濰城區(qū)公開選拔年輕干部到基層掛職

1、1DOE-based Automatic Process Control with Consideration of Model UncertaintiesJan Shi and Jing ZhongThe University of MichiganC. F. Jeff WuGeorgia Institute of Technology2Outline Introduction DOE-based Automatic Process Control with Consideration of Model Uncertainty Process model Control objective

2、function Controller design strategies Simulation and case study Summary3Problem StatementProcess variation is mainly caused by the change of unavoidable noise factors.Process variation reduction is critical for process quality improvement. Offline Robust Parameter Design (RPD) used at the design sta

3、ge To set an optimal constant level for controllable factors that can ensure noise factors have a minimal influence on process responses Based on the noise distribution but not requiring online observations of noise factorsOnline Automatic Process Control (APC) during production With the increasing

4、usage of in-process sensing of noise factors, it will provide an opportunity to online adjust control factors to compensate the change of noise factors, which is expected to achieve a better performance than offline RPD.4Motivation of Using APCx=x1enoise distributiony(x,e)abeeOnline adjust X based o

5、n e2byxx 1ayxx x= x22ayxx 2byx x Offlinefix x=x2Offlinefix x=x11byxx 1ayxx ( , )yf x e5The Objective and Focus DOE-Based APC Design of Experiments(DOE)Automatic Process Control(APC)Statistical Process Control(SPC)The research focuses on the development of automatic process control (APC) methodologie

6、s based on DOE regression models and real-time measurement or estimation of noise factors for complex mfg processes6Literature ReviewFor complex discrete manufacturing processes, the relationship between the responses (outputs) and process variables (inputs) are obtained by DOE using a response surf

7、ace model, rather than using dynamic differential/difference equationsoffline robust parameter design (RPD) (Taguchi, 1986) Improve robust parameter design based on the exact level of the observed uncontrollable noise factors (Pledger,1996) Existing APC literature are mainly for automatic control of

8、 dynamic systems that are described by dynamic differential/difference equations.Certainty Equivalence Control (CEC) (Stengel, 1986): The controller design and state estimator design are conducted separately (The uncertainty of system states is not considered in the controller design) Cautious Contr

9、ol (CC) (Astrom and Wittenmark, 1995): The controller is designed by considering the system state estimation uncertainty, which is extremely difficult for a complex nonlinear dynamic system. Jin and Ding (2005) proposed Doe-Based APC concepts:considering on-line control with estimation of some noise

10、 factors.No interaction terms between noise and control factors in their model.7ObjectiveDevelop a general methodology for controller design based on a regression model with interaction terms.Investigate a new control law considering model parameter estimation uncertainties Compare the performances

11、of CC, CEC, and RPD, as well as performance with sensing uncertainties.8Methodology Development Procedures APC Using Regression Response Models Based on key process variableS1: Conduct DOE and process modelingObtain significant factors & estimated process model S2: Determine APC control strategy

12、 (considering model errors S3: Online adjust controllable factors S4: Control performance evaluationBased on observation uncertainty Based on process operation constraints on controller Use certainty equivalence controlor cautious control Obtain reduced process variation91. Process Variable Characte

13、rizationProcessVariablesControllableFactorsNoiseFactorsUnobservableNoise FactorsObservableNoise FactorsOff-line settingFactorsOn-line adjustableFactorsY= f (X, U, e, n)102. Control System FrameworkControllableFactors (x)ManufacturingProcessUnobservableNoise Factors (n)Observable Noise Factors (e)In-

14、ProcessSensing of eResponse (y)Observer for Noise Factors (e)Feedforward ControllerNoise FactorsPredicted Response ( , , | , )nyE f x e n x eTarget11Observations of measurable noise factors, denoted by , are unbiased, i.e., and . 3 Controller Design3.1 Problem AssumptionsThe manufacturing process is

15、 static with smoothly changing variables over time Parameter StabilityEstimated process parameters denoted by , is estimated from experimental data.)(Coveee0 |eeeEeeee) | (Cove, n and are independent, with E(e)=0, Cov(e)=e, E(n)=0, Cov(n)=n, E()=0, Cov()=. are i.i.d.nBUnBXeBUeBXneUX432143210TTTTTTTT

16、yeUX, |,APCJene, )(2,tycEe 123 Controller Design 3.2 Objective Function), ,(eUXAPCJObjective Function (Quadratic Loss)2432124344342132132213210)(var)(var)(var)(var)( 43230nBUnBXeBUeBXnneeUUXXUBXBUBXBUBXBUBXBeBUeBXeUXnnnneTTTTTTTTTTTTTTTTTTTTTTTEEEt2, tyEeneeenene, , ,2,yVartyEene, )(2,tycEUXUXUX,min

17、 arg ),( 1, 1*APCJOptimization Problem( , , ,)f enX U e 13., |,minarg*1*eUXXeXAPCJEStep 1 Off-line Controllable Factors SettingStep 2 On-line Automatic Control LawProcedure for Solving Optimization ProblemStep 2 obtain X* by solving optimization problem of JAPC ), ,(, ,|,minarg1*neUeXeXUXUhJAPC3 Con

18、troller Design 3.3 Control Strategy*(, , ,)h enUUX e Step 1 Closed form solution of U* by solving0U APCJProcess Control Strategy Two Step Procedure*XX UXUXUX,min arg ),( 1, 1*APCJ144. Case Study : An Injection Molding ProcessProcess DescriptionResponse Variable (y): Percentage Shrinkage of Molded Pa

19、rtsProcess Variables:15DOE ModelingReduced DOE Model after Coefficient Significance Tests Designed Experiment Result (Engel, 1992)1312121113121321321106. 0094. 0125. 0063. 0556. 0588. 0 05. 0144. 0281. 0425. 0231. 0063. 0075. 025. 2nununxnxeuexnuuuxxxy2121-4105.51IParameter Estimation Error16RPD Set

20、tings Robust Parameter Design.)5563. 05875. 0()1063. 00938. 0125. 00625. 005. 0() (223222322111enuxuuxxyVarVariance ModelResponse ModelTx*3*04664. 0XTu02222. 0*1*U, and u1 and x3 are adjusted according to target values as in right table1312121113121321321106. 0094. 0125. 0063. 0556. 0588. 0 05. 0144

21、. 0281. 0425. 0231. 0063. 0075. 025. 2nununxnxeuexnuuuxxxy17Objective Loss Function UUXXUUXXUUXXUBXBUBXBUBXBUBXBeBUeBXeUXeUXBBBBne41312341323022212122221243443421321322132102 ), ,(TnTnTTnTTTTTTTTTTTTTTTTTAPCeeetJ*3424*132212211*131012212424222122122*11412211XBBXBBBBXXBBBBBBUBBTnTeTTTnTnTeTeeeteeeOpt

22、imal Settings DOE-Based APCUXXX,|,minarg1*1*1eJEAPCewhere 112)(21*1*21211121)(|,12|,MiieeAPCAPCeeeieJMeJEUXUX181e )25. 0 , 0(N1n)25. 0 , 0(NAssuming Optimal Off-line Setting Simulation ResultsT0.50850.2817-0.5121*XComparison of RPD, CE control and Cautious ControlControl Strategy Evaluation Cautious

23、 control law performs much better than RPD1e (0,0.025)N19Simulation Results - 2CE controller performs much better than RD when the measurement is perfect, but its advantage decreases when the measurement is not perfect, and will cause a larger quality loss than RPD controller under high measurement

24、uncertainty.0101234567JCE/JRD1122/eeCertainty Equivalence assume observation perfect20050100150-202e0050100150-2-101Oberver Noise Level05010015011.62Percentage ShrinkageObservationsyyceyrdControl strategy with partial sensing failure 1 Sensor noise level change no modeling

25、 error150 observations, sensor noise level increased from point 51 to 100, then restored. t=1.6111122220.1 1eeeeCE Control suffers greatly from noise level changeMean of RPD has deviated from target*(, , ,)h enUUX e 21Control strategy with partial sensing failure 2255 observations, sensor noise leve

26、l increased from point 101 to 200, then restored Sensor noise level changeOverall J/J_ce=16.8%. APC performance is steady over different noise levels. APC considering modeling error*(, , ,)h enUUX e 22Control strategy with partial sensing failure 3 Sensor failure - Assume no modeling error,- 250 obs

27、ervations, sensor failed from point 51 to 150, then repaired 1 . 011eeControl StrategySwitch to RPD setting after the detection of sensor failure- Actual system will have step response050100150200250-202e0050100150200250-202ehat0501001502002502Percentage ShrinkageObservationsyyceyrd232 In-p

28、rocess sensing variables:tonnage signal, shut height, vibration, punch speed, temperature3 In-process part sensing: surface and dimension measurements1 Controllable variables:shut height, punch speed, temperature, binding force casterin-process partformingFormed partDOE-Based APCEstimable noise factors:material properties (hardness, thickness),gib conditions, die/tool wearInestimable noise factors:distribution of lubrication, materialcoating properties, die set-up variati