Presentation on theme: "The University of Michigan Georgia Institute of Technology"— Presentation transcript:
1 The University of Michigan Georgia Institute of Technology DOE-based Automatic Process Control with Consideration of Model UncertaintiesJan Shi and Jing ZhongThe University of MichiganC. F. Jeff WuGeorgia Institute of Technology
2 Outline Introduction Simulation and case study Summary DOE-based Automatic Process Control with Consideration of Model UncertaintyProcess modelControl objective functionController design strategiesSimulation and case studySummary
3 Problem 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 stageTo set an optimal constant level for controllable factors that can ensure noise factors have a minimal influence on process responsesBased on the noise distribution but not requiring online observations of noise factorsOnline Automatic Process Control (APC) during productionWith the increasing 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.
4 Motivation of Using APC Online adjustX based on eOfflinefix x=x1x= x2Offlinefix x=x2y(x,e)x=x1abenoise distribution
5 The Objective and Focus The research focuses on the development of automatic process control (APC) methodologies based on DOE regression models and real-time measurement or estimation of noise factors for complex mfg processesDOE-BasedAPCDesign ofExperiments(DOE)AutomaticProcess Control(APC)Statistical(SPC)
6 Literature ReviewFor complex discrete manufacturing processes, the relationship between the responses (outputs) and process variables (inputs) are obtained by DOE using a response surface 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 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 Control (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 factors.No interaction terms between noise and control factors in their model.
7 ObjectiveDevelop a general methodology for controller design based on a regression model with interaction terms.Investigate a new control law considering model parameter estimation uncertaintiesCompare the performances of CC, CEC, and RPD, as well as performance with sensing uncertainties.
8 S2: Determine APC control strategy (considering model errors Methodology Development Procedures APC Using Regression Response ModelsObtain significant factors & estimated process modelBased on key process variableS1: Conduct DOE and process modelingS2: Determine APC control strategy (considering model errorsBased on observation uncertaintyUse certainty equivalence controlor cautious controlBased on process operation constraints on controllerS3: Online adjust controllable factorsObtain reduced process variationS4: Control performance evaluation
9 1. Process Variable Characterization VariablesControllableFactorsNoiseFactorsOff-line settingFactorsOn-line adjustableFactorsObservableNoise FactorsUnobservableNoise FactorsY= f (X, U, e, n)
10 2. Control System Framework ObservableNoise Factors (e)UnobservableNoise Factors (n)Noise FactorsTargetFeedforwardControllerManufacturingProcessResponse (y)ControllableFactors (x)Predicted ResponseIn-ProcessSensing of eObserver forNoise Factors (e)
11 3 Controller Design 3.1 Problem Assumptions The manufacturing process is static with smoothly changing variables over time – Parameter Stabilitye, n and ε are independent, with E(e)=0, Cov(e)=Σe, E(n)=0, Cov(n)=Σn, E(ε)=0, Cov(ε)=Σε. ε are i.i.d.Estimated process parameters denoted by ,is estimated from experimental data.Observations of measurable noise factors, denoted by , are unbiased, i.e., and
12 3 Controller Design 3.2 Objective Function Objective Function (Quadratic Loss)Optimization Problem
13 3 Controller Design 3.3 Control Strategy Procedure for Solving Optimization ProblemStep 1 Closed form solution of U* by solvingStep 2 obtain X* by solving optimization problem of JAPCProcess Control Strategy – Two Step ProcedureStep 1 Off-line Controllable Factors SettingStep 2 On-line Automatic Control Law
14 4. Case Study : An Injection Molding Process Process DescriptionResponse Variable (y):Percentage Shrinkage of Molded PartsProcess Variables:
15 DOE Modeling Designed Experiment Result (Engel, 1992) Reduced DOE Model after Coefficient Significance TestsParameter Estimation Error
16 Robust Parameter Design Response ModelVariance ModelRPD Settings, andu1 and x3 are adjusted according to target values as in right table
17 DOE-Based APCObjective Loss FunctionOptimal Settingswhere
18 Simulation Results Comparison of RPD, CE control and Cautious Control Assuming~~~Optimal Off-line SettingCautious control law performs much better than RPDControl Strategy Evaluation
19 Simulation Results - 2Certainty Equivalence – assume observation perfectCE 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 uncertainty.
20 Control strategy with partial sensing failure – 1 Sensor noise level change – no modeling error150 observations, sensor noise level increased from point 51 to 100, then restored. t=1.6CE Control suffers greatly from noise level changeMean of RPD has deviated from target
21 Control strategy with partial sensing failure – 2 Sensor noise level change– APC considering modeling error255 observations, sensor noise level increased from point 101 to 200, then restoredOverall J/J_ce=16.8%. APC performance is steady over different noise levels.
22 Control strategy with partial sensing failure – 3 Sensor failure- Assume no modeling error,- 250 observations, sensor failed from point 51 to 150, then repairedControl StrategySwitch to RPD setting after the detection of sensor failure- Actual system will have step response
23 Industrial Collaboration with OG Technologies: DOE-Based APC Test bed in Hot Deformation Processes  In-process sensing variables:tonnage signal, shut height, vibration, punch speed, temperature In-process part sensing: surface and dimension measurements Controllable variables:shut height, punch speed, temperature, binding forcecasterin-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 variationProcess change detection and on-line estimation of estimable noise factors
24 SummaryDOE-Based APC performs better than RPD when measurable noise factors are present with not too large measurement uncertainty.RPD should be employed in case of too large measurement uncertainty or there are no observable noise factors.Cautious control considering measurable noise factors and model estimation uncertainty performs better than RPD and CE strategy.Model updating and adaptive control with supervision are promising or the future study.
25 ImpactsExpanding the DOE from off-line design and analysis to on-line APC applications, and investigates the associated issues in the DOE test design and analysis;Developing a new theory and strategy to achieve APC by using DOE-based models including on-line DOE model updating, cautious control, and supervision.