【正文】 In contrast, a small gain results in a small output response to a large input error, and a less responsive (or sensitive) controller. If the proportional gain is too low, the control action may be too small when responding to system disturbances. In the absence of disturbances, pure proportional control will not settle at its target value, but will retain a steady state error that is a function of the proportional gain and the process gain. Despite the steadystate offset, both tuning theory and industrial practice indicate that it is the proportional term that should contribute the bulk of the output change. term The contribution from the integral term is proportional to both the magnitude of the error and the duration of the error. Summing the instantaneous error over time (integrating the error) gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integral gain and added to the controller output. The magnitude of the contribution of the integral term to the overall control action is determined by the integral gain, Ki. The integral term is given by: Iout: Integral output Ki: Integral Gain, a tuning parameter e: Error = SP ? PV τ: Time in the past contributing to the integral response The integral term (when added to the proportional term) accelerates the movement of the process towards setpoint and eliminates the residual steadystate error that occurs with a proportional only controller. However, since the integral term is responding to accumulated errors from the past, it can cause the present value to overshoot the setpoint value (cross over the setpoint and then create a deviation in the other direction). For further notes regarding integral gain tuning and controller stability, see the section on loop tuning. Derivative term The rate of change of the process error is calculated by determining the slope of the error over time (. its first derivative with respect to time) and multiplying this rate of change by the derivative gain Kd. The magnitude of the contribution of the derivative term to the overall control action is termed the derivative gain, Kd. The derivative term is given by: Dout: Derivative output Kd: Derivative Gain, a tuning parameter e: Error = SP ? PV t: Time or instantaneous time (the present) The derivative term slows the rate of change of the controller output and this effect is most noticeable close to the controller setpoint. Hence, derivative control is used to reduce the magnitude of the overshoot produced by the integral ponent and improve the bined controllerprocess stability. However, differentiation of a signal amplifies noise and thus this term in the controller is highly sensitive to noise in the error term, and can cause a process to bee unstable if the noise and the derivative gain are sufficiently large. Summary The output from the three terms, the proportional, the integral and the derivative terms are summed to calculate the output of the PID controller. Defining u(t) as the controller output, the final form of the PID algorithm is: and the tuning parameters are Kp: Proportional Gain Larger Kp typically means faster response since the larger the error, the larger the Proportional term pensation. An excessively large proportional gain will lead to process instability and oscillation. Ki: Integral Gain Larger Ki implies steady state errors are eliminated quicker. The tradeoff is larger overshoot: any negative error integrated during transient response must be integrated away by positive error before we reach steady state. Kd: Derivative Gain Larger Kd decreases overshoot, but slows down transient response and may lead to instability due to signal noise amplification in the differentiation of the error. 3. Loop tuning If the PID controller parameters (the gains of the proportional, integral and derivative terms) are chosen incorrectly, the controlled process input can be unstable, . its output diverges, with or without oscillation, and is limited only by saturation or mechanical breakage. Tuning a control loop is the adjustment of its control parameters (gain/proportional band, integral gain/reset, derivative gain/rate) to the optimum values for the desired control response. The optimum behavior on a process change or setpoint change varies depending on the application. Some processes must not allow an overshoot of the process variable beyond the setpoint if, for example, this would be unsafe. Other processes must minimize the energy expended in reaching a new setpoint. Generally, stability of response (the reverse of instability) is required and the process must not oscillate for any bination of process conditions and setpoints. Some processes have a degree of nonlinearity and so parameters that work well at fullload conditions don39。 大多數(shù)現(xiàn)代 PID 工業(yè)控制器被 可編程序邏 輯控制器 里的 軟件 實(shí)現(xiàn)或者作為數(shù)字控制器。這些氣動(dòng)控制器曾經(jīng)是工業(yè)標(biāo)準(zhǔn)。另一控制器擔(dān)任內(nèi)環(huán)控制器，讀取外環(huán)控制器的輸出， 通?？刂埔桓淖兏杆俚膮?shù)。 6. 串級(jí)控制 PID 控制器的一個(gè)特別的優(yōu)勢(shì)是兩個(gè) PID 控制器可以一同被使用以產(chǎn)生更好的動(dòng)態(tài)特性。 為了除去高頻率的噪音組成部分，用 低通濾波器 過(guò)濾測(cè)量數(shù)據(jù)是經(jīng)常有幫助的。經(jīng)常 PID 控制器通過(guò)各種方法獲得 PID值 或者 模糊邏輯 來(lái)進(jìn)一步提高。這表明每當(dāng)負(fù)荷被加速或者被降速時(shí)，成比例的力量從那些原動(dòng)力產(chǎn)生而不受反饋值影響任何導(dǎo)致輸出增加或減少的因素，為了降低給定值與反饋值的差值。 PID 控制器還能對(duì)在 SP和 PV的實(shí)際值之間的偏差作出反應(yīng)。在給定值附近擺動(dòng)。就微分而言，取決于對(duì)錯(cuò)誤的積分。 PID 能產(chǎn)生一輸出值，減小系統(tǒng)輸出的頻率。 避免不可缺少的時(shí)間段高于或低于預(yù)設(shè)值。關(guān)于理想 PID實(shí)施的一個(gè)普遍問(wèn)題不可缺少的終了。 而最佳的控制值更難以發(fā)現(xiàn)。這些軟件自動(dòng)收集數(shù)據(jù)，構(gòu)建過(guò)程模型，并且建立最佳的調(diào)節(jié)方式。如同在上面的方法內(nèi)， I和 D常數(shù)開(kāi)始時(shí)先被置零?？焖?PID 環(huán)路調(diào)諧通常越過(guò)微小擾動(dòng)并且能更迅速地達(dá)到給定值；但是，一些系統(tǒng)不能承受超調(diào)，這時(shí)，采用超調(diào)閉環(huán)系統(tǒng)是有必要的，這個(gè)要求 P值確定為引起系統(tǒng)擺動(dòng)的 P值的一半。 然后增加 D直到過(guò)程補(bǔ)償在足夠的時(shí)間內(nèi)是正確的。 方法的選擇基本依賴(lài)于控制環(huán)是否可以協(xié)調(diào)，以及系統(tǒng)的響應(yīng)時(shí)間。這部 分為環(huán)路調(diào)諧描述了一些傳統(tǒng)的手工方法。一些過(guò)程不允許在設(shè)定值以外易變的過(guò)程超限，如果發(fā)生了，將是