Dynamic-Experiments--Chemical-Engineering动态实验化学工程课件.ppt
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- Dynamic Experiments Chemical Engineering 动态 实验 化学工程 课件
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1、Dynamic ExperimentsMaximizing the Information Content for Control ApplicationsCHEE825/435-Fall 20051Outline types of input signals characteristics of input signals pseudo-random binary sequence(PRBS)inputs other input signals inputs for multivariable identification input signals for closed-loop iden
2、tification CHEE825/435-Fall 20052Types of Input Signals deterministic signals steps pulses sinusoids stochastic signals white noise correlated noise what are the important characteristics?CHEE825/435-Fall 20053Outline types of input signals characteristics of input signals pseudo-random binary seque
3、nce(PRBS)inputs other input signals inputs for multivariable identification input signals for closed-loop identification CHEE825/435-Fall 20054Important Characteristics signal-to-noise ratio duration frequency content optimum input(deterministic/random)depends on intended end-use control predictionC
4、HEE825/435-Fall 20055Signal-to-Noise Ratio improves precision of model parameters predictions avoid modeling noise vs.process trade-off short-term pain vs.long-term gain process disruption vs.expensive retesting/poor controller performance note-excessively large inputs can take process into region o
5、f nonlinear behaviourCHEE825/435-Fall 20056Example-Estimating 1st Order Process Model with RBS InputTrue modely tqqu ta t().()()+=-+-106107511051015202530354000.511.522.533.54TimeStep Responseconfidenceintervals aretighter with increasing SNR1:110:1less preciseestimate ofsteady stategainmore precise
6、estimateof transientCHEE825/435-Fall 20057Example-Estimating First-Order Model with Step Input0510152025303540-2-10123456TimeStep Response1:110:1more preciseestimate ofgain vs.RBS inputless precise estimateof transientresponse99%confidenceintervalCHEE825/435-Fall 20058Test Duration how much data sho
7、uld we collect?want to capture complete process dynamic response duration should be at least as long as the settling time for the process(time to 95%of step change)failure to allow sufficient time can lead to misleading estimates of process gain,poor precisionCHEE825/435-Fall 20059Test DurationPreci
8、sion of a dynamic model improves as number of data points increases additional information for estimation0510152025303540-1-0.500.511.522.533.54TimeStep Responseas test duration increases,bias decreasesand precision increasesresponse99%confidenceinterval10 time steps30 time steps50 time stepsCHEE825
9、/435-Fall 200510“Dynamic Content”what types of transients should be present in input signal?excite process over range of interest model is to be used in controller for:setpoint tracking disturbance rejection need orderly way to assess dynamic content high frequency components-fast dynamics low frequ
10、ency components-slow dynamics/steady-state gainCHEE825/435-Fall 200511Frequency Content-Guiding PrincipleThe input signal should have a frequency content matching that for end-use.CHEE825/435-Fall 200512Looking at Frequency Content ideal-match dynamic behaviour of true process as closely as possible
11、 goal-match the frequency behaviour of the true process as closely as possible practical goal-match frequency behaviour of the true process as closely as possible,where it is most important CHEE825/435-Fall 200513Experimental Design ObjectiveDesign input sequence to minimize the following:designcost
12、error inpredicted frequency responseimportancefunction=our designobjectivesdifference in predicted vs.true behaviour-function of frequency,andthe input signal usedCHEE825/435-Fall 200514Accounting for Model Error-InterpretationOptimal solution in terms of frequency content:spectral densityfrequencye
13、rror in model vs.true processspectral densityfrequencyimportance to ourapplicationlowhighvery importantnot important*J=CHEE825/435-Fall 200515Accounting for Model Error Consider frequency content matchingGoal-best model for final application is obtained by minimizing JJG eG eC jdjTjTfrequencyrange=-
14、$()()()wwww2bias in frequencycontent modelingimportanceof matching-weightingfunctionCHEE825/435-Fall 200516Example-Importance Function for Model Predictive Control spectral densityfrequencyhigh frequency disturbance rejectionperformed by base-levelcontrollers-accuracy not importantin this rangerequi
15、re good estimateof steady state gain,slower dynamicsCHEE825/435-Fall 200517Desired Input Signal for Model Predictive Control sequence with frequency content concentrated in low frequency range PRBS(or random binary sequence-RBS)step input will provide for good estimate of gain,but not of transient d
16、ynamics CHEE825/435-Fall 200518Control ApplicationsFor best results,input signal should have frequency content in range of closed-loop process bandwidth recursive requirement!closed-loop bandwidth will depend in part on controller tuning,which we will do with identified modelCHEE825/435-Fall 200519C
17、ontrol ApplicationsOne Approach:Design input frequency content to include:frequency band near bandwidth of open-loop plant(1/time constant)frequency band near desired closed-loop bandwidth lower frequencies to obtain good estimate of steady state gainCHEE825/435-Fall 200520Frequency Content of Some
18、Standard Test Inputsfrequencypowerlow frequency-like a series of long stepshigh frequency-like a series of short stepsCHEE825/435-Fall 200521Frequency Content of Some Standard Test InputsStep Inputpowerfrequency0power is concentrated at low frequency -provides good information about steady state gai
19、n,more limited infoabout higher frequency behaviourCHEE825/435-Fall 200522Example-Estimating First-Order Model with Step Input0510152025303540-2-10123456TimeStep Response1:110:1more preciseestimate ofgain vs.RBS inputless precise estimateof transientresponse99%confidenceintervalCHEE825/435-Fall 2005
20、23Frequency Content of Some Standard Test InputsWhite Noise approximated by pseudo-random or random binary sequencespowerfrequencypower is distributed uniformlyover all frequencies-broader information,but poorerinformation about steady state gainideal curveCHEE825/435-Fall 200524Example-Estimating 1
21、st Order Process Model with RBS Input051015202530354000.511.522.533.54TimeStep Responseless preciseestimate ofsteady stategainmore preciseestimateof transient1:110:1response99%confidenceintervalCHEE825/435-Fall 200525Frequency Content of Some Standard Test InputsSinusoid at one frequencypowerfrequen
22、cypower concentrated at onefrequency correspondingto input signal-poor information aboutsteady state gain,otherfrequenciesCHEE825/435-Fall 200526Frequency Content of Some Standard Test InputsCorrelated noise consider uqucorrwhite=-011091.powerfrequencyvariability is concentrated at lowerfrequencies-
23、will lead to improved estimate ofsteady state gain,poorer estimate ofhigher frequency behaviourCHEE825/435-Fall 200527Persistent ExcitationIn order to obtain a consistent estimate of the process model,the input should excite all modes of the process refers to the ability to uniquely identify all par
24、ts of the process modelCHEE825/435-Fall 200528Persistent ExcitationPersistent excitation implies a richness in the structure of the input input shouldnt be too correlatedExamples constant step input highly correlated signal provides unique info about process gain random binary sequence low correlati
25、on signal provides unique info about additional model parametersCHEE825/435-Fall 200529Persistent Excitation-Detailed Discussion Example-consider an impulse response process representation formulate estimation problem in terms of the covariances of u(t)can we obtain the impulse weights?consider esti
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