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1、1Multiloop SystemsOutlineImproving（disturbance rejection干扰抑制)performance cascade control级联控制feedforward control,前馈控制ratio control,and 比例控制time delay compensation时间延迟补偿with Smith predictor.smith 预估补偿第1页/共47页2Multiloop SystemsImproving the DR PerformanceCascade ControlControl of a furnace temperature；
2、炉温DR:Disturbance Rejection第2页/共47页3TTTCTspMultiloop SystemsImproving the DR干扰抑制 performance S-loop control solution单环开环控制1.measure T by TT,pute p by TC,3.send the p to the valve第3页/共47页4Multiloop SystemsCascade ControlMotivation of动机 Cascade Control If fluctuation波动 in the fuel gas flow rate燃气流速,the
3、 system will not counter计数 the disturbance untilthe controller senses that感知 the temperature has deviated From偏离 the set point(Tsp)第4页/共47页5Multiloop SystemsCascade ControlCascade control solutionIt consisting of包含:master(primary)loopslave(secondary)loopTT:temperature transducer 温度传感器FT:flow transdu
4、cerTC:temperature controllerFC:fuel gas controllerTwo measured variablesdisturbance is now in slave loop副回路fluctuation波动第5页/共47页6Multiloop SystemsCascade ControlCascade control solution TC in master-loop sends its signal to slave-loop 副回路,in terms of依据 the desired flow rate(casual relation)the signa
5、l is the set point of the secondary flow controller(FC).FC in slave loop adjusts the regulating valve调节阀FC compares the desired and measured fuel gas flow rates responding 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.第6页/共47
6、页7Multiloop SystemsCascade ControlCascade 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 secondary variable 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 se
7、condary (cause effect)5.have a faster response than the primary第7页/共47页8Multiloop SystemsCascade ControlCascade Control Solution Reducing the block diagram方块图Setting Gm1=Gm2=1where第8页/共47页9Multiloop SystemsCascade ControlReducing the block diagramFrom the reduced block diagramE=R-C第9页/共47页10Multiloo
8、p SystemsCascade ControlCascade control solutionThe closed-loop characteristic polynomial特征多项式Comments on the slave-loop1.reducing disturbance in the manipulated variable被控变量 减少来自被控变量的干扰.2.accomplish a faster response in the valve,3.make the system more stable第10页/共47页11Multiloop SystemsCascade Cont
9、rolExample 1:the furnace temperature controlthe master loop uses a PI controller,the slave loop uses a p-controller,with the first order functions 第11页/共47页12Problem(a):choosing Kc2 properly for better performanceMultiloop SystemsCascade ControlExample 1.the furnace temperature controlSubstituting取代
10、 Gc2=Kc2 and Gv=Kv/(vs+1)into G*v wheresubstituting GL=KL/(Ls+1)into G*LSolution:第12页/共47页13Multiloop SystemsCascade ControlExample 1.the furnace temperature controlas the proportional gain Kc2 becomes larger1.K*v 1,more effective change in manipulated variable,2K*L 0,manipulated variable is less se
11、nsitive to changes in load,操纵变量对负载的变化敏感度降低3*v smaller,faster response of the regulating valve调节阀Problem(a):choosing Kc2 properly for better performance第13页/共47页14Multiloop SystemsCascade ControlExample 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
12、 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参考方程第14页/共47页15Multiloop SystemsCascade ControlExample 1.the furnace temperature controlProblem(c):Now that既然 certainly an offset偏移 in the inner loop,why do
13、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 ensure that b)there is no steady state error in the controlled variable受控变量第15页/共47页16Multiloop SystemsCascade ControlExample 1.the furnac
14、e temperature controlProblem(d):Choose the proper integral time constant among the given values of 0.05,0.5,and 5 s,such that 1.guaranteeing保证 the system stable,2.allowing a slightly稍微的 underdamped response3.making system response as fast as possible第16页/共47页17Multiloop SystemsCascade ControlExample
15、 1.the furnace temperature controlSolution of解决 problem(d):with PI master controller,the entire closed-loop system is 第17页/共47页18Multiloop SystemsCascade ControlExample 1.the furnace temperature controlProblem(e):determine Kc of PI controller that guarantees system stable when I=0.5 without cascade
16、Solution:system is a single-loop system when no cascade characteristic equation of its closed-loop equation isSystem is stable if and only if Kc7.5第18页/共47页19Multiloop SystemsCascade ControlExample 1(cont.)the furnace temperature controlSolution of problem(e):compared with与相比较 cascade controlcascade
17、 control is always stable when I=0.5,from(d)the system is stable by Routh-Hurwitz劳氏判据analysis第19页/共47页20Multiloop SystemsCascade ControlSummary of总结 cascade control based on基于 example 11.the system becomes more stable,and 2.allowing to use a larger Kc in master controller3.much faster response of th
18、e actuator in the inner loopSingle loop controlCascade control第20页/共47页21Multiloop SystemsImproving the DR PerformanceFeedforward ControlControl of a furnace temperature againDR:Disturbance Rejection第21页/共47页22Multiloop SystemsImproving the DR PerformanceMotivation of feedforward(FF)control前馈控制的动机Te
19、mperature T can also be effected by the cold process stream flow rate FsFsOur ideas are 1.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 stream temperature are presumed being假定为 constant第22页/共47页23Multiloop SystemsFeedforward C
20、ontrolDerive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 functions第23页/共47页24Multiloop SystemsFeedforward ControlDynamic feedforward control model1.Tells how
21、to adjust the manipulated variable(a)when changing R,thus 1/Gp called setpoint tracking设定追踪(b)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 model)第24页/共47页251.GmL is load measurement function2.GFF is the FF controller
22、3.feedback loop is omitted4.If there are two more load variables,the FF controller can be added on each one(theoretically)Multiloop SystemsFeedforward ControlImplementing实现 the FF controller,-GL/GpThe elements基本原理 in the FF systemload负载，omitted省略，be added on被添加在第25页/共47页26Multiloop SystemsFeedforwar
23、d ControlImplementing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=0第26页/共47页27Multiloop SystemsFeedforward ControlImplementing the FF controller,GL/Gpsuppo
24、sing 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 第27页/共47页28Multiloop SystemsFeedforward ControlTuning the FF Controller Parametersbest practice最优方法(1)FLD=m+*v,(2)FLG=0.1 FLD,(3)Gm=Km
25、Lif small m(4)GFF=KFF if small*v with cascade control a=0,b=0.5,c=1.0,d=1.5,e=2.0第28页/共47页29Multiloop SystemsImproving the DR PerformanceFeedforward-Feedback（FB）Control顺馈控制 combine FF with FB Control Feedback trim反馈微调the feedback loop in FF-FB system handlesthe measurement errorserrors in the feedfo
26、rward functionchanges in unmeasured load variablesset point changes第29页/共47页30Multiloop SystemsFeedforward-Feedback(FF-FB)ControlFinding the closed-loop transfer functionmove G*vGp to form Fig.bwrite down the final resultwhererearrange the equation above the FF control doesnt affect the system stabi
27、lity第30页/共47页31Multiloop SystemsFeedforward-Feedback(FF-FB)ControlExample 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 (secondary disturbance)the fuel gas flow rate燃气流速(manipulated variab
28、le)The task are:draw the schematic diagram原理图 of the control system combine FF,FB and cascade controls for load changes负载变化第31页/共47页32Multiloop SystemsFeedforward-Feedback(FF-FB)ControlExample 2.(1)the cascade controlUsing a flow controller(FC)in a slave loop次环 to handle the fuel gas flow disturbanc
29、e FC has the transfer function Gc2Slave loopSolution:Entire transfer function第32页/共47页33Multiloop SystemsFeedforward-Feedback(FF-FB)ControlExample 2(cont.):Solution:(2)The FF ControlFT sends the signals to FFC A summer()combines signals from FFC and TC its output becomes the set point for FC第33页/共47
30、页34Multiloop SystemsFeedforward-Feedback(FF-FB)ControlExample 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 temperature第34页/共47页35Multiloop SystemsImproving the DR PerformanceRatio Control比例控制DR:Disturbance Reject
31、ionAir flowFuel gas第35页/共47页36Multiloop SystemsRatio ControlConsidering air flow rate in the furnace controlMotivation动机:maintaining FFG at a defined proportion R relative to FA,Benefit:好处Ensuring sufficient air flow for efficient combustion有效燃烧Regulating air flow for the reduction of air pollutant污
32、染Application of interests:gases,liquids,powders,slurries or melts气体、液体、粉剂、浆液或熔化物 第36页/共47页37Multiloop SystemsRatio ControlConsidering air flow rate in the furnace controlSimple implementation实现 1.measuring the fuel gas flow rate FFG 2.multiplying the value by R in ratio station FFG 在比值操作器中值增大R倍1.sen
33、d the signal as the set point to the air flow controller.NoticeComputation计算 conducts on actual variable rather than deviation variable第37页/共47页38Multiloop SystemsRatio ControlConsidering air flow rate in the furnace controlFull metering计量 implementation1.Sending the signals from the fuel gas FC and
34、 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 第38页/共47页39Multiloop SystemsImproving the DR PerformanceSmith predictor for time delay compensationSmith预估的时间延迟补
35、偿DR:Disturbance Rejection第39页/共47页40Multiloop SystemsTime Delay Compensation:Smith PredictorSuppose A feedback system with time delayTime lag causes the deficits不足:1.Introducing引入 extra phase lag相位滞后,2.reducing the gain margin增益裕度,3.a significant source of instability.不稳定的一个重要来源The characteristic eq
36、uationMotivation动机:How to cancel the impacts of the time lag of a process?第40页/共47页41Multiloop SystemsTime Delay Compensation:Smith PredictorInterpretation 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 delaypred
37、iction loopExponential terms are canceled out!指数部分被抵消第41页/共47页42Multiloop SystemsTime Delay Compensation:Smith PredictorInterpretation of阐释the transfer function The time delay effect is canceled out due to system with Smith predicatorsystem without Smith predicator第42页/共47页43Multiloop SystemsTime De
38、lay Compensation:Smith PredictorBenefits好处 of Smith predicator Use of a larger Kc without going unstable Making use of利用 state feedbackEquivalent to等价于Output feedback state feedback状态反馈 第43页/共47页44Multiloop SystemsTime Delay Compensation时间延迟补偿:Smith PredictorWhile no precise process model The effect
39、iveness of compensator is diminished补偿效果降低Approximating G and td with H and (HG and td)Now the feedback information is where the right hand side becomes Gc G R if and only if H=G and=td第44页/共47页45Multiloop SystemsTime Delay Compensation:Smith PredictorComments on Smith compensator补偿器1.Reminder提示 a)t
40、he time delay term is an exponential指数 function b)error in the estimation of the dead time is more detrimental 不利的 than error in the estimation of the process function G2.Proverb谚语 a)few things are exact in this world,so do the estimation of G and td b)being conservative in picking controller gains
41、based on 1+GcG=0第45页/共47页46Multiloop SystemsTime Delay Compensation:Smith PredictorComments on Smith compensator3.Industry(e.g.,chemical plants)a)time delay is usually a result of transport lag in pipe管 flow b)the use of the Smith predictor is acceptable if the flow rate is fairly接近 constant c)this compensation method补偿法 will not be effective if the flow rate varies for whatever reasons第46页/共47页47感谢您的观看！第47页/共47页