重庆大学-过程控制-process-control-中文-翻译-第六章说课材料

1、重庆大学-过程控制-process-control-中文-翻译-第六章Design &Tuning of Single Loop SystemsPID Tuning协调 trial实验 P(t)Design &Tuning of Single Loop SystemsTuning Controllers with Empirical RelationsnA practice of designing the controller settings设置pMaking an open (or closed) loop experimentpFitting the system response t

2、o a model拟合模型的系统响应nCalculating计算 the controller gains pusing the fitting curve拟合曲线 (empirical model经验模型)pFollowing some empirical relationsnEmpirical tuning gives a quick starting pointpThough it doesnt dictate system dynamic specifications尽管它不能决定系统动态参数pIt is seldom optimal最佳的, involving包括 field tun

3、ing现场调试1. Cohen-Coon Relation2. Ziegler-Nichols Relation, 3. ITAE relation, 4. Ciancone-Marlin relationDesign &Tuning of Single Loop SystemsTwo Remarks评论 on Empirical Tuning经验调整nTuning relations调整关系 are based onpFitting open loop data to the 1st order with dead time model拟合一阶开环数据的延迟时间模型 Systems is s

4、upposed to被期望 be self-regulating自动调节的 Dead time can approximate multi-stage process, or measuring lag延迟时间可以近似的多阶段过程，或测量滞后pSome tuning relations, e.g., Cohn and Coon being developed（ in term of在方面） decay ratio衰退率 in handling disturbance being not suitable for适合 servo problems (why?)Design& Tuning of

5、Single Loop SystemsController settings Based on PRCnObtaining获取 process reaction curve过程响应曲线 (PRC)pDisabling the controllerp禁用控制器pIntroducing a step change to the actuator执行机构引入阶跃变化pMeasuring the open loop step response, resulting in导致 PRCDesign& Tuning of Single Loop SystemsController settings Base

6、d on PRCnIn this open loop step test开环阶跃测试pThe lumped总的 response can be represented表现 bynUsing GPRC forpDesign of the required controller if the process models are not known in advance预先pA reduced order model降阶模型 for the product乘积 of Ga, Gp, and GmDesign& Tuning of Single Loop SystemsController sett

7、ings Based on PRCnExample: A self-regulating自调整 capacity processpStep test is shown in the figure below阶跃测试结果如下表Note that注意 we assume that the process is self-regulatingDesign& Tuning of Single Loop SystemsController settings Based on PRCnExample: A self-regulating multi-capacity process Step test i

8、s shown in the figure below 一个自我调节的多容量的过程测试步骤如下图所示Open loop test data1st order with dead timeTime constant decided by the initial slope and a visual estimation of dead time td 时间常数由最初的斜坡和目测的延迟时间TD决定sigmoidal formS形Design& Tuning of Single Loop SystemsController settings Based on PRCnExample (cont.):

9、 Why does FOPDT纯滞后过程work?pThe real time data usually takes the sigmoidal form S形pProcess unit operations are generally open-loop stable过程单元操作通常都是开环稳定, thus, the approximation works in realitypReminder提示: there is no underdamped response due to the taking out of拿出 the controller in the step testpThe

10、empirical relations such as Z-N, C-C, C-M, and IAE are usually be used in this case这种情况下Design& Tuning of Single Loop SystemsController settings Based on PRCnComments on评论 the minimum error最小误差 integral criteria 积分标准pCalculating计算 the error by E = R-C, where C is based GPRCpMinimizing极小化的 the error

11、over time超时 (e.g., by Lagrange Multiplier)pThe forms of integral积分的 errorWhy so many forms?Design& Tuning of Single Loop SystemsController settings Based on PRCnComments on the minimum error integral 积分过程(cont.)pIntegral of the absolute error绝对误差pIntegral time-weighted加权的 absolute errorIAE puts the

12、equal weight重要性 to large and small errorIt puts a heavy penalty on errors persisting for long periods of time 很大的误差将持续很长一段时间Resulting controller allows for得到 low settling times建立时间Design& Tuning of Single Loop SystemsController settings Based on PRCnComments on the minimum error integral (cont.)pInt

13、egral of the square error平方误差Squaring e makes it even smaller when e 2 Design& Tuning of Single Loop SystemsDirect Synthesis of ControllersnFurther consideration to（进一步考虑） the desired responseWhen the dead time is inevitably不可避免的 in the process, the desired response can be defined as:Synthesis:前面的方程

14、Design& Tuning of Single Loop SystemsDirect Synthesis of ControllersnExample 3: Derive the controller function for a system with a first order process（推导一个一阶系统的控制器函数） with dead time , andthe desired system response Solution: Assuming =tdThis is a PI controllerGuideline to choosing c:c 1.7 for PI Con

15、troller, 1. c 0.25 for PID ControllerDesign& Tuning of Single Loop SystemsDirect Synthesis of ControllersnSupposing the desired system response iswith the system natural period , and the damping ratio阻尼比 Synthesis:When intentionally simplifying the process当故意简化了过程 Gp, we can obtain获得 Gc as a PID con

16、trollerDesign& Tuning of Single Loop SystemsDirect Synthesis of ControllersnExample 4: Derive the controller function for a system with a second order overdamped process推导一个二阶过阻尼过程的传递函数 , and an underdamped system response Solution:Design& Tuning of Single Loop SystemsDirect Synthesis of Controllers

17、nExample 4 (cont.):Simplifying简化:Suppose that 2 is related to the slower pole, i.e., 21, Set f=2 in order to the effect of pole-zero cancellation 为了实现零极点对消f=2the PI controllerThe final form:The only tunable parameter可调的参数 is the damping ratio Design& Tuning of Single Loop SystemsDirect Synthesis of

18、ControllersnPole-zero (p-z) cancellation (cancellation compensation)Real life problems can not have a perfect p-z cancellationThe analysis below gives a theoretical理论的 understanding of p-zWhat is pole-zero cancellation? Canceling the (undesirable open-loop) poles of our process Replacing them with a

19、 desirable closed-loop pole用我们想要的闭环极点取代开环极点Design& Tuning of Single Loop SystemsDirect Synthesis of ControllersnPole-zero (p-z) cancellation (cancellation compensation)How pole-zero cancellation occurs?Gc is sort of是一种 reciprocal倒数 of Gp, i.e., , thusthe zeros of Gp is the poles of Gc. Therefore, we

20、 haveThe closed-loop poles only depend on c due to 1+GcGp=0 Design& Tuning of Single Loop SystemsDirect Synthesis of Controllers控制器的融合nPole-zero (p-z) cancellation (cancellation compensation)Behaviors作用 of the closed-loop system with p-z cancellationSupposing that a system (Ga=Gm=1) uses PI controll

21、er and Gp is the first order function,If choosing I=p, we have System characteristic equation:Design& Tuning of Single Loop SystemsDirect Synthesis of ControllersnPole-zero (p-z) cancellation (cancellation compensation)Behaviors of the closed-loop system with p-z cancellationRecall example 1, we hav

22、e Kc=p/(Kpc) and I=pChecking GcGp with s=-1/ c and Kc=p/(Kpc)c1sGiving also us the consistent一致的 results Design& Tuning of Single Loop SystemsInternal Model Control内模控制 (IMC)nIMC considers the following以下的 factors:pThe model is only an approximation of the actual真实的 processpMeasurements测量值 of the pr

23、ocess parameters is not accurateGc consists of由组成 p*cG and GIMC （Scheme概形） Design& Tuning of Single Loop SystemsInternal Model Control (IMC)nIMC with PID controllers:The error is The closed-loop functions based on IMC scheme基于内模控制的闭环传递函数The model controller outputRearrangingDesign& Tuning of Single

24、Loop SystemsInternal Model Control (IMC)nIMC with PID controllers:The relationship between Gc and IMC functionsThis will be used to retrieve检索 the PID gainsThe system output:The closed-loop equationDesign& Tuning of Single Loop SystemsInternal Model Control (IMC)nHow to choose *cGSet the approximate

25、 function to avoid the above situation: Recall the basic fact from the direct synthesis直接合成: The poles of Gc are “inherited继承的” from the zeros of Gp, i.e., If Gp has positive zeros, the Gc function with positive poles. where contains包含 all positive zeros, and The controller is designed on the basis

26、of 基于 only pG-pGDesign& Tuning of Single Loop SystemsInternal Model Control (IMC)nDefining the controllerObservations:1. The only tunable可调的 parameter is closed-loop time constant c 2. An integer power整数的大小 of r is used to ensure that the controller is physically Realizable物理可实现3. The example below

27、violate this intention下面的例子违反这个意图just for obtain获得 results that resemble类似 an ideal理想的 PID controller.Design& Tuning of Single Loop SystemsInternal Model Control (IMC)nExample 5: Derive a controller function for a system with a first order process with dead time using IMC获得一个一阶系统控制器函数与延迟时间使用内模控制Solu

28、tion:The experiments has experimental errors实验误差 or uncertainties不确定性 The measured model function is written asDesign& Tuning of Single Loop SystemsInternal Model Control (IMC)nExample 5 (cont.):Using Pad approximation for the dead time functionPadwhere The controller by IMCr = 1Design& Tuning of Si

29、ngle Loop SystemsInternal Model Control (IMC)nExample 5 (cont.):Rearranging the controller function, we have These are the tuning parameters of the ideal PID controllerDesign& Tuning of Single Loop SystemsInternal Model Control (IMC)nExample 6 What is the PID controller settings for the dye mixing problem if using IMC-based tuning relations?如果利用内模控制调整关系，pid控制器设置什么关于燃料混合问题Solution:Using the same dead time in the dye mixing problem, Observations:The integral time constant is relatively相当的 high, thus less integrating action results in less oscillation振荡 of IMC tuningDesign& Tuning o