or . advances, such as Strimvelis (autologous + cells transduced with ADA ) approved by the in 2016 for ADA-SCID, achieve immune reconstitution in eligible patients lacking suitable HSCT donors, with sustained engraftment observed in treated cohorts. Live-attenuated vaccines are contraindicated in uncorrected severe PIDs to avert disseminated , reflecting empirical risks over hypothetical benefits from exposure theories like the , which fail to account for monogenic causality.

Computing and Information Technology

Process identifier

A process identifier (PID) is a unique numerical value assigned by the kernel of an operating system to each executing process, enabling identification, resource allocation, and management in multitasking environments. In POSIX-compliant systems such as Unix-like operating systems including Linux, the PID is typically a positive integer starting from 1, with PID 1 reserved for the initial process (init or its modern replacement like systemd), which adopts orphaned child processes. New PIDs are allocated sequentially during process creation via the fork() system call, establishing a parent-child hierarchy tracked through the parent PID (PPID). PIDs facilitate core operating system functions like scheduling, signal delivery, and , preventing resource conflicts in concurrent execution. Users interact with PIDs through utilities such as for listing active processes with details like PID, PPID, and resource usage; (e.g., kill -9 <PID>) to terminate processes by sending signals like SIGKILL; and for real-time monitoring of PID-associated metrics including CPU and memory consumption. In , the /proc/<PID> filesystem provides runtime introspection, exposing process-specific data such as command lines, open files, and status without requiring privileged access for basic queries. The concept originated in early Unix development at Bell Laboratories in the 1970s, where the process with PID 1 was defined to bootstrap user-space services and manage terminals via shells. Over time, implementations evolved for scalability; for instance, 2.6.24 introduced PID namespaces in 2008, allowing isolated PID spaces within containers (e.g., ), where processes perceive a private numbering starting from 1, enhancing and by limiting visibility across namespaces. Traditionally limited to 1–32767 on 16-bit systems and early 32-bit kernels to fit data structures, modern kernels extend the range via /proc/sys/kernel/pid_max, defaulting to 32768 but configurable up to 4194304 on 64-bit systems to accommodate high-process workloads. Despite these advances, PIDs exhibit limitations including potential exhaustion under extreme loads, where the may delay new forks until reuse occurs, or fail allocations if the fills. Reuse of recently freed PIDs introduces conditions, where a new inherits a terminated one's PID, risking erroneous signals or errors; Linux mitigates immediate reuse via allocation delays but cannot eliminate races entirely, prompting recommendations for pidfd (file descriptor-based handles) in newer . Security concerns arise from such races, enabling attacks like PID squatting for denial-of-service or if tools assume PID uniqueness without verification. In contrast, Windows employs a similar numeric ID but integrates it with handles and, in advanced scenarios like kernel-mode , GUIDs for persistent identification across sessions, diverging from Unix's purely integer-based model.

Organizations and Government

Public Improvement District

A Public Improvement District (PID) constitutes a defined geographic area within a municipality or county, established under Chapter 372 of the Texas Local Government Code to finance and maintain targeted public improvements through voluntary petitions from property owners and subsequent assessments on benefiting properties. These assessments, apportioned according to the specific benefits received—such as enhanced landscaping, street lighting, signage, fountains, roads, or utilities—secure bonds for upfront project costs rather than relying on ad valorem taxes or general municipal funds. This structure ensures fiscal accountability by linking repayments directly to value-adding enhancements, avoiding dilution across non-benefiting taxpayers. PIDs gained prominence in following legislative authorization in the late and early , with the inaugural public bond issuance occurring in 1992 to address demands in expanding suburbs without straining city budgets. By supplementing core services in commercial corridors, they have facilitated developments in areas like and suburbs, where property owners collaborate on enhancements beyond standard provisions. As of the early , PIDs have supported billions in local , contributing to projects that align costs with direct economic returns from improved amenities. Empirical outcomes demonstrate PIDs' role in spurring property value appreciation—often 10-20% in enhanced districts—through market-responsive investments that avoid broad tax hikes, yielding multipliers in local economic activity via development incentives. Default risks remain low due to lien-backed security and benefit-based levies, though post-2008 market downturns exposed vulnerabilities to over-assessment disputes and regressive burdens on individual owners when values decline. Proponents, including fiscal conservatives, highlight this as evidence of efficient, localized financing that prioritizes causal links between expenditures and gains, contrasting with critiques from equity-focused perspectives that emphasize disproportionate impacts on lower-income property holders despite data showing net positive ROI from stabilized districts. Distinct from Municipal Utility Districts (MUDs), which impose property taxes for like and as political subdivisions, PIDs operate under municipal oversight with assessments for broader, non-utility enhancements and require initial owner consent via , rendering obligations binding thereafter. In contrast to Districts (PUDs), which target utility provisioning including electricity and through similar but narrower assessments, PIDs emphasize public realm improvements like parks and streetscapes, fostering opt-in partnerships that align private interests with communal benefits. Emerging trends in the 2020s include applications for resilient amid Texas's transitions, though primary usage persists in conventional funding.

Other Uses

Photoionization detector

A photoionization detector (PID) is a gas chromatography (GC) detector that identifies and quantifies volatile organic compounds (VOCs) by exposing sample molecules to high-energy ultraviolet (UV) photons from a vacuum UV lamp, ionizing those with ionization potentials below the lamp's photon energy, and measuring the resulting ion current between electrodes. Common lamps emit at 10.6 eV using argon or variants like krypton-doped for 10.0 eV or 11.7 eV, enabling selectivity for aromatics, olefins, and other unsaturated hydrocarbons while ignoring permanent gases such as methane (ionization potential 12.6 eV), nitrogen, oxygen, and carbon dioxide. This selectivity arises because only ionizable molecules contribute to the current, with response factors varying significantly—benzene yields a high signal due to its 9.24 eV potential, whereas aliphatics show lower sensitivity. Introduced commercially in 1973 for handheld VOC leak detection, PIDs gained traction in the 1970s as GC alternatives to flame ionization detectors (FIDs), avoiding the need for hydrogen fuel and flame maintenance while providing comparable sensitivity for targeted compounds. Detection limits reach parts per billion (ppb) levels, such as below 40 picograms for benzene under EPA protocols, with linear dynamic ranges spanning 10^5 to 10^7, from sub-ppm to thousands of ppm depending on the compound and instrument. Unlike FIDs, which respond broadly to carbon-hydrogen bonds via combustion, PIDs are non-destructive, preserving the sample for further analysis, and offer dopant-specific tuning for enhanced selectivity. PIDs find primary applications in of VOCs in ambient air and , industrial settings like facilities for solvent and fuel vapor detection, and forensics such as identifying accelerants in residues via aromatic signatures. Their portability supports perimeter and occupational exposure assessments, with empirical data showing effective VOC aggregation in complex matrices without interference from non-ionizable species. Limitations include UV lamp degradation from prolonged exposure, requiring periodic replacement and cleaning to maintain photon output; signal quenching by water vapor or high humidity, where molecules absorb UV without ionizing, reducing sensitivity by up to 50% at relative humidities above 80%; and oxygen's role in low-oxygen environments exacerbating quenching or baseline drift. PIDs exhibit lower universality than mass spectrometry for structural identification and quantification across all hydrocarbons, demanding compound-specific calibrations due to variable response factors, and show empirically inferior sensitivity for saturated aliphatics compared to FIDs or MS in broad-spectrum analyses. Post-2010 advancements in miniaturization, including microfabricated ionization chambers under 1 μL volume, have integrated PIDs into portable GC systems for field use, reducing size and response times while preserving ppb detection.