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A proportional–integral–derivative controller (PID controller) is a control loop feedback mechanism (controller) commonly used in industrial control systems. A PID controller continuously calculates an ''error value'' as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error over time by adjustment of a ''control variable'', such as the position of a control valve, a damper, or the power supplied to a heating element, to a new value determined by a weighted sum: : where , , and , all non-negative, denote the coefficients for the proportional, integral, and derivative terms, respectively (sometimes denoted ''P,'' ''I,'' and ''D''). In this model, * ''P'' accounts for present values of the error (e.g. if the error is large and positive, the control variable will be large and negative), * ''I'' accounts for past values of the error (e.g. if the output is not sufficient to reduce the size of the error, the control variable will accumulate over time, causing the controller to apply a stronger action), and * ''D'' accounts for possible future values of the error, based on its current rate of change. As a PID controller relies only on the measured process variable, not on knowledge of the underlying process, it is broadly applicable.〔 By tuning the three parameters of the model, a PID controller can deal with specific process requirements. The response of the controller can be described in terms of its responsiveness to an error, the degree to which the system overshoots a setpoint, and the degree of any system oscillation. The use of the PID algorithm does not guarantee optimal control of the system or even its stability. Some applications may require using only one or two terms to provide the appropriate system control. This is achieved by setting the other parameters to zero. A PID controller will be called a PI, PD, P or I controller in the absence of the respective control actions. PI controllers are fairly common, since derivative action is sensitive to measurement noise, whereas the absence of an integral term may prevent the system from reaching its target value. For discrete time systems, the term PSD, for proportional-summation-difference, is often used.〔(Veselý, V., Rosinová, D.: Robust PSD Controller Design, Editors: Fikar, M., Kvasnica, M., In Proceedings of the 18th International Conference on Process Control, Tatranská Lomnica, Slovakia, 565–570, 2011 )〕 ==History and applications== PID controllers date to 1890s governor design. PID controllers were subsequently developed in automatic ship steering. One of the earliest examples of a PID-type controller was developed by Elmer Sperry in 1911,〔(【引用サイトリンク】title=A Brief Building Automation History )〕 while the first published theoretical analysis of a PID controller was by Russian American engineer Nicolas Minorsky, . Minorsky was designing automatic steering systems for the US Navy, and based his analysis on observations of a helmsman, noting the helmsman controlled the ship based not only on the current error, but also on past error as well as the current rate of change; this was then made mathematical by Minorsky. His goal was stability, not general control, which simplified the problem significantly. While proportional control provides stability against small disturbances, it was insufficient for dealing with a steady disturbance, notably a stiff gale (due to droop), which required adding the integral term. Finally, the derivative term was added to improve stability and control. Trials were carried out on the USS ''New Mexico'', with the controller controlling the ''angular velocity'' (not 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 was carried out and published by several others in the 1930s. In the early history of automatic process control the PID controller was implemented as a mechanical device. These mechanical controllers used a lever, spring and a mass and were often energized by compressed air. These pneumatic controllers were once the industry standard. Electronic analog controllers can be made from a solid-state or tube amplifier, a capacitor and a resistor. Electronic analog PID control loops were often found within more complex electronic systems, for example, the head positioning of a disk drive, the power conditioning of a power supply, or even the movement-detection circuit of a modern seismometer. Nowadays, electronic controllers have largely been replaced by digital controllers implemented with microcontrollers or FPGAs. However, analog PID controllers are still used in niche applications requiring high-bandwidth and low noise performance, such as laser diode controllers. Most modern PID controllers in industry are implemented in programmable logic controllers (PLCs) or as a panel-mounted digital controller. Software implementations have the advantages that they are relatively cheap and are flexible with respect to the implementation of the PID algorithm. PID temperature controllers are applied in industrial ovens, plastics injection machinery, hot stamping machines and packing industry. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「PID controller」の詳細全文を読む スポンサード リンク
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