重庆大学-过程控制-process-control-中文-翻译-第十章(1)教学提纲

1、重庆大学-过程控制-process-control-中文-翻译-第十章(1)Multiloop SystemsImproving the DR PerformancenCascade ControlpControl of a furnace temperature；炉温DR: Disturbance RejectionTTTCTspMultiloop SystemsImproving the DR干扰抑制 performancen S-loop control solution单环开环控制开环控制1. measure T by TT,2. compute p by TC,3. send the

2、 p to the valveMultiloop SystemsCascade ControlnMotivation of动机 Cascade Control pIf fluctuation波动 in the fuel gas flow rate燃气流速, pthe system will not counter计数 the disturbance untilpthe controller senses that感知 the temperature has deviated From偏离 the set point (Tsp)Multiloop SystemsCascade ControlnC

3、ascade control solutionIt consisting of包含: master (primary) loop slave (secondary) loopTT: temperature transducer 温度传感器FT: flow transducerTC: temperature controllerFC: fuel gas controllerTwo measured variablesdisturbance is now in slave loop副回路fluctuation波动Multiloop SystemsCascade ControlnCascade co

4、ntrol solution pTC in master-loop sends its signal to slave-loop副回路, in terms of依据 the desired flow rate (casual relation) the signal is the set point of the secondary flow controller (FC).pFC in slave loop adjusts the regulating valve调节阀 FC compares the desired and measured fuel gas flow rates resp

5、onding immediately to fluctuations in the fuel gas flow 立即对波动的燃气速率做出反应 to ensure that the proper amount of数量的 fuel is delivered.Multiloop SystemsCascade ControlnCascade Design Criteria设计标准Cascade is desired when1. single-loop performance unacceptable2. a measured variable is available 测量值可用A seconda

6、ry variable 次要变量次要变量must3. Indicate指出 the occurrence of发生的 an important disturbance4. have a causal relationship因果关系 from primary to secondary (cause effect)5. have a faster response than the primaryMultiloop SystemsCascade ControlnCascade Control Solution Reducing the block diagram方块图Setting Gm1=Gm

7、2=1whereMultiloop SystemsCascade ControlnReducing the block diagramFrom the reduced block diagramE=R-CMultiloop SystemsCascade ControlnCascade control solutionThe closed-loop characteristic polynomial特征多项式Comments on the slave-loopreducing disturbance in the manipulated variable被控变量 减少来自被控变量的干扰.2. a

8、ccomplish a faster response in the valve, 3. make the system more stableMultiloop SystemsCascade ControlnExample 1: the furnace temperature controlpthe master loop uses a PI controller,pthe slave loop uses a p-controller,pwith the first order functions Problem (a): choosing Kc2 properly for better p

9、erformanceMultiloop SystemsCascade ControlnExample 1. the furnace temperature controlSubstituting取代 Gc2 = Kc2 and Gv = Kv/(vs+1) into G*v wheresubstituting GL = KL/(Ls+1) into G*LSolution:Multiloop SystemsCascade ControlnExample 1. the furnace temperature controlas the proportional gain Kc2 becomes

10、largerK*v 1, more effective change in manipulated variable, K*L 0, manipulated variable is less sensitive to changes in load,操纵变量对负载的变化敏感度降低 *v smaller, faster response of the regulating valve调节阀Problem (a): choosing Kc2 properly for better performancevcvcvKKKKK221*vcvvKK21*LcLLKKKK21*Multiloop Syst

11、emsCascade ControlnExample 1. the furnace temperature controlProblem (b): find Kc2 while *v = 0.1v with Kv=0.5, v=1 s, and *v=0.1 s, we havethus slave loop has a 10% offset with respective to the desired set point changes in the secondary controller.次循环在二级控制器的设定点有10的偏移变化Solution参考方程Multiloop Systems

12、Cascade ControlnExample 1. the furnace temperature controlProblem (c): Now that既然 certainly an offset偏移 in the inner loop, why do we stay with继续做 p-control here?Solution 1. slave loop with 10% offset is acceptable in most cases 2. master loop has integral action积分作用, a) TC adjust调整 its output to ens

13、ure that b) there is no steady state error in the controlled variable受控变量Multiloop SystemsCascade ControlnExample 1. the furnace temperature controlProblem (d): Choose the proper integral time constant among the given values of 0.05, 0.5, and 5 s, such that guaranteeing保证 the system stable, allowing

14、 a slightly稍微的 underdamped response3. making system response as fast as possibleMultiloop SystemsCascade ControlnExample 1. the furnace temperature controlSolution of解决 problem (d): with PI master controller, the entire closed-loop system is Multiloop SystemsCascade ControlnExample 1. the furnace te

15、mperature controlProblem (e): determine Kc of PI controller that guarantees system stable when I=0.5 without cascade Solution: system is a single-loop system when no cascade characteristic equation of its closed-loop equation isSystem is stable if and only if Kc7.5Multiloop SystemsCascade ControlnEx

16、ample 1 (cont.) the furnace temperature controlSolution of problem (e): compared with与相比较 cascade control cascade control is always stable when I =0.5, from (d) the system is stable by Routh-Hurwitz劳氏判据analysisMultiloop SystemsCascade ControlnSummary of总结 cascade control based on基于 example 1 the sys

17、tem becomes more stable, and allowing to use a larger Kc in master controller much faster response of the actuator in the inner loopSingle loop controlCascade controlMultiloop SystemsImproving the DR PerformancenFeedforward ControlpControl of a furnace temperature againDR: Disturbance RejectionMulti

18、loop SystemsImproving the DR PerformancenMotivation of feedforward (FF) control前馈控制的动机Temperature T can also be effected by the cold process stream flow rate FsFsOur ideas are Measure the disturbance in Fs 测量Fs中的干扰2. Adjust the valve before the change of Fs has no chance to affect T Reminder: the st

19、ream temperature are presumed being假定为 constantMultiloop SystemsFeedforward ControlnDerive导出 process modelusing heat-mass balance热质量平衡 to track R precisely,为了精确地跟踪R we ideally理想的 set R=Cwhere C: the controlled variable, (i.e., T)GL: the heat transfer function, Gp: the mass transfer functionsMultiloo

20、p SystemsFeedforward ControlnDynamic feedforward control model1. Tells how to adjust the manipulated variable when changing R, thus 1/Gp called setpoint tracking设定追踪when changing L, thus -GL/Gp called the FF controller2. Is dynamical because C=GLL+GpM is derived in源至于 a time-domain (a transient瞬态 mo

21、del)GmL is load measurement functionGFF is the FF controllerfeedback loop is omittedIf there are two more load variables, the FF controller can be added on each one (theoretically)Multiloop SystemsFeedforward ControlnImplementing实现 the FF controller, -GL/GpThe elements基本原理 in the FF systemload负载，omi

22、tted省略， be added on被添加在Multiloop SystemsFeedforward ControlnImplementing实现the FF controller, GL/Gpsupposing the set point R has no changes, thus the FF loop is of regulating problem调节supposing that FF controller can perfectly reject很好的抑制 the load change, thus C=0C=0Multiloop SystemsFeedforward Contr

23、olnImplementing the FF controller, GL/Gpsupposing 1seKGpsLLL 1*sKeGGGspvML and Substitute代替 them into the follow Further implement above以上进一步实现 as is called steady state compensator稳态补偿器 FLD= and FLG=p is called dynamic compensator动态补偿器 Multiloop SystemsFeedforward ControlnTuning the FF Controller P

24、arametersbest practice最优方法(1) FLD = m+ *v , (2) FLG = 0.1 FLD, (3) Gm=KmLif small m(4) GFF = KFF if small *v with cascade control a = 0, b =0.5, c = 1.0, d= 1.5, e= 2.0Multiloop SystemsImproving the DR PerformanceFeedforward-Feedback（FB） Control顺馈控制 ncombine FF with FB Control Feedback trim反馈微调nthe

25、feedback loop in FF-FB system handlesthe measurement errorserrors in the feedforward functionchanges in unmeasured load variablesset point changesMultiloop SystemsFeedforward-Feedback (FF-FB) ControlnFinding the closed-loop transfer functionmove G*vGp to form Fig. bwrite down the final resultwherere

26、arrange the equation above the FF control doesnt affect the system stabilityMultiloop SystemsFeedforward-Feedback (FF-FB) ControlnExample 2. the furnace temperature controlSuppose that the probable disturbances includeprocess stream flow rate蒸汽流速 (major disturbance)process stream temperature蒸汽温度 (se

27、condary disturbance)the fuel gas flow rate燃气流速 (manipulated variable) The task are:pdraw the schematic diagram原理图 of the control system pcombine FF, FB and cascade controls for load changes负载变化Multiloop SystemsFeedforward-Feedback (FF-FB) ControlnExample 2.(1) the cascade controlUsing a flow control

28、ler (FC) in a slave loop次环 to handle the fuel gas flow disturbance FC has the transfer function Gc2Slave loopSolution: Entire transfer functionMultiloop SystemsFeedforward-Feedback (FF-FB) ControlnExample 2(cont.):Solution:(2) The FF ControlFT sends the signals to FFC A summer () combines signals fr

29、om FFC and TC its output becomes the set point for FCMultiloop SystemsFeedforward-Feedback (FF-FB) ControlnExample 2(cont.):Solution:(3) The master looptemperature T is measured by (TT)T is sent to TC TT acts to reduce the deviation偏差 in the furnace temperatureMultiloop SystemsImproving the DR Perfo

30、rmanceRatio Control比例控制DR: Disturbance RejectionAir flowFuel gasMultiloop SystemsRatio ControlnConsidering air flow rate in the furnace controlMotivation动机: pmaintaining FFG at a defined proportion R relative to FA, Benefit:好处pEnsuring sufficient air flow for efficient combustion有效燃烧pRegulating air

31、flow for the reduction of air pollutant污染Application of interests:pgases, liquids, powders, slurries or meltsp气体、液体、粉剂、浆液或熔化物p Multiloop SystemsRatio ControlnConsidering air flow rate in the furnace controlSimple implementation实现 measuring the fuel gas flow rate FFG multiplying the value by R in rat

32、io station FFG 在比值操作器中值增大R倍send the signal as the set point to the air flow controller. NoticeComputation计算 conducts on actual variable rather than deviation variableMultiloop SystemsRatio ControlnConsidering air flow rate in the furnace controlFull metering计量 implementationSending the signals from

33、the fuel gas FC and air FT to the ratio controller (RC)2. RC takes the desired R as set point and calculate the proper air rate FA.sp3. Taking FA.sp as the set point for air FC and calculate the control signal Multiloop SystemsImproving the DR PerformanceSmith predictor for time delay compensationSm

34、ith预估的时间延迟补偿DR: Disturbance RejectionMultiloop SystemsTime Delay Compensation: Smith PredictornSuppose A feedback system with time delayTime lag causes the deficits不足:Introducing引入 extra phase lag相位滞后, reducing the gain margin增益裕度, a significant source of instability. 不稳定的一个重要来源The characteristic eq

35、uationMotivation动机: How to cancel the impacts of the time lag of a process?Multiloop SystemsTime Delay Compensation: Smith PredictornInterpretation of阐释 the transfer function assuming that the process model is known, Construct构造 the block diagram （as follow依下列各项）.PredictorActual time delay predictio

36、n loopExponential terms are canceled out!指数部分被抵消Multiloop SystemsTime Delay Compensation: Smith PredictornInterpretation of阐释the transfer function The time delay effect is canceled out due to system with Smith predicatorsystem without Smith predicatorMultiloop SystemsTime Delay Compensation: Smith PredictornBenefits好处 of Smith predicator Use of a larger Kc without going unstable Making use of利用 state feedbackEquiv