58-739: (Redirected from P-I ) [REDACTED] Look up PI in Wiktionary, the free dictionary. PI may refer to: Arts and media [ edit ] Politically Incorrect (blog) , a German political blog Seattle Post-Intelligencer or P-I, a newspaper in the United States Primitive Instinct , an English rock band formed in 1987 P.I. (TV series) , 2017 Singaporean TV series Businesses and organizations [ edit ] Political parties [ edit ] Partido Independiente or Independent Party,
116-428: A robotic arm that can be moved and positioned by a control loop. An electric motor may lift or lower the arm, depending on forward or reverse power applied, but power cannot be a simple function of position because of the inertial mass of the arm, forces due to gravity, external forces on the arm such as a load to lift or work to be done on an external object. By measuring the position (PV), and subtracting it from
174-401: A correction based on proportional , integral , and derivative terms. The controller attempts to minimize the error over time by adjustment of a control variable u ( t ) {\displaystyle u(t)} , such as the opening of a control valve , to a new value determined by a weighted sum of the control terms. In this model: Tuning – The balance of these effects
232-474: A formal control law for what we now call PID or three-term control was first developed using theoretical analysis, by Russian American engineer Nicolas Minorsky . Minorsky was researching and designing automatic ship steering for the US Navy and based his analysis on observations of a helmsman . He noted the helmsman steered the ship based not only on the current course error but also on past error, as well as
290-800: A particular project Other uses [ edit ] Pass interference , a foul in American and Canadian gridiron football People's Initiative , one of the modes in which the constitution of the Philippines could be amended Philippine Islands ( P. I. ), the commonly used name of the Philippines during the US colonial period Pirot , a city located in south-eastern Serbia (license plate code PI) Political incorrectness or politically incorrect, commonly abbreviated to PI or PIC Pro forma invoice, in business Private investigator (P.I.),
348-407: A pendulum that measured the fore and aft pitch of the torpedo was combined with depth measurement to become the pendulum-and-hydrostat control . Pressure control provided only a proportional control that, if the control gain was too high, would become unstable and go into overshoot with considerable instability of depth-holding. The pendulum added what is now known as derivative control, which damped
406-513: A person who can be hired to undertake investigations Profitability index , the ratio of payoff to investment of a proposed project Personal injury See also [ edit ] [REDACTED] Search for "PI" or "P-I" on Misplaced Pages. Pi (disambiguation) P1 (disambiguation) PL (disambiguation) All pages with titles containing P-I All pages with titles beginning with PI All pages with titles containing PI Topics referred to by
464-602: A political party in Uruguay Partido Intransigente or Intransigent Party, an Argentine political party Partit per la Independència , a political party in Catalonia (Spain) of the 1990s Other businesses and organizations [ edit ] Perimeter Institute for Theoretical Physics , a research centre in Ontario, Canada Privacy International , a UK-based charity that supports
522-402: A process. This was invented by Christiaan Huygens in the 17th century to regulate the gap between millstones in windmills depending on the speed of rotation, and thereby compensate for the variable speed of grain feed. With the invention of the low-pressure stationary steam engine there was a need for automatic speed control, and James Watt 's self-designed " conical pendulum " governor,
580-401: A pure D controller cannot bring the system to its setpoint), but rather the rate of change of error, trying to bring this rate to zero. It aims at flattening the error trajectory into a horizontal line, damping the force applied, and so reduces overshoot (error on the other side because of too great applied force). In the interest of achieving a controlled arrival at the desired position (SP) in
638-442: A set of revolving steel balls attached to a vertical spindle by link arms, came to be an industry standard. This was based on the millstone-gap control concept. Rotating-governor speed control, however, was still variable under conditions of varying load, where the shortcoming of what is now known as proportional control alone was evident. The error between the desired speed and the actual speed would increase with increasing load. In
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#1732772336483696-437: A smaller force if the error is low on the upside. That's where the integral and derivative terms play their part. An integral term increases action in relation not only to the error but also the time for which it has persisted. So, if the applied force is not enough to bring the error to zero, this force will be increased as time passes. A pure "I" controller could bring the error to zero, but it would be both weakly reacting at
754-450: A timely and accurate way, the controlled system needs to be critically damped . A well-tuned position control system will also apply the necessary currents to the controlled motor so that the arm pushes and pulls as necessary to resist external forces trying to move it away from the required position. The setpoint itself may be generated by an external system, such as a PLC or other computer system, so that it continuously varies depending on
812-893: A valve for cooling water, where the fail-safe mode, in the case of signal loss, would be 100% opening of the valve; therefore 0% controller output needs to cause 100% valve opening. The overall control function u ( t ) = K p e ( t ) + K i ∫ 0 t e ( τ ) d τ + K d d e ( t ) d t , {\displaystyle u(t)=K_{\text{p}}e(t)+K_{\text{i}}\int _{0}^{t}e(\tau )\,\mathrm {d} \tau +K_{\text{d}}{\frac {\mathrm {d} e(t)}{\mathrm {d} t}},} where K p {\displaystyle K_{\text{p}}} , K i {\displaystyle K_{\text{i}}} , and K d {\displaystyle K_{\text{d}}} , all non-negative, denote
870-414: A wide-band pneumatic controller by combining the nozzle and flapper high-gain pneumatic amplifier, which had been invented in 1914, with negative feedback from the controller output. This dramatically increased the linear range of operation of the nozzle and flapper amplifier, and integral control could also be added by the use of a precision bleed valve and a bellows generating the integral term. The result
928-407: Is achieved by loop tuning to produce the optimal control function. The tuning constants are shown below as "K" and must be derived for each control application, as they depend on the response characteristics of the physical system, external to the controller. These are dependent on the behavior of the measuring sensor, the final control element (such as a control valve), any control signal delays, and
986-455: Is achieved by setting the unused parameters to zero and is called a PI, PD, P, or I controller in the absence of the other control actions. PI controllers are fairly common in applications where derivative action would be sensitive to measurement noise, but the integral term is often needed for the system to reach its target value. The use of the PID algorithm does not guarantee optimal control of
1044-489: Is because the "error" term is not the deviation from the setpoint (actual-desired) but is in fact the correction needed (desired-actual). The system is called reverse acting if it is necessary to apply negative corrective action. For instance, if the valve in the flow loop was 100–0% valve opening for 0–100% control output – meaning that the controller action has to be reversed. Some process control schemes and final control elements require this reverse action. An example would be
1102-536: Is different from Wikidata All article disambiguation pages All disambiguation pages PI">PI The requested page title contains unsupported characters : ">". Return to Main Page . PI controller A proportional–integral–derivative controller ( PID controller or three-term controller ) is a feedback -based control loop mechanism commonly used to manage machines and processes that require continuous control and automatic adjustment. It
1160-414: Is the complex frequency. The proportional term produces an output value that is proportional to the current error value. The proportional response can be adjusted by multiplying the error by a constant K p , called the proportional gain constant. The proportional term is given by A high proportional gain results in a large change in the output for a given change in the error. If the proportional gain
1218-421: Is too high, the system can become unstable (see the section on loop tuning ). In contrast, a small gain results in a small output response to a large input error, and a less responsive or less sensitive controller. If the proportional gain is too low, the control action may be too small when responding to system disturbances. Tuning theory and industrial practice indicate that the proportional term should contribute
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#17327723364831276-521: Is typically used in industrial control systems and various other applications where constant control through modulation is necessary without human intervention. The PID controller automatically compares the desired target value ( setpoint or SP) with the actual value of the system ( process variable or PV). The difference between these two values is called the error value , denoted as e ( t ) {\displaystyle e(t)} . It then applies corrective actions automatically to bring
1334-466: The 19th century, the theoretical basis for the operation of governors was first described by James Clerk Maxwell in 1868 in his now-famous paper On Governors . He explored the mathematical basis for control stability, and progressed a good way towards a solution, but made an appeal for mathematicians to examine the problem. The problem was examined further in 1874 by Edward Routh , Charles Sturm , and in 1895, Adolf Hurwitz , all of whom contributed to
1392-420: The PID controller is the ability to use the three control terms of proportional, integral and derivative influence on the controller output to apply accurate and optimal control. The block diagram on the right shows the principles of how these terms are generated and applied. It shows a PID controller, which continuously calculates an error value e ( t ) {\displaystyle e(t)} as
1450-603: The PV to the same value as the SP using three methods: The proportional ( P ) component responds to the current error value by producing an output that is directly proportional to the magnitude of the error. This provides immediate correction based on how far the system is from the desired setpoint. The integral ( I ) component, in turn, considers the cumulative sum of past errors to address any residual steady-state errors that persist over time, eliminating lingering discrepancies. Lastly,
1508-466: The PV. Variables that affect the process other than the MV are known as disturbances. Generally, controllers are used to reject disturbances and to implement setpoint changes. A change in load on the arm constitutes a disturbance to the robot arm control process. In theory, a controller can be used to control any process that has a measurable output (PV), a known ideal value for that output (SP), and an input to
1566-425: The advantage of this being that T i {\displaystyle T_{\text{i}}} and T d {\displaystyle T_{\text{d}}} have some understandable physical meaning, as they represent an integration time and a derivative time respectively. K p T d {\displaystyle K_{\text{p}}T_{\text{d}}} is the time constant with which
1624-424: The bulk of the output change. The steady-state error is the difference between the desired final output and the actual one. Because a non-zero error is required to drive it, a proportional controller generally operates with a steady-state error. Steady-state error (SSE) is proportional to the process gain and inversely proportional to proportional gain. SSE may be mitigated by adding a compensating bias term to
1682-574: The coefficients for the proportional, integral, and derivative terms respectively (sometimes denoted P , I , and D ). In the standard form of the equation (see later in article), K i {\displaystyle K_{\text{i}}} and K d {\displaystyle K_{\text{d}}} are respectively replaced by K p / T i {\displaystyle K_{\text{p}}/T_{\text{i}}} and K p T d {\displaystyle K_{\text{p}}T_{\text{d}}} ;
1740-409: The controller will attempt to approach the set point. K p / T i {\displaystyle K_{\text{p}}/T_{\text{i}}} determines how long the controller will tolerate the output being consistently above or below the set point. Although a PID controller has three control terms, some applications need only one or two terms to provide appropriate control. This
1798-411: The current rate of change; this was then given a mathematical treatment by Minorsky. His goal was stability, not general control, which simplified the problem significantly. While proportional control provided stability against small disturbances, it was insufficient for dealing with a steady disturbance, notably a stiff gale (due to steady-state error ), which required adding the integral term. Finally,
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1856-479: The derivative ( D ) component predicts future error by assessing the rate of change of the error, which helps to mitigate overshoot and enhance system stability, particularly when the system undergoes rapid changes. The PID controller reduces the likelihood of human error and improves automation . A common example is a vehicle’s cruise control system . When a vehicle encounters a hill, its speed may decrease due to constant engine power. The PID controller adjusts
1914-510: The derivative term was added to improve stability and control. Trials were carried out on the USS New Mexico , with the controllers controlling the angular velocity (not the angle) of the rudder. PI control yielded sustained yaw (angular error) of ±2°. Adding the D element yielded a yaw error of ±1/6°, better than most helmsmen could achieve. The Navy ultimately did not adopt the system due to resistance by personnel. Similar work
1972-437: The desired position, the output would oscillate around the setpoint in either a constant, growing, or decaying sinusoid . If the amplitude of the oscillations increases with time, the system is unstable. If it decreases, the system is stable. If the oscillations remain at a constant magnitude, the system is marginally stable . A derivative term does not consider the magnitude of the error (meaning it cannot bring it to zero:
2030-569: The development of flowers in the ABC model of flower development Phosphatidylinositol , a class of lipids Ponderal index , a measure of leanness of a person (similar to body mass index) Propidium iodide , a chemical used as a DNA stain Primary immunodeficiency Protease inhibitor (pharmacology) , class of drugs used to treat or prevent infection by viruses, including HIV and Hepatitis C Protease inhibitor (biology) , molecules that inhibit
2088-405: The difference between a desired setpoint SP = r ( t ) {\displaystyle {\text{SP}}=r(t)} and a measured process variable PV = y ( t ) {\displaystyle {\text{PV}}=y(t)} : e ( t ) = r ( t ) − y ( t ) {\displaystyle e(t)=r(t)-y(t)} , and applies
2146-669: The engine's power output to restore the vehicle to its desired speed, doing so efficiently with minimal delay and overshoot. The theoretical foundation of PID controllers dates back to the early 1920s with the development of automatic steering systems for ships. This concept was later adopted for automatic process control in manufacturing, first appearing in pneumatic actuators and evolving into electronic controllers. PID controllers are widely used in numerous applications requiring accurate, stable, and optimized automatic control , such as temperature regulation , motor speed control, and industrial process management. The distinguishing feature of
2204-484: The establishment of control stability criteria. In subsequent applications, speed governors were further refined, notably by American scientist Willard Gibbs , who in 1872 theoretically analyzed Watt's conical pendulum governor. About this time, the invention of the Whitehead torpedo posed a control problem that required accurate control of the running depth. Use of a depth pressure sensor alone proved inadequate, and
2262-473: The function of proteases Pulsatility index , a ratio of blood flow rates Computing [ edit ] Persistent identifier , a long-lasting reference to a digital object Processing Instruction , an SGML and XML node type Programmed instruction , a technology invented to improve teaching Provider-independent address space , a type of internet (IP) address Other uses in science and technology [ edit ] Isoelectric point (pI),
2320-478: The head positioning of a disk drive , the power conditioning of a power supply , or even the movement-detection circuit of a modern seismometer . Discrete electronic analog controllers have been largely replaced by digital controllers using microcontrollers or FPGAs to implement PID algorithms. However, discrete analog PID controllers are still used in niche applications requiring high-bandwidth and low-noise performance, such as laser-diode controllers. Consider
2378-516: The industry standard for many decades until the advent of discrete electronic controllers and distributed control systems (DCSs). With these controllers, a pneumatic industry signaling standard of 3–15 psi (0.2–1.0 bar) was established, which had an elevated zero to ensure devices were working within their linear characteristic and represented the control range of 0-100%. In the 1950s, when high gain electronic amplifiers became cheap and reliable, electronic PID controllers became popular, and
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2436-418: The integral gain ( K i ) and added to the controller output. The integral term is given by The integral term accelerates the movement of the process towards setpoint and eliminates the residual steady-state error that occurs with a pure proportional controller. However, since the integral term responds to accumulated errors from the past, it can cause the present value to overshoot the setpoint value (see
2494-472: The manipulated variable (MV). The proportional, integral, and derivative terms are summed to calculate the output of the PID controller. Defining u ( t ) {\displaystyle u(t)} as the controller output, the final form of the PID algorithm is where Equivalently, the transfer function in the Laplace domain of the PID controller is where s {\displaystyle s}
2552-415: The oscillations by detecting the torpedo dive/climb angle and thereby the rate-of-change of depth. This development (named by Whitehead as "The Secret" to give no clue to its action) was around 1868. Another early example of a PID-type controller was developed by Elmer Sperry in 1911 for ship steering, though his work was intuitive rather than mathematically-based. It was not until 1922, however, that
2610-433: The pH at which a particular molecule or surface carries no net electrical charge. Power integrity , in digital electronics PI controller , a concept in automation and control engineering Plasticity index , a measure of the plasticity of a soil Polyimide , a polymer of imide monomers Preußische Instruktionen , a cataloging system for libraries Principal investigator , the lead scientist or engineer for
2668-591: The pneumatic standard was emulated by 10-50 mA and 4–20 mA current loop signals (the latter became the industry standard). Pneumatic field actuators are still widely used because of the advantages of pneumatic energy for control valves in process plant environments. Most modern PID controls in industry are implemented as computer software in DCSs, programmable logic controllers (PLCs), or discrete compact controllers . Electronic analog PID control loops were often found within more complex electronic systems, for example,
2726-399: The process (MV) that will affect the relevant PV. Controllers are used in industry to regulate temperature , pressure , force , feed rate , flow rate , chemical composition (component concentrations ), weight , position , speed , and practically every other variable for which a measurement exists. The PID control scheme is named after its three correcting terms, whose sum constitutes
2784-457: The process itself. Approximate values of constants can usually be initially entered knowing the type of application, but they are normally refined, or tuned, by introducing a setpoint change and observing the system response. Control action – The mathematical model and practical loop above both use a direct control action for all the terms, which means an increasing positive error results in an increasing positive control output correction. This
2842-415: The right to privacy across the world Defunct Piedmont Airlines (1948–89) (IATA airline code PI) Philadelphia International , record label founded in 1971 Science and technology [ edit ] Biology and medicine [ edit ] Parental investment , in evolutionary biology Paternity Index , a value used to calculate probability of paternity Pistillata , a gene that influences
2900-494: The same term [REDACTED] This disambiguation page lists articles associated with the title PI . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=PI&oldid=1183912239 " Category : Disambiguation pages Hidden categories: Articles containing Spanish-language text Articles containing German-language text Short description
2958-417: The setpoint (SP), the error (e) is found, and from it the controller calculates how much electric current to supply to the motor (MV). The obvious method is proportional control: the motor current is set in proportion to the existing error. However, this method fails if, for instance, the arm has to lift different weights: a greater weight needs a greater force applied for the same error on the down side, but
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#17327723364833016-404: The setpoint AND output or corrected dynamically by adding an integral term. The contribution from the integral term is proportional to both the magnitude of the error and the duration of the error. The integral in a PID controller is the sum of the instantaneous error over time and gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by
3074-437: The start (because the action would be small at the beginning, depending on time to become significant) and more aggressive at the end (the action increases as long as the error is positive, even if the error is near zero). Applying too much integral when the error is small and decreasing will lead to overshoot. After overshooting, if the controller were to apply a large correction in the opposite direction and repeatedly overshoot
3132-427: The system overshoots a setpoint, and the degree of any system oscillation . But the PID controller is broadly applicable since it relies only on the response of the measured process variable, not on knowledge or a model of the underlying process. Continuous control, before PID controllers were fully understood and implemented, has one of its origins in the centrifugal governor , which uses rotating weights to control
3190-414: The system or its control stability ( see § Limitations , below ). Situations may occur where there are excessive delays: the measurement of the process value is delayed, or the control action does not apply quickly enough. In these cases lead–lag compensation is required to be effective. The response of the controller can be described in terms of its responsiveness to an error, the degree to which
3248-400: The work that the robotic arm is expected to do. A well-tuned PID control system will enable the arm to meet these changing requirements to the best of its capabilities. If a controller starts from a stable state with zero error (PV = SP), then further changes by the controller will be in response to changes in other measured or unmeasured inputs to the process that affect the process, and hence
3306-489: Was carried out and published by several others in the 1930s. The wide use of feedback controllers did not become feasible until the development of wideband high-gain amplifiers to use the concept of negative feedback . This had been developed in telephone engineering electronics by Harold Black in the late 1920s, but not published until 1934. Independently, Clesson E Mason of the Foxboro Company in 1930 invented
3364-670: Was the "Stabilog" controller which gave both proportional and integral functions using feedback bellows. The integral term was called Reset . Later the derivative term was added by a further bellows and adjustable orifice. From about 1932 onwards, the use of wideband pneumatic controllers increased rapidly in a variety of control applications. Air pressure was used for generating the controller output, and also for powering process modulating devices such as diaphragm-operated control valves. They were simple low maintenance devices that operated well in harsh industrial environments and did not present explosion risks in hazardous locations . They were
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